TPTP Problem File: SEV610+1.p
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%------------------------------------------------------------------------------
% File : SEV610+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - DirectedSets not eal eventually not
% Version : [Kal26] axioms : Especial.
% English :
% Refs : [CK18] Czajka L. & Kaliszyk (2018), Hammer for Coq: Automatio
% : [Kal26] Kalizyk (2026), Email to G. Sutcliffe
% Source : [Kal26]
% Names : DirectedSets.not.eal.eventually.not.p [Kal26]
% Status : Theorem
% Rating : 0.70 v9.3.0
% Syntax : Number of formulae : 2778 ( 910 unt; 0 def)
% Number of atoms : 12065 (2907 equ)
% Maximal formula atoms : 531 ( 4 avg)
% Number of connectives : 9859 ( 572 ~; 902 |;1788 &)
% (1135 <=>;5462 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 511 ( 510 usr; 0 prp; 1-23 aty)
% Number of functors : 1609 (1609 usr;1040 con; 0-22 aty)
% Number of variables : 10361 (9665 !; 696 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.bool$49414',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ( ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
& ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2449414___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) )
| ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
& ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_2449414___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$28251',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428251___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__28252] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28252)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28252)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428251___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__28252)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$28273',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__28274] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28274)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28274)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__28274)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$22024',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__22037___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__22029] :
( t(Vvar__2___24Anonymous__22029,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__22030] :
( t(Vvar__3___24Anonymous__22030,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__22029,Vvar__3___24Anonymous__22030)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2422024___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__22029)),Vvar__3___24Anonymous__22030)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$9675',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__9687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__3 = Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__9691___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__9692___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_249675___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__let__var__var__7__n__9644__9648__9657___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4)) )
| ( Vv__CANONICAL__3 != Vv__CANONICAL__2
& happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__9693___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__prop__9694___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_249675___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__let__var__var__7__n__9644__9648__9657___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__4) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$28268',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428268___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__28269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28269)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28269)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428268___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28269) )
| ? [Vvar__0___24Anonymous__28270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28270)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28270)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428268___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28270) ) ) ) ).
fof('$_def_$_let_11_subst_l_17644',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__17644___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_var_6_p_2480_2483',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2479] : c_24__let__var__6__p__2480__2483___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2479) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2479) ).
fof('$_def_$_let_var_6_p_2482_2484',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2481] : c_24__let__var__6__p__2482__2484___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2481) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2481) ).
fof('$_def_$_let_var_var_7_n_9644_9648_9657',axiom,
! [V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__9641] : c_24__let__var__var__7__n__9644__9648__9657___24a4(V0__A,V1__eq__dec,V4__x,Vvar__2___24Anonymous__9641) = cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,Vvar__2___24Anonymous__9641,V4__x) ).
fof('$_def_Coq.Arith.Between.in_int',axiom,
! [V0__p,V1__q,V2__r] :
( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
<=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r)
& cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q) ) ) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__29525] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29525)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29525)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__29526] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29526)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29526)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__29529] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29529)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29529)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__29526,Vvar__0___24Anonymous__29529) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.has_unique_least_element',axiom,
! [V0__A,V1__R,V2__P] :
( cCoq_2eArith_2eWf__nat_2ehas__unique__least__element___24a3(V0__A,V1__R,V2__P)
<=> cCoq_2eInit_2eLogic_2eex___24a2(V0__A,cCoq_2eInit_2eLogic_2eunique___24a2(V0__A,c_24__lam__46034___24a3(V0__A,V1__R,V2__P))) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.reflect_dec',axiom,
! [V0__P,V1__b,V2__H] :
( cProp___24t(V0__P)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(V0__P,V1__b,V2__H)
=> ( ( p(V0__P)
& V2__H = cCoq_2eBool_2eBool_2eReflectT___24a1(V0__P)
& cCoq_2eBool_2eBool_2ereflect__dec___24a3(V0__P,V1__b,V2__H) = cCoq_2eInit_2eSpecif_2eleft___24a2(V0__P,c_24__prop__39600___24a2(V0__P,V1__b)) )
| ( ~ p(V0__P)
& V2__H = cCoq_2eBool_2eBool_2eReflectF___24a1(V0__P)
& cCoq_2eBool_2eBool_2ereflect__dec___24a3(V0__P,V1__b,V2__H) = cCoq_2eInit_2eSpecif_2eright___24a2(V0__P,c_24__prop__39601___24a2(V0__P,V1__b)) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.reflect_rec',axiom,
! [V0__P,V1__P] : cCoq_2eBool_2eBool_2ereflect__rec___24a2(V0__P,V1__P) = cCoq_2eBool_2eBool_2ereflect__rect___24a2(V0__P,V1__P) ).
fof('$_def_Coq.Bool.Bool.reflect_rect',axiom,
! [V0__P,V1__P,V2__f,V3__f,V4__b,V5__r] :
( cProp___24t(V0__P)
=> ( c_24__type__35134___24t(V0__P,V1__P,V4__b,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(V0__P,V4__b,V5__r)
=> ( ( p(V0__P)
& V5__r = cCoq_2eBool_2eBool_2eReflectT___24a1(V0__P)
& cCoq_2eBool_2eBool_2ereflect__rect___24a6(V0__P,V1__P,V2__f,V3__f,V4__b,V5__r) = V2__f )
| ( ~ p(V0__P)
& V5__r = cCoq_2eBool_2eBool_2eReflectF___24a1(V0__P)
& cCoq_2eBool_2eBool_2ereflect__rect___24a6(V0__P,V1__P,V2__f,V3__f,V4__b,V5__r) = V3__f ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34201] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34201)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34201)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V0__s)
<=> ! [V1__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__a)
=> ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V1__a,V0__s)) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s))
<=> p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27)) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s))
=> p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27)) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& ( ? [Vvar__0___24Anonymous__24790] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24790)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24790)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__24790,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf)) )
| ? [Vvar__0___24Anonymous__24791] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24791)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24791)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__24791,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf),cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ) ) ) )
| ? [Vvar__0___24Anonymous__24792] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24792)
& ? [Vvar__1___24Anonymous__24793] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24793)
& ? [Vvar__2___24Anonymous__24794] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24794)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24792,Vvar__1___24Anonymous__24793,Vvar__2___24Anonymous__24794)
& ( ? [Vvar__0___24Anonymous__24807] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24807)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24807)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24792,Vvar__1___24Anonymous__24793,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__24807,Vvar__2___24Anonymous__24794)) )
| ? [Vvar__0___24Anonymous__24808] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24808)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24808)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(Vvar__0___24Anonymous__24808,Vvar__0___24Anonymous__24792),Vvar__1___24Anonymous__24793,Vvar__2___24Anonymous__24794) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24792,cCoq_2eInit_2eDatatypes_2etrue,Vvar__2___24Anonymous__24794) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__1039] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1039)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1039) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
! [V0__B,V1__f,V2__m,V3__i] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V0__B,V1__f,V2__m,V3__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V0__B,V1__f,V2__m,V3__i,cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.inter',axiom,
! [V1__m,V2__m_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__24860] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24860)
& ? [Vvar__1___24Anonymous__24861] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24861)
& ? [Vvar__2___24Anonymous__24862] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24862)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24860,Vvar__1___24Anonymous__24861,Vvar__2___24Anonymous__24862)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__24878] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24878)
& ? [Vvar__1___24Anonymous__24879] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24879)
& ? [Vvar__2___24Anonymous__24880] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24880)
& V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24878,Vvar__1___24Anonymous__24879,Vvar__2___24Anonymous__24880)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(Vvar__0___24Anonymous__24860,Vvar__0___24Anonymous__24878),cCoq_2eInit_2eDatatypes_2eandb___24a2(Vvar__1___24Anonymous__24861,Vvar__1___24Anonymous__24879),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(Vvar__2___24Anonymous__24862,Vvar__2___24Anonymous__24880)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__1042] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__1042)
& ? [Vvar__1___24Anonymous__1043] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__1043)
& ? [Vvar__2___24Anonymous__1044] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__1044)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__1042,Vvar__1___24Anonymous__1043,Vvar__2___24Anonymous__1044)
& ( ? [Vvar__0___24Anonymous__1057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1057)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1057)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__1057,Vvar__2___24Anonymous__1044) )
| ? [Vvar__0___24Anonymous__1058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1058)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1058)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__1058,Vvar__0___24Anonymous__1042) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__1043 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.remove',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf )
| ? [Vvar__0___24Anonymous__24813] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24813)
& ? [Vvar__1___24Anonymous__24814] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24814)
& ? [Vvar__2___24Anonymous__24815] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24815)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24813,Vvar__1___24Anonymous__24814,Vvar__2___24Anonymous__24815)
& ( ? [Vvar__0___24Anonymous__24828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24828)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24828)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(Vvar__0___24Anonymous__24813,Vvar__1___24Anonymous__24814,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(Vvar__0___24Anonymous__24828,Vvar__2___24Anonymous__24815)) )
| ? [Vvar__0___24Anonymous__24829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24829)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24829)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(Vvar__0___24Anonymous__24829,Vvar__0___24Anonymous__24813),Vvar__1___24Anonymous__24814,Vvar__2___24Anonymous__24815) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(Vvar__0___24Anonymous__24813,cCoq_2eInit_2eDatatypes_2efalse,Vvar__2___24Anonymous__24815) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.singleton',axiom,
! [V0__i] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton___24a1(V0__i) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V0__i,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__1040] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1040)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__1040) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.union',axiom,
! [V1__m,V2__m_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__m)
=> ( ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V2__m_27 )
| ? [Vvar__0___24Anonymous__24832] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24832)
& ? [Vvar__1___24Anonymous__24833] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24833)
& ? [Vvar__2___24Anonymous__24834] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24834)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m_27)
=> ( V1__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24832,Vvar__1___24Anonymous__24833,Vvar__2___24Anonymous__24834)
& ( ( V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = V1__m )
| ? [Vvar__0___24Anonymous__24850] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24850)
& ? [Vvar__1___24Anonymous__24851] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24851)
& ? [Vvar__2___24Anonymous__24852] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24852)
& V2__m_27 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24850,Vvar__1___24Anonymous__24851,Vvar__2___24Anonymous__24852)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V1__m,V2__m_27) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__0___24Anonymous__24832,Vvar__0___24Anonymous__24850),cCoq_2eInit_2eDatatypes_2eorb___24a2(Vvar__1___24Anonymous__24833,Vvar__1___24Anonymous__24851),cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(Vvar__2___24Anonymous__24834,Vvar__2___24Anonymous__24852)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.CompOpp',axiom,
! [V0__r] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__r)
=> ( ( V0__r = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eEq )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eGt )
| ( V0__r = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V0__r) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__4760] :
( t(Vvar__1___24Anonymous__4760,V0__A)
& ? [Vvar__2___24Anonymous__4761] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4761)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4760,Vvar__2___24Anonymous__4761)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4760,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__4761,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__31144] :
( t(Vvar__2___24Anonymous__31144,V0__A)
& ? [Vvar__3___24Anonymous__31145] :
( t(Vvar__3___24Anonymous__31145,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__31144,Vvar__3___24Anonymous__31145)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__31144 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__4750] :
( t(Vvar__1___24Anonymous__4750,V0__A)
& ? [Vvar__2___24Anonymous__4751] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4751)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4750,Vvar__2___24Anonymous__4751)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__4751)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.list_rec',axiom,
! [V0__A,V1__P] : cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V0__A,V1__P) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V0__A,V1__P) ).
fof('$_def_Coq.Init.Datatypes.list_rect',axiom,
! [V0__A,V1__P,V2__f,V3__f,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__40129___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = V2__f )
| ? [Vvar__1___24Anonymous__40123] :
( t(Vvar__1___24Anonymous__40123,V0__A)
& ? [Vvar__2___24Anonymous__40124] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__40124)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__40123,Vvar__2___24Anonymous__40124)
& cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,V5__l) = happ(happ(happ(V3__f,Vvar__1___24Anonymous__40123),Vvar__2___24Anonymous__40124),cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V0__A,V1__P,V2__f,V3__f,Vvar__2___24Anonymous__40124)) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.orb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).
fof('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__4707] :
( t(Vvar__2___24Anonymous__4707,V0__A)
& ? [Vvar__3___24Anonymous__4708] :
( t(Vvar__3___24Anonymous__4708,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__4707,Vvar__3___24Anonymous__4708)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__4708 ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__9809] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9809)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9809)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__9809,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__31508] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31508)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31508)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__31509] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31509)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31509)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__31512] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31512)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31512)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__31509,Vvar__0___24Anonymous__31512) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__9836] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9836)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9836)
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__9836,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__9836)) ) ) ) ).
fof('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31495] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31495)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31495)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__31496] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31496)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31496)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31499] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31499)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31499)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__31496,Vvar__0___24Anonymous__31499) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__9830] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9830)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9830)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9830)
& ( ( Vvar__0___24Anonymous__9830 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__9833] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9833)
& Vvar__0___24Anonymous__9830 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9833)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__9833) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__9841] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9841)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9841)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9841)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9841)) ) ) ) ).
fof('$_def_Coq.Init.Nat.leb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__31502] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31502)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31502)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31505] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31505)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31505)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__31502,Vvar__0___24Anonymous__31505) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__9818] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9818)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9818)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__9821] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9821)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9821)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__9818,Vvar__0___24Anonymous__9821)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__506] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__506)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__506)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__506,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.odd',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eNat_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__511] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__511)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__511)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__511)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__9807] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9807)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9807)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__9807 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__9853,V0__a,c_24__lam__9854) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__9812] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9812)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9812)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__9815] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9815)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9815)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__9812,Vvar__0___24Anonymous__9815) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__9849] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9849)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9849)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__9849) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.absurd_set',axiom,
! [V0__A,V1__C] : cCoq_2eInit_2eSpecif_2eabsurd__set___24a2(V0__A,V1__C) = cCoq_2eInit_2eLogic_2eFalse__rec___24a1(V1__C) ).
fof('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R)
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__9603] :
( t(Vvar__1___24Anonymous__9603,V0__A)
& ? [Vvar__2___24Anonymous__9604] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__9604)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__9603,Vvar__2___24Anonymous__9604)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__9603 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__9604) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.count_occ',axiom,
! [V0__A,V1__eq__dec,V3__l,V4__x] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__9640] :
( t(Vvar__1___24Anonymous__9640,V0__A)
& ? [Vvar__2___24Anonymous__9641] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__9641)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__9640,Vvar__2___24Anonymous__9641)
& cCoq_2eLists_2eList_2ecount__occ___24a4(V0__A,V1__eq__dec,V3__l,V4__x) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_249675___24a5(V0__A,V1__eq__dec,V4__x,Vvar__1___24Anonymous__9640,Vvar__2___24Anonymous__9641) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__37091] :
( t(Vvar__1___24Anonymous__37091,V0__A)
& ? [Vvar__2___24Anonymous__37092] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__37092)
& ( cType___24t(V0__A)
=> ( c_24__type__3375___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__37091,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__37091,Vvar__2___24Anonymous__37092)
& ( ( happ(V1__f,Vvar__1___24Anonymous__37091) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__37091,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__37092)) )
| ( happ(V1__f,Vvar__1___24Anonymous__37091) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__37092) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__31362] :
( t(Vvar__1___24Anonymous__31362,V1__B)
& ? [Vvar__2___24Anonymous__31363] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__31363)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__31362,Vvar__2___24Anonymous__31363)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__31362),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__31363)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__31309] :
( t(Vvar__1___24Anonymous__31309,V0__A)
& ? [Vvar__2___24Anonymous__31310] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__31310)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__31310)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__31309,Vvar__2___24Anonymous__31310)
& ( ( Vvar__2___24Anonymous__31310 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__31309 )
| ? [Vvar__1___24Anonymous__31321] :
( t(Vvar__1___24Anonymous__31321,V0__A)
& ? [Vvar__2___24Anonymous__31322] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__31322)
& Vvar__2___24Anonymous__31310 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__31321,Vvar__2___24Anonymous__31322)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__31310,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__49315] :
( t(Vvar__1___24Anonymous__49315,V0__A)
& ? [Vvar__2___24Anonymous__49316] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__49316)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__49315,Vvar__2___24Anonymous__49316)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__49315),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__49316)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_op',axiom,
! [V0__A,V1__B,V2__eqA,V3__eqB,V4__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V0__A,V1__B,V2__eqA,V3__eqB,V4__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22476___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__5226___24a2(V0__A,V1__B),V2__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V1__B,V1__B,V3__eqB,V3__eqB)),V4__f) ) ).
fof('$_def_Coq.Lists.SetoidList.equivlistA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.findA',axiom,
! [V0__A,V1__B,V3__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B))
& cCoq_2eLists_2eSetoidList_2efindA___24a4(V0__A,V1__B,V3__f,V4__l) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__34692] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__34692)
& ? [Vvar__2___24Anonymous__34693] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__2___24Anonymous__34693)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,Vvar__1___24Anonymous__34692)
=> ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),Vvar__1___24Anonymous__34692,Vvar__2___24Anonymous__34693)
& ? [Vvar__2___24Anonymous__34707] :
( t(Vvar__2___24Anonymous__34707,V0__A)
& ? [Vvar__3___24Anonymous__34708] :
( t(Vvar__3___24Anonymous__34708,V1__B)
& ( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( c_24__type__34714___24t(V0__A,V1__B,V3__f)
=> ( t(Vvar__2___24Anonymous__34707,V0__A)
=> ( Vvar__1___24Anonymous__34692 = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__34707,Vvar__3___24Anonymous__34708)
& ( ( happ(V3__f,Vvar__2___24Anonymous__34707) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eSetoidList_2efindA___24a4(V0__A,V1__B,V3__f,V4__l) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__3___24Anonymous__34708) )
| ( happ(V3__f,Vvar__2___24Anonymous__34707) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eSetoidList_2efindA___24a4(V0__A,V1__B,V3__f,V4__l) = cCoq_2eLists_2eSetoidList_2efindA___24a4(V0__A,V1__B,V3__f,Vvar__2___24Anonymous__34693) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.removeA',axiom,
! [V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__38371___24t(V0__A,V1__eqA,V1__eqA)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__38347] :
( t(Vvar__1___24Anonymous__38347,V0__A)
& ? [Vvar__2___24Anonymous__38348] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__38348)
& ( cType___24t(V0__A)
=> ( c_24__type__38380___24t(V0__A,V1__eqA,V1__eqA)
=> ( c_24__type__38389___24t(V0__A,V1__eqA,V2__eqA__dec)
=> ( t(V4__x,V0__A)
=> ( t(Vvar__1___24Anonymous__38347,V0__A)
=> ( V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38347,Vvar__2___24Anonymous__38348)
& ( ( p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__38347))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__38347) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__38347),c_24__prop__38392___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__38347))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__38348) )
| ( ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__38347))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__38347) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__38347),c_24__prop__38393___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__38347))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__38347,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__38348)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose2',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> ! [V7__z_27] :
( t(V7__z_27,V1__B)
=> ( p(happ(happ(V2__eqB,V6__z),V7__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V7__z_27)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V7__z)))) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose_restr2',axiom,
! [V0__A,V1__B,V2__eqB,V3__R,V4__f] :
( cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V0__A,V1__B,V2__eqB,V3__R,V4__f)
<=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V1__B)
=> ! [V8__z_27] :
( t(V8__z_27,V1__B)
=> ( p(happ(happ(V3__R,V5__x),V6__y))
=> ( p(happ(happ(V2__eqB,V7__z),V8__z_27))
=> p(happ(happ(V2__eqB,happ(happ(V4__f,V5__x),happ(happ(V4__f,V6__y),V7__z))),happ(happ(V4__f,V6__y),happ(happ(V4__f,V5__x),V8__z_27)))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.Minimal',axiom,
! [V0__P,V1__n] :
( cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V0__P,V1__n)
<=> ( p(happ(V0__P,V1__n))
& ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( p(happ(V0__P,V2__k))
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__n,V2__k) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.Minimization_Property',axiom,
! [V0__P] :
( cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V0__P)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(happ(V0__P,V1__n))
=> ? [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
& cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V0__P,V3__m) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.weak_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( ~ ~ p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V0__U)
<=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__5321___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__416] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__416)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__416)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__419] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__419)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__419)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__416,Vvar__0___24Anonymous__419)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__34213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34213)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34213)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__34214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34214)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34214)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__34217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34217)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34217)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__34214,Vvar__0___24Anonymous__34217) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__48688] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48688)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__48688)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__48691] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48691)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__48691)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__48688,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__24660] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24660)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24660)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24660)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34222] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34222)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34222)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__34223] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34223)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34223)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__34226] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34226)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34226)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__34223,Vvar__0___24Anonymous__34226) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__3791] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3791)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3791)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3791)
& ( ? [Vvar__0___24Anonymous__3795] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3795)
& Vvar__0___24Anonymous__3791 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3795)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__3796] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3796)
& Vvar__0___24Anonymous__3791 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3796)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__3791 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__3799] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3799)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3799)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__3802] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3802)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3802)
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__3799,Vvar__0___24Anonymous__3802)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.log2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__24668] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24668)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24668)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24668)
& ( ? [Vvar__0___24Anonymous__24672] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24672)
& Vvar__0___24Anonymous__24668 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24672)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__24672)) )
| ? [Vvar__0___24Anonymous__24673] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24673)
& Vvar__0___24Anonymous__24668 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24673)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__24673)) )
| ( Vvar__0___24Anonymous__24668 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.modulo',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__423] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__423)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__423)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__426] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__426)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__426)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__423,Vvar__0___24Anonymous__426)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.NArith.BinNatDef.N.pow',axiom,
! [V0__n,V1__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__p)
=> ( ( V1__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__24663] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24663)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24663)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__24666] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24666)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24666)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__24666,Vvar__0___24Anonymous__24663)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__24661] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24661)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24661)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__24661) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3781)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3781)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__3786] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3786)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3781)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3786)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3786)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__3781,Vvar__0___24Anonymous__3786) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__3789] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3789)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__3781,Vvar__0___24Anonymous__3786) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__3789)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3789) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__3781,Vvar__0___24Anonymous__3786) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__413] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__413)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__413)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__413)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__24697] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24697)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24697)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__24697,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__34235] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34235)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34235)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__34235) ) ) ) ).
fof('$_def_Coq.NArith.Ndigits.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eNdigits_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ege___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y))
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__432] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__432)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__432)
& ( ? [Vvar__0___24Anonymous__436] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__436)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__436)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__431__1__add__carry___24a2(Vvar__0___24Anonymous__432,Vvar__0___24Anonymous__436)) )
| ? [Vvar__0___24Anonymous__437] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__437)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__437)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__432,Vvar__0___24Anonymous__437)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__432)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__438] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__438)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__438)
& ( ? [Vvar__0___24Anonymous__442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__442)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__442)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__438,Vvar__0___24Anonymous__442)) )
| ? [Vvar__0___24Anonymous__443] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__443)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__443)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__438,Vvar__0___24Anonymous__443)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__438) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__444] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__444)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__444)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__444)) )
| ? [Vvar__0___24Anonymous__445] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__445)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__445)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__445) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare_cont',axiom,
! [V1__r,V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__48708] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48708)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__48708)
& ( ? [Vvar__0___24Anonymous__48712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48712)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__48712)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,Vvar__0___24Anonymous__48708,Vvar__0___24Anonymous__48712) )
| ? [Vvar__0___24Anonymous__48713] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48713)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__48713)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eGt,Vvar__0___24Anonymous__48708,Vvar__0___24Anonymous__48713) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__48714] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48714)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__48714)
& ( ? [Vvar__0___24Anonymous__48718] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48718)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__48718)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(cCoq_2eInit_2eDatatypes_2eLt,Vvar__0___24Anonymous__48714,Vvar__0___24Anonymous__48718) )
| ? [Vvar__0___24Anonymous__48719] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48719)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__48719)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,Vvar__0___24Anonymous__48714,Vvar__0___24Anonymous__48719) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__48720] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48720)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__48720)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__48721] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48721)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__48721)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V1__r,V2__x,V3__y) = V1__r ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__34306] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34306)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34306)
& ( ? [Vvar__0___24Anonymous__34310] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34310)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34310)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__34306,Vvar__0___24Anonymous__34310) )
| ? [Vvar__0___24Anonymous__34311] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34311)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34311)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__34312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34312)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34312)
& ( ? [Vvar__0___24Anonymous__34316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34316)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34316)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__34317] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34317)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34317)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__34312,Vvar__0___24Anonymous__34317) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__34318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34318)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34318)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__34319] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34319)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34319)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__464] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__464)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__464)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__464,V2__y))) )
| ? [Vvar__0___24Anonymous__465] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__465)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__465)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__465,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__34354] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34354)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34354)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34354)
& ( ( Vvar__0___24Anonymous__34354 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__34357] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34357)
& Vvar__0___24Anonymous__34354 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34357)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__34354)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__24756] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24756)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24756)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__24756)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__24736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24736)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24736)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24736) )
| ? [Vvar__0___24Anonymous__24737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24737)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24737)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__24737) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__24734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24734)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24734)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24734)) )
| ? [Vvar__0___24Anonymous__24735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24735)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24735)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__24735)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__24738] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24738)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__24738)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__24738 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__429)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__429)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__429)) )
| ? [Vvar__0___24Anonymous__430] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__430)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__430)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__430) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__34324] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34324)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34324)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__34337___24a1(Vvar__0___24Anonymous__34324) )
| ? [Vvar__0___24Anonymous__34328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34328)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34328)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__34344___24a1(Vvar__0___24Anonymous__34328) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__34348 ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__9962] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9962)
& ? [Vvar__1__Qden__9963] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9963)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9962,Vvar__1__Qden__9963)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__9963 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qeq',axiom,
! [V0__p,V1__q] :
( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__p,V1__q)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__p),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__q))) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__q),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__p))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qle',axiom,
! [V0__x,V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQle___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qlt',axiom,
! [V0__x,V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQlt___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x))))) ) ).
fof('$_def_Coq.QArith.QArith_base.Qmult',axiom,
! [V0__x,V1__y] : cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V0__x,V1__y) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V1__y)),cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__x),cCoq_2eQArith_2eQArith__base_2eQden___24a1(V1__y))) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__9957] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9957)
& ? [Vvar__1__Qden__9958] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9958)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9957,Vvar__1__Qden__9958)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__9957 ) ) ) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.Raxioms.INR',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__10004] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10004)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10004)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10004)
& ( ( Vvar__0___24Anonymous__10004 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__10007] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10007)
& Vvar__0___24Anonymous__10004 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10007)
& cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__n) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(Vvar__0___24Anonymous__10004),cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__2471] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2471)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2471)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__2471) )
| ? [Vvar__0___24Anonymous__2472] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2472)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2472)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__2472)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__22379] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22379)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22379)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__22379)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__22___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Strings.String.length',axiom,
! [V1__s] :
( cCoq_2eStrings_2eString_2estring___24t(V1__s)
=> ( ( V1__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2elength___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__44498] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__44498)
& ? [Vvar__1___24Anonymous__44499] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__44499)
& V1__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44498,Vvar__1___24Anonymous__44499)
& cCoq_2eStrings_2eString_2elength___24a1(V1__s) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eStrings_2eString_2elength___24a1(Vvar__1___24Anonymous__44499)) ) ) ) ) ).
fof('$_def_Coq.Strings.String.substring',axiom,
! [V1__n,V2__m,V3__s] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = cCoq_2eStrings_2eString_2eEmptyString )
| ? [Vvar__0___24Anonymous__44504] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44504)
& ( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> ( V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44504)
& ( ( V3__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = V3__s )
| ? [Vvar__0___24Anonymous__44508] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__44508)
& ? [Vvar__1___24Anonymous__44509] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__44509)
& V3__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44508,Vvar__1___24Anonymous__44509)
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44508,cCoq_2eStrings_2eString_2esubstring___24a3(cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__44504,Vvar__1___24Anonymous__44509)) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__44511] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44511)
& ( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44511)
& ( ( V3__s = cCoq_2eStrings_2eString_2eEmptyString
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = V3__s )
| ? [Vvar__0___24Anonymous__44515] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__44515)
& ? [Vvar__1___24Anonymous__44516] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__44516)
& V3__s = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__44515,Vvar__1___24Anonymous__44516)
& cCoq_2eStrings_2eString_2esubstring___24a3(V1__n,V2__m,V3__s) = cCoq_2eStrings_2eString_2esubstring___24a3(Vvar__0___24Anonymous__44511,V2__m,Vvar__1___24Anonymous__44516) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__29314] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__29314)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__29314) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30825)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30825)
& ( ? [Vvar__0___24Anonymous__30829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30829)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30829)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__30825,Vvar__0___24Anonymous__30829) ) )
| ? [Vvar__0___24Anonymous__30830] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30830)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30830)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__30831] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30831)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30831)
& ( ? [Vvar__0___24Anonymous__30835] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30835)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30835)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30836] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30836)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30836)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__30831,Vvar__0___24Anonymous__30836) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__30837] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30837)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30837)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30838)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30838)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__29281] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__29281)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29281) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt = cCoq_2ePArith_2eBinPos_2ePos_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__29315] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__29315)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29315) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq = c_3d___24a1(cCoq_2eStrings_2eString_2estring) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__30935] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__30935)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__30935) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__25134] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25134)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25134)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25134) )
| ? [Vvar__0___24Anonymous__25135] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25135)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25135)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25135) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.add',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__3901] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3901)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3901)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__3905] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3905)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3905)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__3901,Vvar__0___24Anonymous__3905)) )
| ? [Vvar__0___24Anonymous__3906] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3906)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3906)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__3901,Vvar__0___24Anonymous__3906) ) ) ) ) )
| ? [Vvar__0___24Anonymous__3907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3907)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3907)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__3911] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3911)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3911)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__3911,Vvar__0___24Anonymous__3907) )
| ? [Vvar__0___24Anonymous__3912] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3912)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3912)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__3907,Vvar__0___24Anonymous__3912)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.compare',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__25117] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25117)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25117)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__25118] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25118)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25118)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__25119] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25119)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25119)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__25123] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25123)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25123)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__25119,Vvar__0___24Anonymous__25123) )
| ? [Vvar__0___24Anonymous__25124] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25124)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25124)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__25125] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25125)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25125)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__25129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25129)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25129)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__25130] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25130)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25130)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__25125,Vvar__0___24Anonymous__25130)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__25148] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__25148)
& ? [Vvar__3___24Anonymous__25149] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__25149)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__25148,Vvar__3___24Anonymous__25149)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__25148 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.eqb',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__468] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__468)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__468)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__469] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__469)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__469)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__470] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__470)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__470)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__474] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__474)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__474)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__470,Vvar__0___24Anonymous__474) )
| ? [Vvar__0___24Anonymous__475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__475)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__475)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__476)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__476)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__480] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__480)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__480)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__481] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__481)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__481)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__476,Vvar__0___24Anonymous__481) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__25228] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25228)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25228)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25228)
& ( ? [Vvar__0___24Anonymous__25232] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25232)
& Vvar__0___24Anonymous__25228 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25232)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__25233] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25233)
& Vvar__0___24Anonymous__25228 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25233)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__25228 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__25234] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25234)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25234)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25234)
& ( ? [Vvar__0___24Anonymous__25238] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25238)
& Vvar__0___24Anonymous__25234 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25238)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__25239] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25239)
& Vvar__0___24Anonymous__25234 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25239)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__25234 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b) )
| ? [Vvar__0___24Anonymous__25273] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25273)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25273)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__25277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25277)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25277)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__25273,Vvar__0___24Anonymous__25277)) )
| ? [Vvar__0___24Anonymous__25278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25278)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25278)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__25273,Vvar__0___24Anonymous__25278)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__25279] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25279)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25279)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__25283] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25283)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25283)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__25279,Vvar__0___24Anonymous__25283)) )
| ? [Vvar__0___24Anonymous__25284] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25284)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25284)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__25279,Vvar__0___24Anonymous__25284)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.log2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__25266] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25266)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25266)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25266)
& ( ? [Vvar__0___24Anonymous__25270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25270)
& Vvar__0___24Anonymous__25266 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25270)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__25270)) )
| ? [Vvar__0___24Anonymous__25271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25271)
& Vvar__0___24Anonymous__25266 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25271)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__25271)) )
| ( Vvar__0___24Anonymous__25266 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__25272] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25272)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25272)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.ltb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__25156] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__25156)
& ? [Vvar__3___24Anonymous__25157] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__25157)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__25156,Vvar__3___24Anonymous__25157)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__25157 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.mul',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__182)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__182)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__186)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__186)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__182,Vvar__0___24Anonymous__186)) )
| ? [Vvar__0___24Anonymous__187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__187)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__187)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__182,Vvar__0___24Anonymous__187)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__188)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__188)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__192)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__192)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__188,Vvar__0___24Anonymous__192)) )
| ? [Vvar__0___24Anonymous__193] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__193)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__193)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__188,Vvar__0___24Anonymous__193)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__25242] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25242)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25242)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25242)
& ( ? [Vvar__0___24Anonymous__25246] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25246)
& Vvar__0___24Anonymous__25242 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25246)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__25247] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25247)
& Vvar__0___24Anonymous__25242 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25247)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__25242 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__25248] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25248)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25248)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25248)
& ( ? [Vvar__0___24Anonymous__25252] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25252)
& Vvar__0___24Anonymous__25248 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25252)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__25253] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25253)
& Vvar__0___24Anonymous__25248 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25253)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__25248 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3917] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3917)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3917)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3917) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__34398] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34398)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34398)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__34398)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1066] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1066)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1066)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1066) )
| ? [Vvar__0___24Anonymous__1067] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1067)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1067)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1067) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__1068] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1068)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1068)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__1068) )
| ? [Vvar__0___24Anonymous__1069] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1069)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1069)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quot',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
| ? [Vvar__0___24Anonymous__25160] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25160)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25160)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__25170] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25170)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25160)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25170)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25170)
& ? [Vvar__2___24Anonymous__25178] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25178)
& ? [Vvar__3___24Anonymous__25179] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__25179)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__25160,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25170)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__25178,Vvar__3___24Anonymous__25179)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__25178),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__25179)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__25181] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25181)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25160)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25181)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25181)
& ? [Vvar__2___24Anonymous__25189] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25189)
& ? [Vvar__3___24Anonymous__25190] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__25190)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__25160,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25181)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__25189,Vvar__3___24Anonymous__25190)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__25189)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__25190)) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__25192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25192)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25192)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
| ? [Vvar__0___24Anonymous__25202] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25202)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25192)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25202)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__25202)
& ? [Vvar__2___24Anonymous__25210] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25210)
& ? [Vvar__3___24Anonymous__25211] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__25211)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__25192,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25202)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__25210,Vvar__3___24Anonymous__25211)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__25210)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__25211))) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__25213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25213)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25192)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25213)
=> ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__25213)
& ? [Vvar__2___24Anonymous__25221] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25221)
& ? [Vvar__3___24Anonymous__25222] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__25222)
& cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__25192,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__25213)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__25221,Vvar__3___24Anonymous__25222)
& cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__25221),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__25222))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.rem',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__49280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__49280)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__49280)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__49281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__49281)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__49281)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ( ( V1__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__485] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__485)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__485)
& ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__489] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__489)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__489)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__489,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__485)) )
| ? [Vvar__0___24Anonymous__490] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__490)
& V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__490)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__490),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__485))) ) ) ) ) )
| ? [Vvar__0___24Anonymous__491] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__491)
& V1__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__491)
& cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__34396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34396)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34396)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__34396) )
| ? [Vvar__0___24Anonymous__34397] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34397)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34397)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V0__r,V1__b)
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b)) )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zeven',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__24377] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24377)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24377)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__24377)
& ( ? [Vvar__0___24Anonymous__24381] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24381)
& Vvar__0___24Anonymous__24377 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24381)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__24382] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24382)
& Vvar__0___24Anonymous__24377 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24382)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__24377 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__24383] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24383)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24383)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__24383)
& ( ? [Vvar__0___24Anonymous__24387] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24387)
& Vvar__0___24Anonymous__24383 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24387)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__24388] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24388)
& Vvar__0___24Anonymous__24383 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24388)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__24383 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zeven.Zodd',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30771] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30771)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30771)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30771)
& ( ? [Vvar__0___24Anonymous__30775] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30775)
& Vvar__0___24Anonymous__30771 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30775)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30776] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30776)
& Vvar__0___24Anonymous__30771 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30776)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__30771 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__30777] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30777)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30777)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30777)
& ( ? [Vvar__0___24Anonymous__30781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30781)
& Vvar__0___24Anonymous__30777 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30781)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30782] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30782)
& Vvar__0___24Anonymous__30777 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30782)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__30777 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30784)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30784)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30785] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30785)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30785)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__30785) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Znat.neq',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.Znumtheory.rel_prime',axiom,
! [V0__a,V1__b] :
( cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V0__a,V1__b)
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__32096] :
( t(Vvar__1___24Anonymous__32096,V1__A)
& ? [Vvar__2___24Anonymous__32097] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__32097)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__32097)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__32096,Vvar__2___24Anonymous__32097)
& ( ( Vvar__2___24Anonymous__32097 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__32096)) ) )
| ? [Vvar__1___24Anonymous__32108] :
( t(Vvar__1___24Anonymous__32108,V1__A)
& ? [Vvar__2___24Anonymous__32109] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__32109)
& Vvar__2___24Anonymous__32097 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__32108,Vvar__2___24Anonymous__32109)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__32096))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__32097) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__10030] :
( t(Vvar__1___24Anonymous__10030,V1__A)
& ? [Vvar__2___24Anonymous__10031] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10031)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__10030,Vvar__2___24Anonymous__10031)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__10030))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__10031,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.NFormula',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V0__C) = cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_def_Coq.micromega.RingMicromega.PolC',axiom,
! [V0__C] : cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V0__C) ).
fof('$_def_Coq.micromega.RingMicromega.PolEnv',axiom,
! [V0__R] : cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V0__R) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__R) ).
fof('$_def_Coq.micromega.RingMicromega.cneqb',axiom,
! [V0__C,V1__ceqb,V2__x,V3__y] : cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__ceqb,V2__x),V3__y)) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__15716___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__15724___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__15732___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__15740___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__33283___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__33291___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__33299___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__33307___24a2(V0__R,V3__rlt) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf_tt',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.eval_clause',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl] :
( cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__cl)
<=> ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__cl) ) ).
fof('$_def_Coq.micromega.Tauto.eval_cnf',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f] :
( cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__f)
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(cCoq_2emicromega_2eTauto_2eclause___24a2(V1__Term_27,V2__Annot),cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env),V5__f) ) ).
fof('$_def_Coq.micromega.Tauto.eval_f',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
=> ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24True) ) )
| ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24False) ) )
| ? [Vvar__4___24Anonymous__44686] :
( t(Vvar__4___24Anonymous__44686,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44686)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V4__ex,Vvar__4___24Anonymous__44686)) ) )
| ? [Vvar__4___24Anonymous__44691] :
( t(Vvar__4___24Anonymous__44691,V0__TA)
& ? [Vvar__5___24Anonymous__44692] :
( t(Vvar__5___24Anonymous__44692,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44691,Vvar__5___24Anonymous__44692)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V5__ea,Vvar__4___24Anonymous__44691)) ) ) )
| ? [Vvar__4___24Anonymous__44698] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44698)
& ? [Vvar__5___24Anonymous__44699] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__44699)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44698,Vvar__5___24Anonymous__44699)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__44698)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__44699) ) ) ) )
| ? [Vvar__4___24Anonymous__44705] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44705)
& ? [Vvar__5___24Anonymous__44706] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__44706)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44705,Vvar__5___24Anonymous__44706)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__44705)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__44706) ) ) ) )
| ? [Vvar__4___24Anonymous__44712] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44712)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44712)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ~ cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__44712) ) )
| ? [Vvar__4___24Anonymous__44717] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44717)
& ? [Vvar__5___24Anonymous__44718] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__44718)
& ? [Vvar__6___24Anonymous__44719] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__44719)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__44717,Vvar__5___24Anonymous__44718,Vvar__6___24Anonymous__44719)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__44717)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__44719) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_tt',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt] :
( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt)
<=> p(happ(happ(V3__eval_27,V4__env),cCoq_2eInit_2eDatatypes_2efst___24a3(V1__Term_27,V2__Annot,V5__tt))) ) ).
fof('$_def_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
! [V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp] : cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.Add',axiom,
! [V0__x,V1__s,V2__s_27] :
( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd___24a3(V0__x,V1__s,V2__s_27)
<=> ! [V3__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__y)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V3__y,V2__s_27))
<=> ( V0__x = V3__y
| p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V3__y,V1__s)) ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( V0__x = V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__49428___24a2(V0__x,V1__y),c_24__prop__49429___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__x != V1__y
& cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__49430___24a2(V0__x,V1__y),c_24__prop__49431___24a2(V0__x,V1__y))
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.Zeval_op2',axiom,
! [V0__o] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V0__o)
=> ( ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = c_24__lam__49406 )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2ele )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2ege )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2elt )
| ( V0__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V0__o) = cCoq_2eZArith_2eBinInt_2eZ_2egt ) ) ) ).
fof('$_def_Coq.micromega.ZMicromega.isZ0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34195] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34195)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34195)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__34196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34196)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34196)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__36191] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36191)
& ? [Vvar__2___24Anonymous__36192] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__36192)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__36191,Vvar__2___24Anonymous__36192)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__36191),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__36192,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons00',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V10__e)
=> ( ( V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ( V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__36261] :
( t(Vvar__1___24Anonymous__36261,V0__C)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__36261)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__36263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__36263)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__36263)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__36265] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36265)
& ? [Vvar__2___24Anonymous__36266] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__36266)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__36265,Vvar__2___24Anonymous__36266)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) ) )
| ? [Vvar__1___24Anonymous__36269] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36269)
& ? [Vvar__2___24Anonymous__36270] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__36270)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__36269,Vvar__2___24Anonymous__36270)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) ) )
| ? [Vvar__1___24Anonymous__36273] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36273)
& ? [Vvar__2___24Anonymous__36274] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__36274)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__36273,Vvar__2___24Anonymous__36274)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__1___24Anonymous__36273,cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__36274,V11__l)) ) )
| ? [Vvar__1___24Anonymous__36277] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36277)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__36277)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) )
| ? [Vvar__1___24Anonymous__36279] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__36279)
& ? [Vvar__2___24Anonymous__36280] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__36280)
& V10__e = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__36279,Vvar__2___24Anonymous__36280)
& cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__e,V11__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__1___24Anonymous__36279,V11__l) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fcons2',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l] : cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__e,V10__l) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V9__e),V10__l) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27] :
( cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27)
<=> ! [V15__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V15__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V13__e)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V14__e_27))) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEmul',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V6__x)
=> ( ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7246] :
( t(Vvar__1___24Anonymous__7246,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7246,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7246)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7246),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7246,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7246),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7246),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7246),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7250] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7250)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7250)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7252] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7252)
& ? [Vvar__2___24Anonymous__7253] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7253)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7252,Vvar__2___24Anonymous__7253)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7256] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7256)
& ? [Vvar__2___24Anonymous__7257] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7257)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7256,Vvar__2___24Anonymous__7257)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7260] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7260)
& ? [Vvar__2___24Anonymous__7261] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7261)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7260,Vvar__2___24Anonymous__7261)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7264] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7264)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7264)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7266] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7266)
& ? [Vvar__2___24Anonymous__7267] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7267)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7266,Vvar__2___24Anonymous__7267)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7274] :
( t(Vvar__1___24Anonymous__7274,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7274,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7274)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7274),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7274,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7274),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7274),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7274),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7278)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7278)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7280] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7280)
& ? [Vvar__2___24Anonymous__7281] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7281)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7280,Vvar__2___24Anonymous__7281)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7284] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7284)
& ? [Vvar__2___24Anonymous__7285] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7285)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7284,Vvar__2___24Anonymous__7285)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7288] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7288)
& ? [Vvar__2___24Anonymous__7289] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7289)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7288,Vvar__2___24Anonymous__7289)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7292] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7292)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7292)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7294] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7294)
& ? [Vvar__2___24Anonymous__7295] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7295)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7294,Vvar__2___24Anonymous__7295)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7298] :
( t(Vvar__1___24Anonymous__7298,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7298)
& ( ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7331] :
( t(Vvar__1___24Anonymous__7331,V0__C)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7331)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,happ(happ(V3__cmul,Vvar__1___24Anonymous__7298),Vvar__1___24Anonymous__7331)) )
| ? [Vvar__1___24Anonymous__7333] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7333)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7333)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7337] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7337)
& ? [Vvar__2___24Anonymous__7338] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7338)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7337,Vvar__2___24Anonymous__7338)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7345] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7345)
& ? [Vvar__2___24Anonymous__7346] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7346)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7345,Vvar__2___24Anonymous__7346)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7353] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7353)
& ? [Vvar__2___24Anonymous__7354] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7354)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7353,Vvar__2___24Anonymous__7354)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7361] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7361)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7361)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7365] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7365)
& ? [Vvar__2___24Anonymous__7366] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7366)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7365,Vvar__2___24Anonymous__7366)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V7__y )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7298,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7298),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7373] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7373)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7373)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7392] :
( t(Vvar__1___24Anonymous__7392,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7392,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7392)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7392),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7392,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7392),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7392),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7392),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7396)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7396)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7398] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7398)
& ? [Vvar__2___24Anonymous__7399] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7399)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7398,Vvar__2___24Anonymous__7399)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7402] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7402)
& ? [Vvar__2___24Anonymous__7403] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7403)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7402,Vvar__2___24Anonymous__7403)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7406] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7406)
& ? [Vvar__2___24Anonymous__7407] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7407)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7406,Vvar__2___24Anonymous__7407)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7410] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7410)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7410)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7412] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7412)
& ? [Vvar__2___24Anonymous__7413] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7413)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7412,Vvar__2___24Anonymous__7413)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7416] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7416)
& ? [Vvar__2___24Anonymous__7417] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7417)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7416,Vvar__2___24Anonymous__7417)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7451] :
( t(Vvar__1___24Anonymous__7451,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7451,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7451)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7451),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7451,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7451),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7451),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7451),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7455] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7455)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7455)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7457] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7457)
& ? [Vvar__2___24Anonymous__7458] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7458)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7457,Vvar__2___24Anonymous__7458)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7461] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7461)
& ? [Vvar__2___24Anonymous__7462] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7462)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7461,Vvar__2___24Anonymous__7462)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7465] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7465)
& ? [Vvar__2___24Anonymous__7466] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7466)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7465,Vvar__2___24Anonymous__7466)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7469] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7469)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7469)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7471] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7471)
& ? [Vvar__2___24Anonymous__7472] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7472)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7471,Vvar__2___24Anonymous__7472)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7475] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7475)
& ? [Vvar__2___24Anonymous__7476] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7476)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7475,Vvar__2___24Anonymous__7476)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7510] :
( t(Vvar__1___24Anonymous__7510,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7510,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7510)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7510),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7510,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7510),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7510),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7510),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7514)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7514)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7516] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7516)
& ? [Vvar__2___24Anonymous__7517] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7517)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7516,Vvar__2___24Anonymous__7517)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7520] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7520)
& ? [Vvar__2___24Anonymous__7521] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7521)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7520,Vvar__2___24Anonymous__7521)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7524] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7524)
& ? [Vvar__2___24Anonymous__7525] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7525)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7524,Vvar__2___24Anonymous__7525)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7528] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7528)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7528)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7530] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7530)
& ? [Vvar__2___24Anonymous__7531] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7531)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7530,Vvar__2___24Anonymous__7531)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7534] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7534)
& ? [Vvar__2___24Anonymous__7535] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7535)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7534,Vvar__2___24Anonymous__7535)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7569] :
( t(Vvar__1___24Anonymous__7569,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7569,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7569)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7569),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7569,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7569),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7569),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7569),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7573] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7573)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7573)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7575] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7575)
& ? [Vvar__2___24Anonymous__7576] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7576)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7575,Vvar__2___24Anonymous__7576)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7579] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7579)
& ? [Vvar__2___24Anonymous__7580] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7580)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7579,Vvar__2___24Anonymous__7580)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7583] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7583)
& ? [Vvar__2___24Anonymous__7584] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7584)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7583,Vvar__2___24Anonymous__7584)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7587] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7587)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7587)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7589] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7589)
& ? [Vvar__2___24Anonymous__7590] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7590)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7589,Vvar__2___24Anonymous__7590)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7593] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7593)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7593)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7612] :
( t(Vvar__1___24Anonymous__7612,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7612,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7612)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7612),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7612,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7612),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7612),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7612),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7616] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7616)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7616)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7618] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7618)
& ? [Vvar__2___24Anonymous__7619] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7619)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7618,Vvar__2___24Anonymous__7619)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7622] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7622)
& ? [Vvar__2___24Anonymous__7623] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7623)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7622,Vvar__2___24Anonymous__7623)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7626] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7626)
& ? [Vvar__2___24Anonymous__7627] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7627)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7626,Vvar__2___24Anonymous__7627)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7630] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7630)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7630)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7632] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7632)
& ? [Vvar__2___24Anonymous__7633] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7633)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7632,Vvar__2___24Anonymous__7633)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7636] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7636)
& ? [Vvar__2___24Anonymous__7637] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7637)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,V7__y)
=> ( V6__x = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7636,Vvar__2___24Anonymous__7637)
& ( ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V0__C)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7673] :
( t(Vvar__1___24Anonymous__7673,V0__C)
& ( cType___24t(V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7673,V0__C)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,Vvar__1___24Anonymous__7673)
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7673),V2__cI) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = V6__x )
| ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( c_24__type__5134___24t(V0__C,V4__ceqb)
=> ( t(Vvar__1___24Anonymous__7673,V0__C)
=> ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7673),V2__cI) = cCoq_2eInit_2eDatatypes_2efalse
& ( ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7673),V1__cO) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO) )
| ( happ(happ(V4__ceqb,Vvar__1___24Anonymous__7673),V1__cO) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__7677] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7677)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V0__C,Vvar__1___24Anonymous__7677)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7679] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7679)
& ? [Vvar__2___24Anonymous__7680] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7680)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V0__C,Vvar__1___24Anonymous__7679,Vvar__2___24Anonymous__7680)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7683] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7683)
& ? [Vvar__2___24Anonymous__7684] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7684)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V0__C,Vvar__1___24Anonymous__7683,Vvar__2___24Anonymous__7684)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7687] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7687)
& ? [Vvar__2___24Anonymous__7688] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__7688)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,Vvar__1___24Anonymous__7687,Vvar__2___24Anonymous__7688)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) )
| ? [Vvar__1___24Anonymous__7691] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7691)
& V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V0__C,Vvar__1___24Anonymous__7691)
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) )
| ? [Vvar__1___24Anonymous__7693] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__7693)
& ? [Vvar__2___24Anonymous__7694] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7694)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7637)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7694)
=> ( V7__y = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V0__C,Vvar__1___24Anonymous__7693,Vvar__2___24Anonymous__7694)
& ( ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__7637,Vvar__2___24Anonymous__7694) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,Vvar__1___24Anonymous__7636,Vvar__1___24Anonymous__7693),Vvar__2___24Anonymous__7637) )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(Vvar__2___24Anonymous__7637,Vvar__2___24Anonymous__7694) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V6__x,V7__y) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V0__C,V6__x,V7__y) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__8625] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__8625)
& ? [Vvar__2___24Anonymous__8626] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__8626)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__8626)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__8625,Vvar__2___24Anonymous__8626)
& ( ( Vvar__2___24Anonymous__8626 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__8625)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__8637] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__8637)
& ? [Vvar__2___24Anonymous__8638] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__8638)
& Vvar__2___24Anonymous__8626 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__8637,Vvar__2___24Anonymous__8638)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__8625)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__8626) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.absurd_PCond',axiom,
! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond___24a2(V0__C,V1__cO) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V0__C,V1__cO),cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__8612] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__8612)
& ? [Vvar__2__denum__8613] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__8613)
& ? [Vvar__3__condition__8614] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__8614)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__8612,Vvar__2__denum__8613,Vvar__3__condition__8614)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__8614 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__8603] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__8603)
& ? [Vvar__2__denum__8604] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__8604)
& ? [Vvar__3__condition__8605] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__8605)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__8603,Vvar__2__denum__8604,Vvar__3__condition__8605)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__8604 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__8592] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__8592)
& ? [Vvar__2__denum__8593] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__8593)
& ? [Vvar__3__condition__8594] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__8594)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__8592,Vvar__2__denum__8593,Vvar__3__condition__8594)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__8592 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__35976] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__35976)
& ? [Vvar__2__rsplit__common__35977] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__35977)
& ? [Vvar__3__rsplit__right__35978] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__35978)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__35976,Vvar__2__rsplit__common__35977,Vvar__3__rsplit__right__35978)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__35977 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__9150] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__9150)
& ? [Vvar__2__rsplit__common__9151] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__9151)
& ? [Vvar__3__rsplit__right__9152] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__9152)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__9150,Vvar__2__rsplit__common__9151,Vvar__3__rsplit__right__9152)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__9150 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__9161] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__9161)
& ? [Vvar__2__rsplit__common__9162] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__9162)
& ? [Vvar__3__rsplit__right__9163] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__9163)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__9161,Vvar__2__rsplit__common__9162,Vvar__3__rsplit__right__9163)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__9163 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.split',axiom,
! [V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2] : cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,V6__e2) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V0__C,V1__cO,V2__cI,V3__cmul,V4__ceqb,V5__e1,cCoq_2eNumbers_2eBinNums_2exH,V6__e2) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nsub',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNsub = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__1305] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1305)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1305)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__1305) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__1263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1263)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1263)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1263)
& ( ? [Vvar__0___24Anonymous__1267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1267)
& Vvar__0___24Anonymous__1263 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1267)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__1263))) )
| ? [Vvar__0___24Anonymous__1268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1268)
& Vvar__0___24Anonymous__1263 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1268)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__1263))) )
| ( Vvar__0___24Anonymous__1263 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1269)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1269)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1269)
& ( ? [Vvar__0___24Anonymous__1273] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1273)
& Vvar__0___24Anonymous__1269 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1273)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__1269)) )
| ? [Vvar__0___24Anonymous__1274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1274)
& Vvar__0___24Anonymous__1269 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1274)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__1269)) )
| ( Vvar__0___24Anonymous__1269 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__9555] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9555)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9555)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__9555))) )
| ? [Vvar__0___24Anonymous__9556] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9556)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__9556)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__9556)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__31243] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31243)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31243)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__31243) )
| ? [Vvar__0___24Anonymous__31244] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31244)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31244)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__31244)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__17432] :
( t(Vvar__1___24Anonymous__17432,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__17432)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__17432) )
| ? [Vvar__1___24Anonymous__17434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17434)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__17434)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__17434,V13__l) )
| ? [Vvar__1___24Anonymous__17436] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__17436)
& ? [Vvar__2___24Anonymous__17437] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__17437)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__17436,Vvar__2___24Anonymous__17437)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__17436)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__17437)) ) )
| ? [Vvar__1___24Anonymous__17440] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__17440)
& ? [Vvar__2___24Anonymous__17441] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__17441)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__17440,Vvar__2___24Anonymous__17441)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__17440)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__17441)) ) )
| ? [Vvar__1___24Anonymous__17444] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__17444)
& ? [Vvar__2___24Anonymous__17445] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__17445)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__17444,Vvar__2___24Anonymous__17445)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__17444)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__17445)) ) )
| ? [Vvar__1___24Anonymous__17448] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__17448)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__17448)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__17448)) )
| ? [Vvar__1___24Anonymous__17450] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__17450)
& ? [Vvar__2___24Anonymous__17451] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__17451)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__17450,Vvar__2___24Anonymous__17451)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__17450)),happ(V10__Cp__phi,Vvar__2___24Anonymous__17451)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
! [V0__C,V1__ceqb,V3__P,V4__P_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__16937] :
( t(Vvar__1___24Anonymous__16937,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__16937)
& ( ? [Vvar__1___24Anonymous__16947] :
( t(Vvar__1___24Anonymous__16947,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__16947)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__16937),Vvar__1___24Anonymous__16947) )
| ? [Vvar__1___24Anonymous__16949] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__16949)
& ? [Vvar__2___24Anonymous__16950] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__16950)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__16949,Vvar__2___24Anonymous__16950)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__16953] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__16953)
& ? [Vvar__2___24Anonymous__16954] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__16954)
& ? [Vvar__3___24Anonymous__16955] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__16955)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__16953,Vvar__2___24Anonymous__16954,Vvar__3___24Anonymous__16955)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__16960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__16960)
& ? [Vvar__2___24Anonymous__16961] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__16961)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__16960,Vvar__2___24Anonymous__16961)
& ( ? [Vvar__1___24Anonymous__16981] :
( t(Vvar__1___24Anonymous__16981,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__16981)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__16983] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__16983)
& ? [Vvar__2___24Anonymous__16984] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__16984)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__16960)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__16983)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__16983,Vvar__2___24Anonymous__16984)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__16960,Vvar__1___24Anonymous__16983) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__16961,Vvar__2___24Anonymous__16984) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__16960,Vvar__1___24Anonymous__16983) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__16960,Vvar__1___24Anonymous__16983) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__16989] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__16989)
& ? [Vvar__2___24Anonymous__16990] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__16990)
& ? [Vvar__3___24Anonymous__16991] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__16991)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__16989,Vvar__2___24Anonymous__16990,Vvar__3___24Anonymous__16991)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__16996] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__16996)
& ? [Vvar__2___24Anonymous__16997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__16997)
& ? [Vvar__3___24Anonymous__16998] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__16998)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__16996,Vvar__2___24Anonymous__16997,Vvar__3___24Anonymous__16998)
& ( ? [Vvar__1___24Anonymous__17031] :
( t(Vvar__1___24Anonymous__17031,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__17031)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__17033] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17033)
& ? [Vvar__2___24Anonymous__17034] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__17034)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__17033,Vvar__2___24Anonymous__17034)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__17037] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17037)
& ? [Vvar__2___24Anonymous__17038] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17038)
& ? [Vvar__3___24Anonymous__17039] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__17039)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__16997)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__17038)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__17037,Vvar__2___24Anonymous__17038,Vvar__3___24Anonymous__17039)
& ( ( cType___24t(V0__C)
=> ( c_24__type__5134___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__16996)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__17037)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__16997,Vvar__2___24Anonymous__17038) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__16996,Vvar__1___24Anonymous__17037) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__16998,Vvar__3___24Anonymous__17039) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__16996,Vvar__1___24Anonymous__17037) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__16997,Vvar__2___24Anonymous__17038) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__16997,Vvar__2___24Anonymous__17038) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),V15__lpe)
=> ( ( V15__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__17872] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__17872)
& ? [Vvar__2___24Anonymous__17873] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__17873)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__17872)
=> ( V15__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__17872,Vvar__2___24Anonymous__17873)
& ? [Vvar__2___24Anonymous__17891] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__2___24Anonymous__17891)
& ? [Vvar__3___24Anonymous__17892] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__3___24Anonymous__17892)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__17873)
=> ( Vvar__1___24Anonymous__17872 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__17891,Vvar__3___24Anonymous__17892)
& ( ( Vvar__2___24Anonymous__17873 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)))
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__17891)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__17892))) ) )
| ? [Vvar__1___24Anonymous__17903] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__17903)
& ? [Vvar__2___24Anonymous__17904] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__2___24Anonymous__17904)
& Vvar__2___24Anonymous__17873 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C)),Vvar__1___24Anonymous__17903,Vvar__2___24Anonymous__17904)
& ( cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__lpe)
<=> ( p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__17891)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__3___24Anonymous__17892)))
& cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__17873) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
=> ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
| ? [Vvar__1___24Anonymous__18135] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__18135)
& ? [Vvar__2___24Anonymous__18136] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__18136)
& ( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__18135)
=> ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__18135,Vvar__2___24Anonymous__18136)
& ? [Vvar__2___24Anonymous__18152] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__18152)
& ? [Vvar__3___24Anonymous__18153] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__18153)
& ( cType___24t(V0__C)
=> ( t(V1__cO,V0__C)
=> ( t(V2__cI,V0__C)
=> ( c_24__type__780___24t(V0__C,V3__cadd)
=> ( c_24__type__780___24t(V0__C,V4__cmul)
=> ( c_24__type__780___24t(V0__C,V5__csub)
=> ( c_24__type__169___24t(V0__C,V6__copp)
=> ( c_24__type__5134___24t(V0__C,V7__ceqb)
=> ( c_24__type__17866___24t(V0__C,V8__cdiv)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__18152)
=> ( Vvar__1___24Anonymous__18135 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__18152,Vvar__3___24Anonymous__18153)
& ( ? [Vvar__1___24Anonymous__18161] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__18161)
& cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__18152)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__18161)
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__18161,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__18153)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__18136)) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__18152)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
& cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__18136) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__17716___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__18867] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18867)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__18867)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__18867) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__2479] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2479)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2479)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__2480__2483___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2479)),c_24__let__var__6__p__2480__2483___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2479))) )
| ? [Vvar__0___24Anonymous__2481] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2481)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2481)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__2482__2484___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2481)),c_24__let__var__6__p__2482__2484___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__2481)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_DirectedSets.DS_ord',axiom,
! [V0__d] :
( cDirectedSets_2eDirectedSet___24t(V0__d)
=> ? [Vvar__0__DS__set__225] :
( cType___24t(Vvar__0__DS__set__225)
& ? [Vvar__1__DS__ord__226] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__225,Vvar__1__DS__ord__226)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__225,Vvar__1__DS__ord__226)
& ! [Vvar__var__3__i__229__232] :
( t(Vvar__var__3__i__229__232,Vvar__0__DS__set__225)
=> ! [Vvar__var__4__j__231__234] :
( t(Vvar__var__4__j__231__234,Vvar__0__DS__set__225)
=> ? [Vvar__var__5__k__230__233] :
( t(Vvar__var__5__k__230__233,Vvar__0__DS__set__225)
& p(happ(happ(Vvar__1__DS__ord__226,Vvar__var__3__i__229__232),Vvar__var__5__k__230__233))
& p(happ(happ(Vvar__1__DS__ord__226,Vvar__var__4__j__231__234),Vvar__var__5__k__230__233)) ) ) )
& V0__d = cDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__225,Vvar__1__DS__ord__226)
& cDirectedSets_2eDS__ord___24a1(V0__d) = Vvar__1__DS__ord__226 ) ) ) ).
fof('$_def_DirectedSets.DS_set',axiom,
! [V0__d] :
( cDirectedSets_2eDirectedSet___24t(V0__d)
=> ? [Vvar__0__DS__set__255] :
( cType___24t(Vvar__0__DS__set__255)
& ? [Vvar__1__DS__ord__256] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__255,Vvar__1__DS__ord__256)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__255,Vvar__1__DS__ord__256)
& ! [Vvar__var__3__i__259__262] :
( t(Vvar__var__3__i__259__262,Vvar__0__DS__set__255)
=> ! [Vvar__var__4__j__261__264] :
( t(Vvar__var__4__j__261__264,Vvar__0__DS__set__255)
=> ? [Vvar__var__5__k__260__263] :
( t(Vvar__var__5__k__260__263,Vvar__0__DS__set__255)
& p(happ(happ(Vvar__1__DS__ord__256,Vvar__var__3__i__259__262),Vvar__var__5__k__260__263))
& p(happ(happ(Vvar__1__DS__ord__256,Vvar__var__4__j__261__264),Vvar__var__5__k__260__263)) ) ) )
& V0__d = cDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__255,Vvar__1__DS__ord__256)
& cDirectedSets_2eDS__set___24a1(V0__d) = Vvar__0__DS__set__255 ) ) ) ).
fof('$_def_DirectedSets.for_large.eventually',axiom,
! [V0__P] :
( cDirectedSets_2efor__large_2eeventually___24a1(V0__P)
<=> ? [V1__i] :
( cDirectedSets_2eDS__set___24t(cI,V1__i)
& ! [V2__j] :
( cDirectedSets_2eDS__set___24t(cI,V2__j)
=> ( cDirectedSets_2eDS__ord___24a3(cI,V1__i,V2__j)
=> p(happ(V0__P,V2__j)) ) ) ) ) ).
fof('$_def_DirectedSets.for_large.exists_arbitrarily_large',axiom,
! [V0__P] :
( cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(V0__P)
<=> ! [V1__i] :
( cDirectedSets_2eDS__set___24t(cI,V1__i)
=> ? [V2__j] :
( cDirectedSets_2eDS__set___24t(cI,V2__j)
& cDirectedSets_2eDS__ord___24a3(cI,V1__i,V2__j)
& p(happ(V0__P,V2__j)) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__26589,Vvar__1___24Anonymous__26590,Vvar__0__P__26591,Vvar__1___24Anonymous__26592] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__26589) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__26591) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__24775,Vvar__1___24Anonymous__24776,Vvar__2___24Anonymous__24777] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24775,Vvar__1___24Anonymous__24776,Vvar__2___24Anonymous__24777) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__353] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__353) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__4653,Vvar__1___24Anonymous__4654,Vvar__0__A__4655] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4653,Vvar__1___24Anonymous__4654) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4655) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__4721,Vvar__0__A__4722,Vvar__1___24Anonymous__4723,Vvar__2___24Anonymous__4724] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4721) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4722,Vvar__1___24Anonymous__4723,Vvar__2___24Anonymous__4724) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__29160,Vvar__1__B__29161,Vvar__2___24Anonymous__29162,Vvar__0__A__29163,Vvar__1__B__29164,Vvar__2___24Anonymous__29165] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29160,Vvar__1__B__29161,Vvar__2___24Anonymous__29162) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29163,Vvar__1__B__29164) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__3403,Vvar__1__B__3404,Vvar__2___24Anonymous__3405,Vvar__0__A__3406,Vvar__1__B__3407,Vvar__2___24Anonymous__3408] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3403,Vvar__1__B__3404) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3406,Vvar__1__B__3407) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__500] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__500) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__13] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__339,Vvar__0___24Anonymous__340] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__339) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__340) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__28291,Vvar__1___24Anonymous__28292,Vvar__0__x__28293,Vvar__1__n__28294,Vvar__2___24Anonymous__28295] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28291) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28293,Vvar__1__n__28294) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__22585,Vvar__1___24Anonymous__22586] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22585,Vvar__1___24Anonymous__22586) ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__1132,Vvar__0__n__1133,Vvar__1___24Anonymous__1134] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1132) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1133,Vvar__1___24Anonymous__1134) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__3432,Vvar__0__A__3433,Vvar__1__h__3434,Vvar__2__n__3435,Vvar__3___24Anonymous__3436] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3432) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3433,Vvar__1__h__3434,Vvar__2__n__3435,Vvar__3___24Anonymous__3436) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__26041,Vvar__1___24Anonymous__26042,Vvar__0__C__26043,Vvar__1___24Anonymous__26044] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__26041,Vvar__1___24Anonymous__26042) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__26043,Vvar__1___24Anonymous__26044) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__4975,Vvar__1___24Anonymous__4976,Vvar__0__C__4977,Vvar__1___24Anonymous__4978,Vvar__2___24Anonymous__4979] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4975,Vvar__1___24Anonymous__4976) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4977,Vvar__1___24Anonymous__4978,Vvar__2___24Anonymous__4979) ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__22940,Vvar__1__TX__22941,Vvar__2__AA__22942,Vvar__3__AF__22943,Vvar__0__TA__22944,Vvar__1__TX__22945,Vvar__2__AA__22946,Vvar__3__AF__22947] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22940,Vvar__1__TX__22941,Vvar__2__AA__22942,Vvar__3__AF__22943) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22944,Vvar__1__TX__22945,Vvar__2__AA__22946,Vvar__3__AF__22947) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__8239,Vvar__0__C__8240] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8239) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8240) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__17365,Vvar__0__C__17366] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__17365) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__17366) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__16895,Vvar__1___24Anonymous__16896,Vvar__0__C__16897,Vvar__1___24Anonymous__16898,Vvar__2___24Anonymous__16899] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__16895,Vvar__1___24Anonymous__16896) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__16897,Vvar__1___24Anonymous__16898,Vvar__2___24Anonymous__16899) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__17094,Vvar__1___24Anonymous__17095] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__17094,Vvar__1___24Anonymous__17095) ).
fof('$_fix_431_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__446)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__446)
& ( ? [Vvar__0___24Anonymous__450] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__450)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__450)
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__431__1__add__carry___24a2(Vvar__0___24Anonymous__446,Vvar__0___24Anonymous__450)) )
| ? [Vvar__0___24Anonymous__451] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__451)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__451)
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__431__1__add__carry___24a2(Vvar__0___24Anonymous__446,Vvar__0___24Anonymous__451)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__446)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__452] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__452)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__452)
& ( ? [Vvar__0___24Anonymous__456] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__456)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__456)
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__431__1__add__carry___24a2(Vvar__0___24Anonymous__452,Vvar__0___24Anonymous__456)) )
| ? [Vvar__0___24Anonymous__457] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__457)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__457)
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__452,Vvar__0___24Anonymous__457)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__452)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__458] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__458)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__458)
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__458)) )
| ? [Vvar__0___24Anonymous__459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__459)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__459)
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__459)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__431__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__26597,Vvar__0__P__26598,Vvar__1___24Anonymous__26599,Vvar__1___24Anonymous__26600] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__26597) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__26598)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__26597 = Vvar__0__P__26598 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__26593,Vvar__0__P__26594,Vvar__1___24Anonymous__26595,Vvar__1___24Anonymous__26596] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__26593) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__26594)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__26593 = Vvar__0__P__26594 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__24778,Vvar__0___24Anonymous__24779,Vvar__1___24Anonymous__24780,Vvar__1___24Anonymous__24781,Vvar__2___24Anonymous__24782,Vvar__2___24Anonymous__24783] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24778,Vvar__1___24Anonymous__24780,Vvar__2___24Anonymous__24782) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24779,Vvar__1___24Anonymous__24781,Vvar__2___24Anonymous__24783)
=> ( Vvar__2___24Anonymous__24782 = Vvar__2___24Anonymous__24783
& Vvar__1___24Anonymous__24780 = Vvar__1___24Anonymous__24781
& Vvar__0___24Anonymous__24778 = Vvar__0___24Anonymous__24779 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__4660,Vvar__0__A__4661] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4660) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4661)
=> Vvar__0__A__4660 = Vvar__0__A__4661 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__354,Vvar__0___24Anonymous__355] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__354) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__355)
=> Vvar__0___24Anonymous__354 = Vvar__0___24Anonymous__355 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__4656,Vvar__0__A__4657,Vvar__1___24Anonymous__4658,Vvar__1___24Anonymous__4659] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4656,Vvar__1___24Anonymous__4658) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4657,Vvar__1___24Anonymous__4659)
=> ( Vvar__1___24Anonymous__4658 = Vvar__1___24Anonymous__4659
& Vvar__0__A__4656 = Vvar__0__A__4657 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__4727,Vvar__0__A__4728,Vvar__1___24Anonymous__4729,Vvar__1___24Anonymous__4730,Vvar__2___24Anonymous__4731,Vvar__2___24Anonymous__4732] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4727,Vvar__1___24Anonymous__4729,Vvar__2___24Anonymous__4731) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4728,Vvar__1___24Anonymous__4730,Vvar__2___24Anonymous__4732)
=> ( Vvar__2___24Anonymous__4731 = Vvar__2___24Anonymous__4732
& Vvar__1___24Anonymous__4729 = Vvar__1___24Anonymous__4730
& Vvar__0__A__4727 = Vvar__0__A__4728 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__4725,Vvar__0__A__4726] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4725) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4726)
=> Vvar__0__A__4725 = Vvar__0__A__4726 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__397,Vvar__0__A__398,Vvar__1__B__399,Vvar__1__B__400,Vvar__2___24Anonymous__401,Vvar__2___24Anonymous__402,Vvar__3___24Anonymous__403,Vvar__3___24Anonymous__404] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__397,Vvar__1__B__399,Vvar__2___24Anonymous__401,Vvar__3___24Anonymous__403) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__398,Vvar__1__B__400,Vvar__2___24Anonymous__402,Vvar__3___24Anonymous__404)
=> ( Vvar__3___24Anonymous__403 = Vvar__3___24Anonymous__404
& Vvar__2___24Anonymous__401 = Vvar__2___24Anonymous__402
& Vvar__1__B__399 = Vvar__1__B__400
& Vvar__0__A__397 = Vvar__0__A__398 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__22554,Vvar__0__A__22555,Vvar__1__P__22556,Vvar__1__P__22557,Vvar__2__x__22558,Vvar__2__x__22559,Vvar__3___24Anonymous__22560,Vvar__3___24Anonymous__22561] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__22554,Vvar__1__P__22556,Vvar__2__x__22558) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__22555,Vvar__1__P__22557,Vvar__2__x__22559)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__22558 = Vvar__2__x__22559
& Vvar__1__P__22556 = Vvar__1__P__22557
& Vvar__0__A__22554 = Vvar__0__A__22555 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__29084,Vvar__0__A__29085,Vvar__1__P__29086,Vvar__1__P__29087,Vvar__2__x__29088,Vvar__2__x__29089,Vvar__3___24Anonymous__29090,Vvar__3___24Anonymous__29091] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__29084,Vvar__1__P__29086,Vvar__2__x__29088,Vvar__3___24Anonymous__29090) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__29085,Vvar__1__P__29087,Vvar__2__x__29089,Vvar__3___24Anonymous__29091)
=> ( Vvar__3___24Anonymous__29090 = Vvar__3___24Anonymous__29091
& Vvar__2__x__29088 = Vvar__2__x__29089
& Vvar__1__P__29086 = Vvar__1__P__29087
& Vvar__0__A__29084 = Vvar__0__A__29085 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__29166,Vvar__0__A__29167,Vvar__1__B__29168,Vvar__1__B__29169,Vvar__2___24Anonymous__29170,Vvar__2___24Anonymous__29171] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29166,Vvar__1__B__29168,Vvar__2___24Anonymous__29170) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29167,Vvar__1__B__29169,Vvar__2___24Anonymous__29171)
=> ( Vvar__2___24Anonymous__29170 = Vvar__2___24Anonymous__29171
& Vvar__1__B__29168 = Vvar__1__B__29169
& Vvar__0__A__29166 = Vvar__0__A__29167 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__29172,Vvar__0__A__29173,Vvar__1__B__29174,Vvar__1__B__29175,Vvar__2___24Anonymous__29176,Vvar__2___24Anonymous__29177] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29172,Vvar__1__B__29174) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29173,Vvar__1__B__29175)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__29174 = Vvar__1__B__29175
& Vvar__0__A__29172 = Vvar__0__A__29173 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__3409,Vvar__0__A__3410,Vvar__1__B__3411,Vvar__1__B__3412,Vvar__2___24Anonymous__3413,Vvar__2___24Anonymous__3414] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3409,Vvar__1__B__3411) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3410,Vvar__1__B__3412)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__3411 = Vvar__1__B__3412
& Vvar__0__A__3409 = Vvar__0__A__3410 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__3415,Vvar__0__A__3416,Vvar__1__B__3417,Vvar__1__B__3418,Vvar__2___24Anonymous__3419,Vvar__2___24Anonymous__3420] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3415,Vvar__1__B__3417) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3416,Vvar__1__B__3418)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__3417 = Vvar__1__B__3418
& Vvar__0__A__3415 = Vvar__0__A__3416 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__501,Vvar__0___24Anonymous__502] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__501) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__502)
=> Vvar__0___24Anonymous__501 = Vvar__0___24Anonymous__502 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__16,Vvar__0___24Anonymous__17] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__16) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__17)
=> Vvar__0___24Anonymous__16 = Vvar__0___24Anonymous__17 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__14,Vvar__0___24Anonymous__15] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15)
=> Vvar__0___24Anonymous__14 = Vvar__0___24Anonymous__15 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__341,Vvar__0___24Anonymous__342] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__341) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__342)
=> Vvar__0___24Anonymous__341 = Vvar__0___24Anonymous__342 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__343,Vvar__0___24Anonymous__344] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__343) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__344)
=> Vvar__0___24Anonymous__343 = Vvar__0___24Anonymous__344 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__526,Vvar__0__Qnum__527,Vvar__1__Qden__528,Vvar__1__Qden__529] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__526,Vvar__1__Qden__528) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__527,Vvar__1__Qden__529)
=> ( Vvar__1__Qden__528 = Vvar__1__Qden__529
& Vvar__0__Qnum__526 = Vvar__0__Qnum__527 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__29566,Vvar__0__nonzero__29567,Vvar__1__cond__nonzero__29568,Vvar__1__cond__nonzero__29569] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__29566) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__29567)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__29566 = Vvar__0__nonzero__29567 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__28306,Vvar__0__x__28307,Vvar__1__n__28308,Vvar__1__n__28309,Vvar__2___24Anonymous__28310,Vvar__2___24Anonymous__28311] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__28306,Vvar__1__n__28308) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__28307,Vvar__1__n__28309)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__28308 = Vvar__1__n__28309
& Vvar__0__x__28306 = Vvar__0__x__28307 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__28296,Vvar__0__x__28297,Vvar__1___24Anonymous__28298,Vvar__1___24Anonymous__28299] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28296) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28297)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__28296 = Vvar__0__x__28297 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__28300,Vvar__0__x__28301,Vvar__1__n__28302,Vvar__1__n__28303,Vvar__2___24Anonymous__28304,Vvar__2___24Anonymous__28305] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28300,Vvar__1__n__28302) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28301,Vvar__1__n__28303)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__28302 = Vvar__1__n__28303
& Vvar__0__x__28300 = Vvar__0__x__28301 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__25884,Vvar__0___24Anonymous__25885,Vvar__1___24Anonymous__25886,Vvar__1___24Anonymous__25887,Vvar__2___24Anonymous__25888,Vvar__2___24Anonymous__25889,Vvar__3___24Anonymous__25890,Vvar__3___24Anonymous__25891,Vvar__4___24Anonymous__25892,Vvar__4___24Anonymous__25893,Vvar__5___24Anonymous__25894,Vvar__5___24Anonymous__25895,Vvar__6___24Anonymous__25896,Vvar__6___24Anonymous__25897,Vvar__7___24Anonymous__25898,Vvar__7___24Anonymous__25899] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__25884,Vvar__1___24Anonymous__25886,Vvar__2___24Anonymous__25888,Vvar__3___24Anonymous__25890,Vvar__4___24Anonymous__25892,Vvar__5___24Anonymous__25894,Vvar__6___24Anonymous__25896,Vvar__7___24Anonymous__25898) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__25885,Vvar__1___24Anonymous__25887,Vvar__2___24Anonymous__25889,Vvar__3___24Anonymous__25891,Vvar__4___24Anonymous__25893,Vvar__5___24Anonymous__25895,Vvar__6___24Anonymous__25897,Vvar__7___24Anonymous__25899)
=> ( Vvar__7___24Anonymous__25898 = Vvar__7___24Anonymous__25899
& Vvar__6___24Anonymous__25896 = Vvar__6___24Anonymous__25897
& Vvar__5___24Anonymous__25894 = Vvar__5___24Anonymous__25895
& Vvar__4___24Anonymous__25892 = Vvar__4___24Anonymous__25893
& Vvar__3___24Anonymous__25890 = Vvar__3___24Anonymous__25891
& Vvar__2___24Anonymous__25888 = Vvar__2___24Anonymous__25889
& Vvar__1___24Anonymous__25886 = Vvar__1___24Anonymous__25887
& Vvar__0___24Anonymous__25884 = Vvar__0___24Anonymous__25885 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__22587,Vvar__0___24Anonymous__22588,Vvar__1___24Anonymous__22589,Vvar__1___24Anonymous__22590] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22587,Vvar__1___24Anonymous__22589) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22588,Vvar__1___24Anonymous__22590)
=> ( Vvar__1___24Anonymous__22589 = Vvar__1___24Anonymous__22590
& Vvar__0___24Anonymous__22587 = Vvar__0___24Anonymous__22588 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__1135,Vvar__0__n__1136] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1135) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1136)
=> Vvar__0__n__1135 = Vvar__0__n__1136 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__1137,Vvar__0__n__1138,Vvar__1___24Anonymous__1139,Vvar__1___24Anonymous__1140] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1137,Vvar__1___24Anonymous__1139) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1138,Vvar__1___24Anonymous__1140)
=> ( Vvar__1___24Anonymous__1139 = Vvar__1___24Anonymous__1140
& Vvar__0__n__1137 = Vvar__0__n__1138 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__3439,Vvar__0__A__3440,Vvar__1__h__3441,Vvar__1__h__3442,Vvar__2__n__3443,Vvar__2__n__3444,Vvar__3___24Anonymous__3445,Vvar__3___24Anonymous__3446] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3439,Vvar__1__h__3441,Vvar__2__n__3443,Vvar__3___24Anonymous__3445) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3440,Vvar__1__h__3442,Vvar__2__n__3444,Vvar__3___24Anonymous__3446)
=> ( Vvar__3___24Anonymous__3445 = Vvar__3___24Anonymous__3446
& Vvar__2__n__3443 = Vvar__2__n__3444
& Vvar__1__h__3441 = Vvar__1__h__3442
& Vvar__0__A__3439 = Vvar__0__A__3440 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__3437,Vvar__0__A__3438] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3437) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3438)
=> Vvar__0__A__3437 = Vvar__0__A__3438 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__26049,Vvar__0__C__26050,Vvar__1___24Anonymous__26051,Vvar__1___24Anonymous__26052] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__26049,Vvar__1___24Anonymous__26051) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__26050,Vvar__1___24Anonymous__26052)
=> ( Vvar__1___24Anonymous__26051 = Vvar__1___24Anonymous__26052
& Vvar__0__C__26049 = Vvar__0__C__26050 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__26053,Vvar__0__C__26054,Vvar__1___24Anonymous__26055,Vvar__1___24Anonymous__26056,Vvar__2___24Anonymous__26057,Vvar__2___24Anonymous__26058] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__26053,Vvar__1___24Anonymous__26055,Vvar__2___24Anonymous__26057) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__26054,Vvar__1___24Anonymous__26056,Vvar__2___24Anonymous__26058)
=> ( Vvar__2___24Anonymous__26057 = Vvar__2___24Anonymous__26058
& Vvar__1___24Anonymous__26055 = Vvar__1___24Anonymous__26056
& Vvar__0__C__26053 = Vvar__0__C__26054 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__26045,Vvar__0__C__26046,Vvar__1___24Anonymous__26047,Vvar__1___24Anonymous__26048] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__26045,Vvar__1___24Anonymous__26047) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__26046,Vvar__1___24Anonymous__26048)
=> ( Vvar__1___24Anonymous__26047 = Vvar__1___24Anonymous__26048
& Vvar__0__C__26045 = Vvar__0__C__26046 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__26065,Vvar__0__C__26066,Vvar__1___24Anonymous__26067,Vvar__1___24Anonymous__26068,Vvar__2___24Anonymous__26069,Vvar__2___24Anonymous__26070] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__26065,Vvar__1___24Anonymous__26067,Vvar__2___24Anonymous__26069) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__26066,Vvar__1___24Anonymous__26068,Vvar__2___24Anonymous__26070)
=> ( Vvar__2___24Anonymous__26069 = Vvar__2___24Anonymous__26070
& Vvar__1___24Anonymous__26067 = Vvar__1___24Anonymous__26068
& Vvar__0__C__26065 = Vvar__0__C__26066 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__26071,Vvar__0__C__26072,Vvar__1___24Anonymous__26073,Vvar__1___24Anonymous__26074] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__26071,Vvar__1___24Anonymous__26073) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__26072,Vvar__1___24Anonymous__26074)
=> ( Vvar__1___24Anonymous__26073 = Vvar__1___24Anonymous__26074
& Vvar__0__C__26071 = Vvar__0__C__26072 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__26075,Vvar__0__C__26076,Vvar__1___24Anonymous__26077,Vvar__1___24Anonymous__26078,Vvar__2___24Anonymous__26079,Vvar__2___24Anonymous__26080] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__26075,Vvar__1___24Anonymous__26077,Vvar__2___24Anonymous__26079) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__26076,Vvar__1___24Anonymous__26078,Vvar__2___24Anonymous__26080)
=> ( Vvar__2___24Anonymous__26079 = Vvar__2___24Anonymous__26080
& Vvar__1___24Anonymous__26077 = Vvar__1___24Anonymous__26078
& Vvar__0__C__26075 = Vvar__0__C__26076 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__26059,Vvar__0__C__26060,Vvar__1___24Anonymous__26061,Vvar__1___24Anonymous__26062,Vvar__2___24Anonymous__26063,Vvar__2___24Anonymous__26064] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__26059,Vvar__1___24Anonymous__26061,Vvar__2___24Anonymous__26063) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__26060,Vvar__1___24Anonymous__26062,Vvar__2___24Anonymous__26064)
=> ( Vvar__2___24Anonymous__26063 = Vvar__2___24Anonymous__26064
& Vvar__1___24Anonymous__26061 = Vvar__1___24Anonymous__26062
& Vvar__0__C__26059 = Vvar__0__C__26060 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__4990,Vvar__0__C__4991,Vvar__1___24Anonymous__4992,Vvar__1___24Anonymous__4993,Vvar__2___24Anonymous__4994,Vvar__2___24Anonymous__4995,Vvar__3___24Anonymous__4996,Vvar__3___24Anonymous__4997] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4990,Vvar__1___24Anonymous__4992,Vvar__2___24Anonymous__4994,Vvar__3___24Anonymous__4996) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4991,Vvar__1___24Anonymous__4993,Vvar__2___24Anonymous__4995,Vvar__3___24Anonymous__4997)
=> ( Vvar__3___24Anonymous__4996 = Vvar__3___24Anonymous__4997
& Vvar__2___24Anonymous__4994 = Vvar__2___24Anonymous__4995
& Vvar__1___24Anonymous__4992 = Vvar__1___24Anonymous__4993
& Vvar__0__C__4990 = Vvar__0__C__4991 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__4980,Vvar__0__C__4981,Vvar__1___24Anonymous__4982,Vvar__1___24Anonymous__4983] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4980,Vvar__1___24Anonymous__4982) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4981,Vvar__1___24Anonymous__4983)
=> ( Vvar__1___24Anonymous__4982 = Vvar__1___24Anonymous__4983
& Vvar__0__C__4980 = Vvar__0__C__4981 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__4984,Vvar__0__C__4985,Vvar__1___24Anonymous__4986,Vvar__1___24Anonymous__4987,Vvar__2___24Anonymous__4988,Vvar__2___24Anonymous__4989] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4984,Vvar__1___24Anonymous__4986,Vvar__2___24Anonymous__4988) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4985,Vvar__1___24Anonymous__4987,Vvar__2___24Anonymous__4989)
=> ( Vvar__2___24Anonymous__4988 = Vvar__2___24Anonymous__4989
& Vvar__1___24Anonymous__4986 = Vvar__1___24Anonymous__4987
& Vvar__0__C__4984 = Vvar__0__C__4985 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__551,Vvar__0__T__552,Vvar__1__Flhs__553,Vvar__1__Flhs__554,Vvar__2__Fop__555,Vvar__2__Fop__556,Vvar__3__Frhs__557,Vvar__3__Frhs__558] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__551,Vvar__1__Flhs__553,Vvar__2__Fop__555,Vvar__3__Frhs__557) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__552,Vvar__1__Flhs__554,Vvar__2__Fop__556,Vvar__3__Frhs__558)
=> ( Vvar__3__Frhs__557 = Vvar__3__Frhs__558
& Vvar__2__Fop__555 = Vvar__2__Fop__556
& Vvar__1__Flhs__553 = Vvar__1__Flhs__554
& Vvar__0__T__551 = Vvar__0__T__552 ) ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__22974,Vvar__0__TA__22975,Vvar__1__TX__22976,Vvar__1__TX__22977,Vvar__2__AA__22978,Vvar__2__AA__22979,Vvar__3__AF__22980,Vvar__3__AF__22981,Vvar__4___24Anonymous__22982,Vvar__4___24Anonymous__22983,Vvar__5___24Anonymous__22984,Vvar__5___24Anonymous__22985] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22974,Vvar__1__TX__22976,Vvar__2__AA__22978,Vvar__3__AF__22980,Vvar__4___24Anonymous__22982,Vvar__5___24Anonymous__22984) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22975,Vvar__1__TX__22977,Vvar__2__AA__22979,Vvar__3__AF__22981,Vvar__4___24Anonymous__22983,Vvar__5___24Anonymous__22985)
=> ( Vvar__5___24Anonymous__22984 = Vvar__5___24Anonymous__22985
& Vvar__4___24Anonymous__22982 = Vvar__4___24Anonymous__22983
& Vvar__3__AF__22980 = Vvar__3__AF__22981
& Vvar__2__AA__22978 = Vvar__2__AA__22979
& Vvar__1__TX__22976 = Vvar__1__TX__22977
& Vvar__0__TA__22974 = Vvar__0__TA__22975 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__22986,Vvar__0__TA__22987,Vvar__1__TX__22988,Vvar__1__TX__22989,Vvar__2__AA__22990,Vvar__2__AA__22991,Vvar__3__AF__22992,Vvar__3__AF__22993,Vvar__4___24Anonymous__22994,Vvar__4___24Anonymous__22995,Vvar__5___24Anonymous__22996,Vvar__5___24Anonymous__22997] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22986,Vvar__1__TX__22988,Vvar__2__AA__22990,Vvar__3__AF__22992,Vvar__4___24Anonymous__22994,Vvar__5___24Anonymous__22996) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22987,Vvar__1__TX__22989,Vvar__2__AA__22991,Vvar__3__AF__22993,Vvar__4___24Anonymous__22995,Vvar__5___24Anonymous__22997)
=> ( Vvar__5___24Anonymous__22996 = Vvar__5___24Anonymous__22997
& Vvar__4___24Anonymous__22994 = Vvar__4___24Anonymous__22995
& Vvar__3__AF__22992 = Vvar__3__AF__22993
& Vvar__2__AA__22990 = Vvar__2__AA__22991
& Vvar__1__TX__22988 = Vvar__1__TX__22989
& Vvar__0__TA__22986 = Vvar__0__TA__22987 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__22998,Vvar__0__TA__22999,Vvar__1__TX__23000,Vvar__1__TX__23001,Vvar__2__AA__23002,Vvar__2__AA__23003,Vvar__3__AF__23004,Vvar__3__AF__23005,Vvar__4___24Anonymous__23006,Vvar__4___24Anonymous__23007,Vvar__5___24Anonymous__23008,Vvar__5___24Anonymous__23009] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22998,Vvar__1__TX__23000,Vvar__2__AA__23002,Vvar__3__AF__23004,Vvar__4___24Anonymous__23006,Vvar__5___24Anonymous__23008) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22999,Vvar__1__TX__23001,Vvar__2__AA__23003,Vvar__3__AF__23005,Vvar__4___24Anonymous__23007,Vvar__5___24Anonymous__23009)
=> ( Vvar__5___24Anonymous__23008 = Vvar__5___24Anonymous__23009
& Vvar__4___24Anonymous__23006 = Vvar__4___24Anonymous__23007
& Vvar__3__AF__23004 = Vvar__3__AF__23005
& Vvar__2__AA__23002 = Vvar__2__AA__23003
& Vvar__1__TX__23000 = Vvar__1__TX__23001
& Vvar__0__TA__22998 = Vvar__0__TA__22999 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__22956,Vvar__0__TA__22957,Vvar__1__TX__22958,Vvar__1__TX__22959,Vvar__2__AA__22960,Vvar__2__AA__22961,Vvar__3__AF__22962,Vvar__3__AF__22963] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22956,Vvar__1__TX__22958,Vvar__2__AA__22960,Vvar__3__AF__22962) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22957,Vvar__1__TX__22959,Vvar__2__AA__22961,Vvar__3__AF__22963)
=> ( Vvar__3__AF__22962 = Vvar__3__AF__22963
& Vvar__2__AA__22960 = Vvar__2__AA__22961
& Vvar__1__TX__22958 = Vvar__1__TX__22959
& Vvar__0__TA__22956 = Vvar__0__TA__22957 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__23020,Vvar__0__TA__23021,Vvar__1__TX__23022,Vvar__1__TX__23023,Vvar__2__AA__23024,Vvar__2__AA__23025,Vvar__3__AF__23026,Vvar__3__AF__23027,Vvar__4___24Anonymous__23028,Vvar__4___24Anonymous__23029,Vvar__5___24Anonymous__23030,Vvar__5___24Anonymous__23031,Vvar__6___24Anonymous__23032,Vvar__6___24Anonymous__23033] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__23020,Vvar__1__TX__23022,Vvar__2__AA__23024,Vvar__3__AF__23026,Vvar__4___24Anonymous__23028,Vvar__5___24Anonymous__23030,Vvar__6___24Anonymous__23032) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__23021,Vvar__1__TX__23023,Vvar__2__AA__23025,Vvar__3__AF__23027,Vvar__4___24Anonymous__23029,Vvar__5___24Anonymous__23031,Vvar__6___24Anonymous__23033)
=> ( Vvar__6___24Anonymous__23032 = Vvar__6___24Anonymous__23033
& Vvar__5___24Anonymous__23030 = Vvar__5___24Anonymous__23031
& Vvar__4___24Anonymous__23028 = Vvar__4___24Anonymous__23029
& Vvar__3__AF__23026 = Vvar__3__AF__23027
& Vvar__2__AA__23024 = Vvar__2__AA__23025
& Vvar__1__TX__23022 = Vvar__1__TX__23023
& Vvar__0__TA__23020 = Vvar__0__TA__23021 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__23010,Vvar__0__TA__23011,Vvar__1__TX__23012,Vvar__1__TX__23013,Vvar__2__AA__23014,Vvar__2__AA__23015,Vvar__3__AF__23016,Vvar__3__AF__23017,Vvar__4___24Anonymous__23018,Vvar__4___24Anonymous__23019] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__23010,Vvar__1__TX__23012,Vvar__2__AA__23014,Vvar__3__AF__23016,Vvar__4___24Anonymous__23018) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__23011,Vvar__1__TX__23013,Vvar__2__AA__23015,Vvar__3__AF__23017,Vvar__4___24Anonymous__23019)
=> ( Vvar__4___24Anonymous__23018 = Vvar__4___24Anonymous__23019
& Vvar__3__AF__23016 = Vvar__3__AF__23017
& Vvar__2__AA__23014 = Vvar__2__AA__23015
& Vvar__1__TX__23012 = Vvar__1__TX__23013
& Vvar__0__TA__23010 = Vvar__0__TA__23011 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__22948,Vvar__0__TA__22949,Vvar__1__TX__22950,Vvar__1__TX__22951,Vvar__2__AA__22952,Vvar__2__AA__22953,Vvar__3__AF__22954,Vvar__3__AF__22955] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22948,Vvar__1__TX__22950,Vvar__2__AA__22952,Vvar__3__AF__22954) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22949,Vvar__1__TX__22951,Vvar__2__AA__22953,Vvar__3__AF__22955)
=> ( Vvar__3__AF__22954 = Vvar__3__AF__22955
& Vvar__2__AA__22952 = Vvar__2__AA__22953
& Vvar__1__TX__22950 = Vvar__1__TX__22951
& Vvar__0__TA__22948 = Vvar__0__TA__22949 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__22964,Vvar__0__TA__22965,Vvar__1__TX__22966,Vvar__1__TX__22967,Vvar__2__AA__22968,Vvar__2__AA__22969,Vvar__3__AF__22970,Vvar__3__AF__22971,Vvar__4___24Anonymous__22972,Vvar__4___24Anonymous__22973] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22964,Vvar__1__TX__22966,Vvar__2__AA__22968,Vvar__3__AF__22970,Vvar__4___24Anonymous__22972) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22965,Vvar__1__TX__22967,Vvar__2__AA__22969,Vvar__3__AF__22971,Vvar__4___24Anonymous__22973)
=> ( Vvar__4___24Anonymous__22972 = Vvar__4___24Anonymous__22973
& Vvar__3__AF__22970 = Vvar__3__AF__22971
& Vvar__2__AA__22968 = Vvar__2__AA__22969
& Vvar__1__TX__22966 = Vvar__1__TX__22967
& Vvar__0__TA__22964 = Vvar__0__TA__22965 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__8243,Vvar__0__C__8244] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8243) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8244)
=> Vvar__0__C__8243 = Vvar__0__C__8244 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__8241,Vvar__0__C__8242] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8241) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8242)
=> Vvar__0__C__8241 = Vvar__0__C__8242 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__8249,Vvar__0__C__8250,Vvar__1___24Anonymous__8251,Vvar__1___24Anonymous__8252] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8249,Vvar__1___24Anonymous__8251) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8250,Vvar__1___24Anonymous__8252)
=> ( Vvar__1___24Anonymous__8251 = Vvar__1___24Anonymous__8252
& Vvar__0__C__8249 = Vvar__0__C__8250 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__8253,Vvar__0__C__8254,Vvar__1___24Anonymous__8255,Vvar__1___24Anonymous__8256,Vvar__2___24Anonymous__8257,Vvar__2___24Anonymous__8258] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8253,Vvar__1___24Anonymous__8255,Vvar__2___24Anonymous__8257) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8254,Vvar__1___24Anonymous__8256,Vvar__2___24Anonymous__8258)
=> ( Vvar__2___24Anonymous__8257 = Vvar__2___24Anonymous__8258
& Vvar__1___24Anonymous__8255 = Vvar__1___24Anonymous__8256
& Vvar__0__C__8253 = Vvar__0__C__8254 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__8245,Vvar__0__C__8246,Vvar__1___24Anonymous__8247,Vvar__1___24Anonymous__8248] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8245,Vvar__1___24Anonymous__8247) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8246,Vvar__1___24Anonymous__8248)
=> ( Vvar__1___24Anonymous__8247 = Vvar__1___24Anonymous__8248
& Vvar__0__C__8245 = Vvar__0__C__8246 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__8279,Vvar__0__C__8280,Vvar__1___24Anonymous__8281,Vvar__1___24Anonymous__8282,Vvar__2___24Anonymous__8283,Vvar__2___24Anonymous__8284] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8279,Vvar__1___24Anonymous__8281,Vvar__2___24Anonymous__8283) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8280,Vvar__1___24Anonymous__8282,Vvar__2___24Anonymous__8284)
=> ( Vvar__2___24Anonymous__8283 = Vvar__2___24Anonymous__8284
& Vvar__1___24Anonymous__8281 = Vvar__1___24Anonymous__8282
& Vvar__0__C__8279 = Vvar__0__C__8280 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__8275,Vvar__0__C__8276,Vvar__1___24Anonymous__8277,Vvar__1___24Anonymous__8278] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8275,Vvar__1___24Anonymous__8277) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8276,Vvar__1___24Anonymous__8278)
=> ( Vvar__1___24Anonymous__8277 = Vvar__1___24Anonymous__8278
& Vvar__0__C__8275 = Vvar__0__C__8276 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__8265,Vvar__0__C__8266,Vvar__1___24Anonymous__8267,Vvar__1___24Anonymous__8268,Vvar__2___24Anonymous__8269,Vvar__2___24Anonymous__8270] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8265,Vvar__1___24Anonymous__8267,Vvar__2___24Anonymous__8269) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8266,Vvar__1___24Anonymous__8268,Vvar__2___24Anonymous__8270)
=> ( Vvar__2___24Anonymous__8269 = Vvar__2___24Anonymous__8270
& Vvar__1___24Anonymous__8267 = Vvar__1___24Anonymous__8268
& Vvar__0__C__8265 = Vvar__0__C__8266 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__8271,Vvar__0__C__8272,Vvar__1___24Anonymous__8273,Vvar__1___24Anonymous__8274] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8271,Vvar__1___24Anonymous__8273) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8272,Vvar__1___24Anonymous__8274)
=> ( Vvar__1___24Anonymous__8273 = Vvar__1___24Anonymous__8274
& Vvar__0__C__8271 = Vvar__0__C__8272 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__8285,Vvar__0__C__8286,Vvar__1___24Anonymous__8287,Vvar__1___24Anonymous__8288,Vvar__2___24Anonymous__8289,Vvar__2___24Anonymous__8290] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8285,Vvar__1___24Anonymous__8287,Vvar__2___24Anonymous__8289) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8286,Vvar__1___24Anonymous__8288,Vvar__2___24Anonymous__8290)
=> ( Vvar__2___24Anonymous__8289 = Vvar__2___24Anonymous__8290
& Vvar__1___24Anonymous__8287 = Vvar__1___24Anonymous__8288
& Vvar__0__C__8285 = Vvar__0__C__8286 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__8259,Vvar__0__C__8260,Vvar__1___24Anonymous__8261,Vvar__1___24Anonymous__8262,Vvar__2___24Anonymous__8263,Vvar__2___24Anonymous__8264] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8259,Vvar__1___24Anonymous__8261,Vvar__2___24Anonymous__8263) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8260,Vvar__1___24Anonymous__8262,Vvar__2___24Anonymous__8264)
=> ( Vvar__2___24Anonymous__8263 = Vvar__2___24Anonymous__8264
& Vvar__1___24Anonymous__8261 = Vvar__1___24Anonymous__8262
& Vvar__0__C__8259 = Vvar__0__C__8260 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__8582,Vvar__0__C__8583,Vvar__1__num__8584,Vvar__1__num__8585,Vvar__2__denum__8586,Vvar__2__denum__8587,Vvar__3__condition__8588,Vvar__3__condition__8589] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8582,Vvar__1__num__8584,Vvar__2__denum__8586,Vvar__3__condition__8588) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8583,Vvar__1__num__8585,Vvar__2__denum__8587,Vvar__3__condition__8589)
=> ( Vvar__3__condition__8588 = Vvar__3__condition__8589
& Vvar__2__denum__8586 = Vvar__2__denum__8587
& Vvar__1__num__8584 = Vvar__1__num__8585
& Vvar__0__C__8582 = Vvar__0__C__8583 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__17369,Vvar__0__C__17370] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__17369) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__17370)
=> Vvar__0__C__17369 = Vvar__0__C__17370 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__17367,Vvar__0__C__17368] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__17367) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__17368)
=> Vvar__0__C__17367 = Vvar__0__C__17368 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__17375,Vvar__0__C__17376,Vvar__1___24Anonymous__17377,Vvar__1___24Anonymous__17378] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__17375,Vvar__1___24Anonymous__17377) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__17376,Vvar__1___24Anonymous__17378)
=> ( Vvar__1___24Anonymous__17377 = Vvar__1___24Anonymous__17378
& Vvar__0__C__17375 = Vvar__0__C__17376 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__17379,Vvar__0__C__17380,Vvar__1___24Anonymous__17381,Vvar__1___24Anonymous__17382,Vvar__2___24Anonymous__17383,Vvar__2___24Anonymous__17384] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__17379,Vvar__1___24Anonymous__17381,Vvar__2___24Anonymous__17383) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__17380,Vvar__1___24Anonymous__17382,Vvar__2___24Anonymous__17384)
=> ( Vvar__2___24Anonymous__17383 = Vvar__2___24Anonymous__17384
& Vvar__1___24Anonymous__17381 = Vvar__1___24Anonymous__17382
& Vvar__0__C__17379 = Vvar__0__C__17380 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__17371,Vvar__0__C__17372,Vvar__1___24Anonymous__17373,Vvar__1___24Anonymous__17374] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__17371,Vvar__1___24Anonymous__17373) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__17372,Vvar__1___24Anonymous__17374)
=> ( Vvar__1___24Anonymous__17373 = Vvar__1___24Anonymous__17374
& Vvar__0__C__17371 = Vvar__0__C__17372 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__17391,Vvar__0__C__17392,Vvar__1___24Anonymous__17393,Vvar__1___24Anonymous__17394,Vvar__2___24Anonymous__17395,Vvar__2___24Anonymous__17396] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__17391,Vvar__1___24Anonymous__17393,Vvar__2___24Anonymous__17395) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__17392,Vvar__1___24Anonymous__17394,Vvar__2___24Anonymous__17396)
=> ( Vvar__2___24Anonymous__17395 = Vvar__2___24Anonymous__17396
& Vvar__1___24Anonymous__17393 = Vvar__1___24Anonymous__17394
& Vvar__0__C__17391 = Vvar__0__C__17392 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__17397,Vvar__0__C__17398,Vvar__1___24Anonymous__17399,Vvar__1___24Anonymous__17400] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__17397,Vvar__1___24Anonymous__17399) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__17398,Vvar__1___24Anonymous__17400)
=> ( Vvar__1___24Anonymous__17399 = Vvar__1___24Anonymous__17400
& Vvar__0__C__17397 = Vvar__0__C__17398 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__17401,Vvar__0__C__17402,Vvar__1___24Anonymous__17403,Vvar__1___24Anonymous__17404,Vvar__2___24Anonymous__17405,Vvar__2___24Anonymous__17406] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__17401,Vvar__1___24Anonymous__17403,Vvar__2___24Anonymous__17405) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__17402,Vvar__1___24Anonymous__17404,Vvar__2___24Anonymous__17406)
=> ( Vvar__2___24Anonymous__17405 = Vvar__2___24Anonymous__17406
& Vvar__1___24Anonymous__17403 = Vvar__1___24Anonymous__17404
& Vvar__0__C__17401 = Vvar__0__C__17402 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__17385,Vvar__0__C__17386,Vvar__1___24Anonymous__17387,Vvar__1___24Anonymous__17388,Vvar__2___24Anonymous__17389,Vvar__2___24Anonymous__17390] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__17385,Vvar__1___24Anonymous__17387,Vvar__2___24Anonymous__17389) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__17386,Vvar__1___24Anonymous__17388,Vvar__2___24Anonymous__17390)
=> ( Vvar__2___24Anonymous__17389 = Vvar__2___24Anonymous__17390
& Vvar__1___24Anonymous__17387 = Vvar__1___24Anonymous__17388
& Vvar__0__C__17385 = Vvar__0__C__17386 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__16910,Vvar__0__C__16911,Vvar__1___24Anonymous__16912,Vvar__1___24Anonymous__16913,Vvar__2___24Anonymous__16914,Vvar__2___24Anonymous__16915,Vvar__3___24Anonymous__16916,Vvar__3___24Anonymous__16917] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__16910,Vvar__1___24Anonymous__16912,Vvar__2___24Anonymous__16914,Vvar__3___24Anonymous__16916) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__16911,Vvar__1___24Anonymous__16913,Vvar__2___24Anonymous__16915,Vvar__3___24Anonymous__16917)
=> ( Vvar__3___24Anonymous__16916 = Vvar__3___24Anonymous__16917
& Vvar__2___24Anonymous__16914 = Vvar__2___24Anonymous__16915
& Vvar__1___24Anonymous__16912 = Vvar__1___24Anonymous__16913
& Vvar__0__C__16910 = Vvar__0__C__16911 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__16900,Vvar__0__C__16901,Vvar__1___24Anonymous__16902,Vvar__1___24Anonymous__16903] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__16900,Vvar__1___24Anonymous__16902) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__16901,Vvar__1___24Anonymous__16903)
=> ( Vvar__1___24Anonymous__16902 = Vvar__1___24Anonymous__16903
& Vvar__0__C__16900 = Vvar__0__C__16901 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__16904,Vvar__0__C__16905,Vvar__1___24Anonymous__16906,Vvar__1___24Anonymous__16907,Vvar__2___24Anonymous__16908,Vvar__2___24Anonymous__16909] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__16904,Vvar__1___24Anonymous__16906,Vvar__2___24Anonymous__16908) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__16905,Vvar__1___24Anonymous__16907,Vvar__2___24Anonymous__16909)
=> ( Vvar__2___24Anonymous__16908 = Vvar__2___24Anonymous__16909
& Vvar__1___24Anonymous__16906 = Vvar__1___24Anonymous__16907
& Vvar__0__C__16904 = Vvar__0__C__16905 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__17100,Vvar__0___24Anonymous__17101,Vvar__1___24Anonymous__17102,Vvar__1___24Anonymous__17103] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__17100,Vvar__1___24Anonymous__17102) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__17101,Vvar__1___24Anonymous__17103)
=> ( Vvar__1___24Anonymous__17102 = Vvar__1___24Anonymous__17103
& Vvar__0___24Anonymous__17100 = Vvar__0___24Anonymous__17101 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__17096,Vvar__0___24Anonymous__17097,Vvar__1___24Anonymous__17098,Vvar__1___24Anonymous__17099] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__17096,Vvar__1___24Anonymous__17098) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__17097,Vvar__1___24Anonymous__17099)
=> ( Vvar__1___24Anonymous__17098 = Vvar__1___24Anonymous__17099
& Vvar__0___24Anonymous__17096 = Vvar__0___24Anonymous__17097 ) ) ).
fof('$_inj_DirectedSets.Build_DirectedSet',axiom,
! [Vvar__0__DS__set__299,Vvar__0__DS__set__300,Vvar__1__DS__ord__301,Vvar__1__DS__ord__302,Vvar__2__DS__ord__cond__303,Vvar__2__DS__ord__cond__304,Vvar__3__DS__join__cond__305,Vvar__3__DS__join__cond__306] :
( cDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__299,Vvar__1__DS__ord__301) = cDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__300,Vvar__1__DS__ord__302)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__DS__ord__301 = Vvar__1__DS__ord__302
& Vvar__0__DS__set__299 = Vvar__0__DS__set__300 ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__29322,Vvar__1__k__29324,Vvar__2___24Anonymous__29325] :
( c_24__type__29339___24t(Vvar__0__P__29322,Vvar__1__k__29324,Vvar__2___24Anonymous__29325,Vvar__0__P__29322)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__29324)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__29325)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__29322,Vvar__1__k__29324,Vvar__2___24Anonymous__29325)
=> ( Vvar__2___24Anonymous__29325 = Vvar__1__k__29324
| ? [Vvar__2__l__29333] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__29333)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__29322,Vvar__1__k__29324,Vvar__2__l__29333)
& p(happ(Vvar__0__P__29322,Vvar__2__l__29333))
& Vvar__2___24Anonymous__29325 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__29333) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__29341,Vvar__1__k__29343,Vvar__2___24Anonymous__29344] :
( c_24__type__29360___24t(Vvar__0__Q__29341,Vvar__1__k__29343,Vvar__2___24Anonymous__29344,Vvar__0__Q__29341)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__29343)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__29344)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__29341,Vvar__1__k__29343,Vvar__2___24Anonymous__29344)
=> ( ? [Vvar__2__l__29349] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__29349)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__29341,Vvar__1__k__29343,Vvar__2__l__29349)
& Vvar__2___24Anonymous__29344 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__29349) )
| ? [Vvar__2__l__29354] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__29354)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__29343,Vvar__2__l__29354)
& p(happ(Vvar__0__Q__29341,Vvar__2__l__29354))
& Vvar__2___24Anonymous__29344 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__29354) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__26579,Vvar__1___24Anonymous__26580,VX26581] :
( cProp___24t(Vvar__0__P__26579)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__26580)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__26579,Vvar__1___24Anonymous__26580,VX26581)
=> ( ( p(Vvar__0__P__26579)
& Vvar__1___24Anonymous__26580 = cCoq_2eInit_2eDatatypes_2etrue
& VX26581 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__26579) )
| ( ~ p(Vvar__0__P__26579)
& Vvar__1___24Anonymous__26580 = cCoq_2eInit_2eDatatypes_2efalse
& VX26581 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__26579) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX24771] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX24771)
=> ( VX24771 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__24772] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__24772)
& ? [Vvar__1___24Anonymous__24773] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__24773)
& ? [Vvar__2___24Anonymous__24774] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__24774)
& VX24771 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__24772,Vvar__1___24Anonymous__24773,Vvar__2___24Anonymous__24774) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX3941] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX3941)
=> ( VX3941 = cCoq_2eInit_2eByte_2ex00
| VX3941 = cCoq_2eInit_2eByte_2ex01
| VX3941 = cCoq_2eInit_2eByte_2ex02
| VX3941 = cCoq_2eInit_2eByte_2ex03
| VX3941 = cCoq_2eInit_2eByte_2ex04
| VX3941 = cCoq_2eInit_2eByte_2ex05
| VX3941 = cCoq_2eInit_2eByte_2ex06
| VX3941 = cCoq_2eInit_2eByte_2ex07
| VX3941 = cCoq_2eInit_2eByte_2ex08
| VX3941 = cCoq_2eInit_2eByte_2ex09
| VX3941 = cCoq_2eInit_2eByte_2ex0a
| VX3941 = cCoq_2eInit_2eByte_2ex0b
| VX3941 = cCoq_2eInit_2eByte_2ex0c
| VX3941 = cCoq_2eInit_2eByte_2ex0d
| VX3941 = cCoq_2eInit_2eByte_2ex0e
| VX3941 = cCoq_2eInit_2eByte_2ex0f
| VX3941 = cCoq_2eInit_2eByte_2ex10
| VX3941 = cCoq_2eInit_2eByte_2ex11
| VX3941 = cCoq_2eInit_2eByte_2ex12
| VX3941 = cCoq_2eInit_2eByte_2ex13
| VX3941 = cCoq_2eInit_2eByte_2ex14
| VX3941 = cCoq_2eInit_2eByte_2ex15
| VX3941 = cCoq_2eInit_2eByte_2ex16
| VX3941 = cCoq_2eInit_2eByte_2ex17
| VX3941 = cCoq_2eInit_2eByte_2ex18
| VX3941 = cCoq_2eInit_2eByte_2ex19
| VX3941 = cCoq_2eInit_2eByte_2ex1a
| VX3941 = cCoq_2eInit_2eByte_2ex1b
| VX3941 = cCoq_2eInit_2eByte_2ex1c
| VX3941 = cCoq_2eInit_2eByte_2ex1d
| VX3941 = cCoq_2eInit_2eByte_2ex1e
| VX3941 = cCoq_2eInit_2eByte_2ex1f
| VX3941 = cCoq_2eInit_2eByte_2ex20
| VX3941 = cCoq_2eInit_2eByte_2ex21
| VX3941 = cCoq_2eInit_2eByte_2ex22
| VX3941 = cCoq_2eInit_2eByte_2ex23
| VX3941 = cCoq_2eInit_2eByte_2ex24
| VX3941 = cCoq_2eInit_2eByte_2ex25
| VX3941 = cCoq_2eInit_2eByte_2ex26
| VX3941 = cCoq_2eInit_2eByte_2ex27
| VX3941 = cCoq_2eInit_2eByte_2ex28
| VX3941 = cCoq_2eInit_2eByte_2ex29
| VX3941 = cCoq_2eInit_2eByte_2ex2a
| VX3941 = cCoq_2eInit_2eByte_2ex2b
| VX3941 = cCoq_2eInit_2eByte_2ex2c
| VX3941 = cCoq_2eInit_2eByte_2ex2d
| VX3941 = cCoq_2eInit_2eByte_2ex2e
| VX3941 = cCoq_2eInit_2eByte_2ex2f
| VX3941 = cCoq_2eInit_2eByte_2ex30
| VX3941 = cCoq_2eInit_2eByte_2ex31
| VX3941 = cCoq_2eInit_2eByte_2ex32
| VX3941 = cCoq_2eInit_2eByte_2ex33
| VX3941 = cCoq_2eInit_2eByte_2ex34
| VX3941 = cCoq_2eInit_2eByte_2ex35
| VX3941 = cCoq_2eInit_2eByte_2ex36
| VX3941 = cCoq_2eInit_2eByte_2ex37
| VX3941 = cCoq_2eInit_2eByte_2ex38
| VX3941 = cCoq_2eInit_2eByte_2ex39
| VX3941 = cCoq_2eInit_2eByte_2ex3a
| VX3941 = cCoq_2eInit_2eByte_2ex3b
| VX3941 = cCoq_2eInit_2eByte_2ex3c
| VX3941 = cCoq_2eInit_2eByte_2ex3d
| VX3941 = cCoq_2eInit_2eByte_2ex3e
| VX3941 = cCoq_2eInit_2eByte_2ex3f
| VX3941 = cCoq_2eInit_2eByte_2ex40
| VX3941 = cCoq_2eInit_2eByte_2ex41
| VX3941 = cCoq_2eInit_2eByte_2ex42
| VX3941 = cCoq_2eInit_2eByte_2ex43
| VX3941 = cCoq_2eInit_2eByte_2ex44
| VX3941 = cCoq_2eInit_2eByte_2ex45
| VX3941 = cCoq_2eInit_2eByte_2ex46
| VX3941 = cCoq_2eInit_2eByte_2ex47
| VX3941 = cCoq_2eInit_2eByte_2ex48
| VX3941 = cCoq_2eInit_2eByte_2ex49
| VX3941 = cCoq_2eInit_2eByte_2ex4a
| VX3941 = cCoq_2eInit_2eByte_2ex4b
| VX3941 = cCoq_2eInit_2eByte_2ex4c
| VX3941 = cCoq_2eInit_2eByte_2ex4d
| VX3941 = cCoq_2eInit_2eByte_2ex4e
| VX3941 = cCoq_2eInit_2eByte_2ex4f
| VX3941 = cCoq_2eInit_2eByte_2ex50
| VX3941 = cCoq_2eInit_2eByte_2ex51
| VX3941 = cCoq_2eInit_2eByte_2ex52
| VX3941 = cCoq_2eInit_2eByte_2ex53
| VX3941 = cCoq_2eInit_2eByte_2ex54
| VX3941 = cCoq_2eInit_2eByte_2ex55
| VX3941 = cCoq_2eInit_2eByte_2ex56
| VX3941 = cCoq_2eInit_2eByte_2ex57
| VX3941 = cCoq_2eInit_2eByte_2ex58
| VX3941 = cCoq_2eInit_2eByte_2ex59
| VX3941 = cCoq_2eInit_2eByte_2ex5a
| VX3941 = cCoq_2eInit_2eByte_2ex5b
| VX3941 = cCoq_2eInit_2eByte_2ex5c
| VX3941 = cCoq_2eInit_2eByte_2ex5d
| VX3941 = cCoq_2eInit_2eByte_2ex5e
| VX3941 = cCoq_2eInit_2eByte_2ex5f
| VX3941 = cCoq_2eInit_2eByte_2ex60
| VX3941 = cCoq_2eInit_2eByte_2ex61
| VX3941 = cCoq_2eInit_2eByte_2ex62
| VX3941 = cCoq_2eInit_2eByte_2ex63
| VX3941 = cCoq_2eInit_2eByte_2ex64
| VX3941 = cCoq_2eInit_2eByte_2ex65
| VX3941 = cCoq_2eInit_2eByte_2ex66
| VX3941 = cCoq_2eInit_2eByte_2ex67
| VX3941 = cCoq_2eInit_2eByte_2ex68
| VX3941 = cCoq_2eInit_2eByte_2ex69
| VX3941 = cCoq_2eInit_2eByte_2ex6a
| VX3941 = cCoq_2eInit_2eByte_2ex6b
| VX3941 = cCoq_2eInit_2eByte_2ex6c
| VX3941 = cCoq_2eInit_2eByte_2ex6d
| VX3941 = cCoq_2eInit_2eByte_2ex6e
| VX3941 = cCoq_2eInit_2eByte_2ex6f
| VX3941 = cCoq_2eInit_2eByte_2ex70
| VX3941 = cCoq_2eInit_2eByte_2ex71
| VX3941 = cCoq_2eInit_2eByte_2ex72
| VX3941 = cCoq_2eInit_2eByte_2ex73
| VX3941 = cCoq_2eInit_2eByte_2ex74
| VX3941 = cCoq_2eInit_2eByte_2ex75
| VX3941 = cCoq_2eInit_2eByte_2ex76
| VX3941 = cCoq_2eInit_2eByte_2ex77
| VX3941 = cCoq_2eInit_2eByte_2ex78
| VX3941 = cCoq_2eInit_2eByte_2ex79
| VX3941 = cCoq_2eInit_2eByte_2ex7a
| VX3941 = cCoq_2eInit_2eByte_2ex7b
| VX3941 = cCoq_2eInit_2eByte_2ex7c
| VX3941 = cCoq_2eInit_2eByte_2ex7d
| VX3941 = cCoq_2eInit_2eByte_2ex7e
| VX3941 = cCoq_2eInit_2eByte_2ex7f
| VX3941 = cCoq_2eInit_2eByte_2ex80
| VX3941 = cCoq_2eInit_2eByte_2ex81
| VX3941 = cCoq_2eInit_2eByte_2ex82
| VX3941 = cCoq_2eInit_2eByte_2ex83
| VX3941 = cCoq_2eInit_2eByte_2ex84
| VX3941 = cCoq_2eInit_2eByte_2ex85
| VX3941 = cCoq_2eInit_2eByte_2ex86
| VX3941 = cCoq_2eInit_2eByte_2ex87
| VX3941 = cCoq_2eInit_2eByte_2ex88
| VX3941 = cCoq_2eInit_2eByte_2ex89
| VX3941 = cCoq_2eInit_2eByte_2ex8a
| VX3941 = cCoq_2eInit_2eByte_2ex8b
| VX3941 = cCoq_2eInit_2eByte_2ex8c
| VX3941 = cCoq_2eInit_2eByte_2ex8d
| VX3941 = cCoq_2eInit_2eByte_2ex8e
| VX3941 = cCoq_2eInit_2eByte_2ex8f
| VX3941 = cCoq_2eInit_2eByte_2ex90
| VX3941 = cCoq_2eInit_2eByte_2ex91
| VX3941 = cCoq_2eInit_2eByte_2ex92
| VX3941 = cCoq_2eInit_2eByte_2ex93
| VX3941 = cCoq_2eInit_2eByte_2ex94
| VX3941 = cCoq_2eInit_2eByte_2ex95
| VX3941 = cCoq_2eInit_2eByte_2ex96
| VX3941 = cCoq_2eInit_2eByte_2ex97
| VX3941 = cCoq_2eInit_2eByte_2ex98
| VX3941 = cCoq_2eInit_2eByte_2ex99
| VX3941 = cCoq_2eInit_2eByte_2ex9a
| VX3941 = cCoq_2eInit_2eByte_2ex9b
| VX3941 = cCoq_2eInit_2eByte_2ex9c
| VX3941 = cCoq_2eInit_2eByte_2ex9d
| VX3941 = cCoq_2eInit_2eByte_2ex9e
| VX3941 = cCoq_2eInit_2eByte_2ex9f
| VX3941 = cCoq_2eInit_2eByte_2exa0
| VX3941 = cCoq_2eInit_2eByte_2exa1
| VX3941 = cCoq_2eInit_2eByte_2exa2
| VX3941 = cCoq_2eInit_2eByte_2exa3
| VX3941 = cCoq_2eInit_2eByte_2exa4
| VX3941 = cCoq_2eInit_2eByte_2exa5
| VX3941 = cCoq_2eInit_2eByte_2exa6
| VX3941 = cCoq_2eInit_2eByte_2exa7
| VX3941 = cCoq_2eInit_2eByte_2exa8
| VX3941 = cCoq_2eInit_2eByte_2exa9
| VX3941 = cCoq_2eInit_2eByte_2exaa
| VX3941 = cCoq_2eInit_2eByte_2exab
| VX3941 = cCoq_2eInit_2eByte_2exac
| VX3941 = cCoq_2eInit_2eByte_2exad
| VX3941 = cCoq_2eInit_2eByte_2exae
| VX3941 = cCoq_2eInit_2eByte_2exaf
| VX3941 = cCoq_2eInit_2eByte_2exb0
| VX3941 = cCoq_2eInit_2eByte_2exb1
| VX3941 = cCoq_2eInit_2eByte_2exb2
| VX3941 = cCoq_2eInit_2eByte_2exb3
| VX3941 = cCoq_2eInit_2eByte_2exb4
| VX3941 = cCoq_2eInit_2eByte_2exb5
| VX3941 = cCoq_2eInit_2eByte_2exb6
| VX3941 = cCoq_2eInit_2eByte_2exb7
| VX3941 = cCoq_2eInit_2eByte_2exb8
| VX3941 = cCoq_2eInit_2eByte_2exb9
| VX3941 = cCoq_2eInit_2eByte_2exba
| VX3941 = cCoq_2eInit_2eByte_2exbb
| VX3941 = cCoq_2eInit_2eByte_2exbc
| VX3941 = cCoq_2eInit_2eByte_2exbd
| VX3941 = cCoq_2eInit_2eByte_2exbe
| VX3941 = cCoq_2eInit_2eByte_2exbf
| VX3941 = cCoq_2eInit_2eByte_2exc0
| VX3941 = cCoq_2eInit_2eByte_2exc1
| VX3941 = cCoq_2eInit_2eByte_2exc2
| VX3941 = cCoq_2eInit_2eByte_2exc3
| VX3941 = cCoq_2eInit_2eByte_2exc4
| VX3941 = cCoq_2eInit_2eByte_2exc5
| VX3941 = cCoq_2eInit_2eByte_2exc6
| VX3941 = cCoq_2eInit_2eByte_2exc7
| VX3941 = cCoq_2eInit_2eByte_2exc8
| VX3941 = cCoq_2eInit_2eByte_2exc9
| VX3941 = cCoq_2eInit_2eByte_2exca
| VX3941 = cCoq_2eInit_2eByte_2excb
| VX3941 = cCoq_2eInit_2eByte_2excc
| VX3941 = cCoq_2eInit_2eByte_2excd
| VX3941 = cCoq_2eInit_2eByte_2exce
| VX3941 = cCoq_2eInit_2eByte_2excf
| VX3941 = cCoq_2eInit_2eByte_2exd0
| VX3941 = cCoq_2eInit_2eByte_2exd1
| VX3941 = cCoq_2eInit_2eByte_2exd2
| VX3941 = cCoq_2eInit_2eByte_2exd3
| VX3941 = cCoq_2eInit_2eByte_2exd4
| VX3941 = cCoq_2eInit_2eByte_2exd5
| VX3941 = cCoq_2eInit_2eByte_2exd6
| VX3941 = cCoq_2eInit_2eByte_2exd7
| VX3941 = cCoq_2eInit_2eByte_2exd8
| VX3941 = cCoq_2eInit_2eByte_2exd9
| VX3941 = cCoq_2eInit_2eByte_2exda
| VX3941 = cCoq_2eInit_2eByte_2exdb
| VX3941 = cCoq_2eInit_2eByte_2exdc
| VX3941 = cCoq_2eInit_2eByte_2exdd
| VX3941 = cCoq_2eInit_2eByte_2exde
| VX3941 = cCoq_2eInit_2eByte_2exdf
| VX3941 = cCoq_2eInit_2eByte_2exe0
| VX3941 = cCoq_2eInit_2eByte_2exe1
| VX3941 = cCoq_2eInit_2eByte_2exe2
| VX3941 = cCoq_2eInit_2eByte_2exe3
| VX3941 = cCoq_2eInit_2eByte_2exe4
| VX3941 = cCoq_2eInit_2eByte_2exe5
| VX3941 = cCoq_2eInit_2eByte_2exe6
| VX3941 = cCoq_2eInit_2eByte_2exe7
| VX3941 = cCoq_2eInit_2eByte_2exe8
| VX3941 = cCoq_2eInit_2eByte_2exe9
| VX3941 = cCoq_2eInit_2eByte_2exea
| VX3941 = cCoq_2eInit_2eByte_2exeb
| VX3941 = cCoq_2eInit_2eByte_2exec
| VX3941 = cCoq_2eInit_2eByte_2exed
| VX3941 = cCoq_2eInit_2eByte_2exee
| VX3941 = cCoq_2eInit_2eByte_2exef
| VX3941 = cCoq_2eInit_2eByte_2exf0
| VX3941 = cCoq_2eInit_2eByte_2exf1
| VX3941 = cCoq_2eInit_2eByte_2exf2
| VX3941 = cCoq_2eInit_2eByte_2exf3
| VX3941 = cCoq_2eInit_2eByte_2exf4
| VX3941 = cCoq_2eInit_2eByte_2exf5
| VX3941 = cCoq_2eInit_2eByte_2exf6
| VX3941 = cCoq_2eInit_2eByte_2exf7
| VX3941 = cCoq_2eInit_2eByte_2exf8
| VX3941 = cCoq_2eInit_2eByte_2exf9
| VX3941 = cCoq_2eInit_2eByte_2exfa
| VX3941 = cCoq_2eInit_2eByte_2exfb
| VX3941 = cCoq_2eInit_2eByte_2exfc
| VX3941 = cCoq_2eInit_2eByte_2exfd
| VX3941 = cCoq_2eInit_2eByte_2exfe
| VX3941 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__26652,Vvar__1__Q__26653,Vvar__2___24Anonymous__26654] :
( cProp___24t(Vvar__0__P__26652)
=> ( cProp___24t(Vvar__1__Q__26653)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__26654)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__26652,Vvar__1__Q__26653,Vvar__2___24Anonymous__26654)
=> ( ( p(Vvar__0__P__26652)
& Vvar__2___24Anonymous__26654 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__26653)
& Vvar__2___24Anonymous__26654 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__25900,Vvar__1__Plt__25901,Vvar__2__Pgt__25902,Vvar__3___24Anonymous__25903] :
( cProp___24t(Vvar__0__Peq__25900)
=> ( cProp___24t(Vvar__1__Plt__25901)
=> ( cProp___24t(Vvar__2__Pgt__25902)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__25903)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__25900,Vvar__1__Plt__25901,Vvar__2__Pgt__25902,Vvar__3___24Anonymous__25903)
=> ( ( p(Vvar__0__Peq__25900)
& Vvar__3___24Anonymous__25903 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__25901)
& Vvar__3___24Anonymous__25903 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__25902)
& Vvar__3___24Anonymous__25903 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX347] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX347)
=> ( VX347 = cCoq_2eInit_2eDatatypes_2etrue
| VX347 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX4768] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX4768)
=> ( VX4768 = cCoq_2eInit_2eDatatypes_2eEq
| VX4768 = cCoq_2eInit_2eDatatypes_2eLt
| VX4768 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__4715,VX4716] :
( cType___24t(Vvar__0__A__4715)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4715,VX4716)
=> ( VX4716 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4715)
| ? [Vvar__1___24Anonymous__4719] :
( t(Vvar__1___24Anonymous__4719,Vvar__0__A__4715)
& ? [Vvar__2___24Anonymous__4720] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4715,Vvar__2___24Anonymous__4720)
& VX4716 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4715,Vvar__1___24Anonymous__4719,Vvar__2___24Anonymous__4720) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX351] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX351)
=> ( VX351 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__352] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__352)
& VX351 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__352) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__4648,VX4649] :
( cType___24t(Vvar__0__A__4648)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__4648,VX4649)
=> ( ? [Vvar__1___24Anonymous__4651] :
( t(Vvar__1___24Anonymous__4651,Vvar__0__A__4648)
& VX4649 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__4648,Vvar__1___24Anonymous__4651) )
| VX4649 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__4648) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__387,Vvar__1__B__388,VX389] :
( cType___24t(Vvar__0__A__387)
=> ( cType___24t(Vvar__1__B__388)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__387,Vvar__1__B__388,VX389)
=> ? [Vvar__2___24Anonymous__392] :
( t(Vvar__2___24Anonymous__392,Vvar__0__A__387)
& ? [Vvar__3___24Anonymous__393] :
( t(Vvar__3___24Anonymous__393,Vvar__1__B__388)
& VX389 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__387,Vvar__1__B__388,Vvar__2___24Anonymous__392,Vvar__3___24Anonymous__393) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX18] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX18)
=> VX18 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__513,Vvar__1___24Anonymous__514] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__513)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__514)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__513,Vvar__1___24Anonymous__514)
=> ( Vvar__1___24Anonymous__514 = Vvar__0__n__513
| ? [Vvar__1__m__518] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__518)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__513,Vvar__1__m__518)
& Vvar__1___24Anonymous__514 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__518) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__22533,Vvar__1__P__22534,VX22537] :
( cType___24t(Vvar__0__A__22533)
=> ( c_24__type__22547___24t(Vvar__0__A__22533,Vvar__1__P__22534,Vvar__1__P__22534)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__22533,Vvar__1__P__22534,VX22537)
=> ? [Vvar__2__x__22542] :
( t(Vvar__2__x__22542,Vvar__0__A__22533)
& p(happ(Vvar__1__P__22534,Vvar__2__x__22542))
& VX22537 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__22533,Vvar__1__P__22534,Vvar__2__x__22542) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__29063,Vvar__1__P__29064,VX29067] :
( cType___24t(Vvar__0__A__29063)
=> ( c_24__type__29077___24t(Vvar__0__A__29063,Vvar__1__P__29064,Vvar__1__P__29064)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__29063,Vvar__1__P__29064,VX29067)
=> ? [Vvar__2__x__29072] :
( t(Vvar__2__x__29072,Vvar__0__A__29063)
& ? [Vvar__3___24Anonymous__29073] :
( t(Vvar__3___24Anonymous__29073,happ(Vvar__1__P__29064,Vvar__2__x__29072))
& VX29067 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__29063,Vvar__1__P__29064,Vvar__2__x__29072,Vvar__3___24Anonymous__29073) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__3391,Vvar__1__B__3392,VX3393] :
( cProp___24t(Vvar__0__A__3391)
=> ( cProp___24t(Vvar__1__B__3392)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__3391,Vvar__1__B__3392,VX3393)
=> ( ( p(Vvar__0__A__3391)
& VX3393 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__3391,Vvar__1__B__3392) )
| ( p(Vvar__1__B__3392)
& VX3393 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__3391,Vvar__1__B__3392) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__29148,Vvar__1__B__29149,VX29150] :
( cType___24t(Vvar__0__A__29148)
=> ( cProp___24t(Vvar__1__B__29149)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__29148,Vvar__1__B__29149,VX29150)
=> ( ? [Vvar__2___24Anonymous__29153] :
( t(Vvar__2___24Anonymous__29153,Vvar__0__A__29148)
& VX29150 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29148,Vvar__1__B__29149,Vvar__2___24Anonymous__29153) )
| ( p(Vvar__1__B__29149)
& VX29150 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29148,Vvar__1__B__29149) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__31389,Vvar__1__a__31390,Vvar__2___24Anonymous__31391,Vvar__3___24Anonymous__31392] :
( cType___24t(Vvar__0__A__31389)
=> ( t(Vvar__1__a__31390,Vvar__0__A__31389)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31389,Vvar__2___24Anonymous__31391)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31389,Vvar__3___24Anonymous__31392)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__31389,Vvar__1__a__31390,Vvar__2___24Anonymous__31391,Vvar__3___24Anonymous__31392)
=> ( ? [Vvar__2__l__31396] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31389,Vvar__2__l__31396)
& Vvar__3___24Anonymous__31392 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31389,Vvar__1__a__31390,Vvar__2__l__31396)
& Vvar__2___24Anonymous__31391 = Vvar__2__l__31396 )
| ? [Vvar__2__x__31399] :
( t(Vvar__2__x__31399,Vvar__0__A__31389)
& ? [Vvar__3__l__31400] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31389,Vvar__3__l__31400)
& ? [Vvar__4__l_27__31401] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31389,Vvar__4__l_27__31401)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__31389,Vvar__1__a__31390,Vvar__3__l__31400,Vvar__4__l_27__31401)
& Vvar__3___24Anonymous__31392 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31389,Vvar__2__x__31399,Vvar__4__l_27__31401)
& Vvar__2___24Anonymous__31391 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31389,Vvar__2__x__31399,Vvar__3__l__31400) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__9743,Vvar__1__P__9744,Vvar__2___24Anonymous__9747] :
( cType___24t(Vvar__0__A__9743)
=> ( c_24__type__9767___24t(Vvar__0__A__9743,Vvar__1__P__9744,Vvar__2___24Anonymous__9747,Vvar__1__P__9744)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9743,Vvar__2___24Anonymous__9747)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__9743,Vvar__1__P__9744,Vvar__2___24Anonymous__9747)
=> ( ? [Vvar__2__x__9753] :
( t(Vvar__2__x__9753,Vvar__0__A__9743)
& ? [Vvar__3__l__9754] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9743,Vvar__3__l__9754)
& p(happ(Vvar__1__P__9744,Vvar__2__x__9753))
& Vvar__2___24Anonymous__9747 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9743,Vvar__2__x__9753,Vvar__3__l__9754) ) )
| ? [Vvar__2__x__9760] :
( t(Vvar__2__x__9760,Vvar__0__A__9743)
& ? [Vvar__3__l__9761] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9743,Vvar__3__l__9761)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__9743,Vvar__1__P__9744,Vvar__3__l__9761)
& Vvar__2___24Anonymous__9747 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9743,Vvar__2__x__9760,Vvar__3__l__9761) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__9782,Vvar__1__P__9783,Vvar__2___24Anonymous__9786] :
( cType___24t(Vvar__0__A__9782)
=> ( c_24__type__9804___24t(Vvar__0__A__9782,Vvar__1__P__9783,Vvar__2___24Anonymous__9786,Vvar__1__P__9783)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9782,Vvar__2___24Anonymous__9786)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__9782,Vvar__1__P__9783,Vvar__2___24Anonymous__9786)
=> ( Vvar__2___24Anonymous__9786 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9782)
| ? [Vvar__2__x__9796] :
( t(Vvar__2__x__9796,Vvar__0__A__9782)
& ? [Vvar__3__l__9797] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9782,Vvar__3__l__9797)
& p(happ(Vvar__1__P__9783,Vvar__2__x__9796))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__9782,Vvar__1__P__9783,Vvar__3__l__9797)
& Vvar__2___24Anonymous__9786 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9782,Vvar__2__x__9796,Vvar__3__l__9797) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__31459,Vvar__1__R__31460,Vvar__2___24Anonymous__31465] :
( cType___24t(Vvar__0__A__31459)
=> ( c_24__type__31492___24t(Vvar__0__A__31459,Vvar__1__R__31460,Vvar__2___24Anonymous__31465,Vvar__1__R__31460)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31459,Vvar__2___24Anonymous__31465)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__31459,Vvar__1__R__31460,Vvar__2___24Anonymous__31465)
=> ( Vvar__2___24Anonymous__31465 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31459)
| ? [Vvar__2__a__31479] :
( t(Vvar__2__a__31479,Vvar__0__A__31459)
& ? [Vvar__3__l__31480] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31459,Vvar__3__l__31480)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__31459,happ(Vvar__1__R__31460,Vvar__2__a__31479),Vvar__3__l__31480)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__31459,Vvar__1__R__31460,Vvar__3__l__31480)
& Vvar__2___24Anonymous__31465 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31459,Vvar__2__a__31479,Vvar__3__l__31480) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__31403,Vvar__1___24Anonymous__31404] :
( cType___24t(Vvar__0__A__31403)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31403,Vvar__1___24Anonymous__31404)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__31403,Vvar__1___24Anonymous__31404)
=> ( Vvar__1___24Anonymous__31404 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__31403)
| ? [Vvar__1__x__31408] :
( t(Vvar__1__x__31408,Vvar__0__A__31403)
& ? [Vvar__2__l__31409] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__31403,Vvar__2__l__31409)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__31403,Vvar__1__x__31408,Vvar__2__l__31409)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__31403,Vvar__2__l__31409)
& Vvar__1___24Anonymous__31404 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__31403,Vvar__1__x__31408,Vvar__2__l__31409) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__22386,Vvar__1__eqA__22387,Vvar__2__x__22392,Vvar__3___24Anonymous__22393] :
( cType___24t(Vvar__0__A__22386)
=> ( c_24__type__22426___24t(Vvar__0__A__22386,Vvar__1__eqA__22387,Vvar__2__x__22392,Vvar__3___24Anonymous__22393,Vvar__1__eqA__22387)
=> ( t(Vvar__2__x__22392,Vvar__0__A__22386)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22386,Vvar__3___24Anonymous__22393)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22386,Vvar__1__eqA__22387,Vvar__2__x__22392,Vvar__3___24Anonymous__22393)
=> ( ? [Vvar__3__y__22402] :
( t(Vvar__3__y__22402,Vvar__0__A__22386)
& ? [Vvar__4__l__22403] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22386,Vvar__4__l__22403)
& p(happ(happ(Vvar__1__eqA__22387,Vvar__2__x__22392),Vvar__3__y__22402))
& Vvar__3___24Anonymous__22393 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22386,Vvar__3__y__22402,Vvar__4__l__22403) ) )
| ? [Vvar__3__y__22412] :
( t(Vvar__3__y__22412,Vvar__0__A__22386)
& ? [Vvar__4__l__22413] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22386,Vvar__4__l__22413)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22386,Vvar__1__eqA__22387,Vvar__2__x__22392,Vvar__4__l__22413)
& Vvar__3___24Anonymous__22393 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22386,Vvar__3__y__22412,Vvar__4__l__22413) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__30596,Vvar__1__eqA__30597,Vvar__2___24Anonymous__30602] :
( cType___24t(Vvar__0__A__30596)
=> ( c_24__type__30629___24t(Vvar__0__A__30596,Vvar__1__eqA__30597,Vvar__2___24Anonymous__30602,Vvar__1__eqA__30597)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30596,Vvar__2___24Anonymous__30602)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__30596,Vvar__1__eqA__30597,Vvar__2___24Anonymous__30602)
=> ( Vvar__2___24Anonymous__30602 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__30596)
| ? [Vvar__2__x__30616] :
( t(Vvar__2__x__30616,Vvar__0__A__30596)
& ? [Vvar__3__l__30617] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__30596,Vvar__3__l__30617)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__30596,Vvar__1__eqA__30597,Vvar__2__x__30616,Vvar__3__l__30617)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__30596,Vvar__1__eqA__30597,Vvar__3__l__30617)
& Vvar__2___24Anonymous__30602 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__30596,Vvar__2__x__30616,Vvar__3__l__30617) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__26731,Vvar__1__P__26732,Vvar__2__p__26735,Vvar__3__x__26736,Vvar__4__q__26737,Vvar__5___24Anonymous__26738] :
( cType___24t(Vvar__0__U__26731)
=> ( c_24__type__26753___24t(Vvar__0__U__26731,Vvar__1__P__26732,Vvar__2__p__26735,Vvar__3__x__26736,Vvar__4__q__26737,Vvar__5___24Anonymous__26738,Vvar__1__P__26732)
=> ( t(Vvar__2__p__26735,Vvar__0__U__26731)
=> ( t(Vvar__3__x__26736,happ(Vvar__1__P__26732,Vvar__2__p__26735))
=> ( t(Vvar__4__q__26737,Vvar__0__U__26731)
=> ( t(Vvar__5___24Anonymous__26738,happ(Vvar__1__P__26732,Vvar__4__q__26737))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__26731,Vvar__1__P__26732,Vvar__2__p__26735,Vvar__3__x__26736,Vvar__4__q__26737,Vvar__5___24Anonymous__26738)
=> ( Vvar__5___24Anonymous__26738 = Vvar__3__x__26736
& Vvar__4__q__26737 = Vvar__2__p__26735 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX498] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX498)
=> ( VX498 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__499] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__499)
& VX498 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__499) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX7] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX7)
=> ( VX7 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__8] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8)
& VX7 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__8) )
| ? [Vvar__0___24Anonymous__9] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9)
& VX7 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__9) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX334] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX334)
=> ( ? [Vvar__0___24Anonymous__335] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__335)
& VX334 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__335) )
| ? [Vvar__0___24Anonymous__336] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__336)
& VX334 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__336) )
| VX334 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX523] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX523)
=> ? [Vvar__0__Qnum__524] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__524)
& ? [Vvar__1__Qden__525] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__525)
& VX523 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__524,Vvar__1__Qden__525) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX29563] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX29563)
=> ? [Vvar__0__nonzero__29564] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__29564)
& Vvar__0__nonzero__29564 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX29563 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__29564) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__28225,Vvar__1___24Anonymous__28226,VX28227] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__28225)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__28226)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__28225,Vvar__1___24Anonymous__28226,VX28227)
=> ( ( Vvar__0__x__28225 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__28226 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX28227 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28225) )
| ? [Vvar__1__n__28231] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__28231)
& Vvar__0__x__28225 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__28231)
& Vvar__1___24Anonymous__28226 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2428251___24a3(Vvar__0__x__28225,Vvar__1___24Anonymous__28226,Vvar__1__n__28231)
& VX28227 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28225,Vvar__1__n__28231) )
| ? [Vvar__1__n__28236] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__28236)
& Vvar__0__x__28225 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__28236))
& Vvar__1___24Anonymous__28226 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428268___24a3(Vvar__0__x__28225,Vvar__1___24Anonymous__28226,Vvar__1__n__28236)
& VX28227 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__28225,Vvar__1__n__28236) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__26,Vvar__1__R__27] :
( cType___24t(Vvar__0__A__26)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__26,Vvar__1__R__27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__26,Vvar__1__R__27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__26,Vvar__1__R__27)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__26,Vvar__1__R__27)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX25875] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX25875)
=> ? [Vvar__0___24Anonymous__25876] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__25876)
& ? [Vvar__1___24Anonymous__25877] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__25877)
& ? [Vvar__2___24Anonymous__25878] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__25878)
& ? [Vvar__3___24Anonymous__25879] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__25879)
& ? [Vvar__4___24Anonymous__25880] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__25880)
& ? [Vvar__5___24Anonymous__25881] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__25881)
& ? [Vvar__6___24Anonymous__25882] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__25882)
& ? [Vvar__7___24Anonymous__25883] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__25883)
& VX25875 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__25876,Vvar__1___24Anonymous__25877,Vvar__2___24Anonymous__25878,Vvar__3___24Anonymous__25879,Vvar__4___24Anonymous__25880,Vvar__5___24Anonymous__25881,Vvar__6___24Anonymous__25882,Vvar__7___24Anonymous__25883) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX22582] :
( cCoq_2eStrings_2eString_2estring___24t(VX22582)
=> ( VX22582 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__22583] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__22583)
& ? [Vvar__1___24Anonymous__22584] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__22584)
& VX22582 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22583,Vvar__1___24Anonymous__22584) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__30936,Vvar__1___24Anonymous__30937] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__30936)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__30937)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__30936,Vvar__1___24Anonymous__30937)
=> ( ? [Vvar__0__a__30939] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__30939)
& ? [Vvar__1__s__30940] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__30940)
& Vvar__1___24Anonymous__30937 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30939,Vvar__1__s__30940)
& Vvar__0___24Anonymous__30936 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__30941] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__30941)
& ? [Vvar__1__s1__30942] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__30942)
& ? [Vvar__2__s2__30943] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__30943)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__30942,Vvar__2__s2__30943)
& Vvar__1___24Anonymous__30937 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30941,Vvar__2__s2__30943)
& Vvar__0___24Anonymous__30936 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30941,Vvar__1__s1__30942) ) ) )
| ? [Vvar__0__a__30945] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__30945)
& ? [Vvar__1__b__30946] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__30946)
& ? [Vvar__2__s1__30947] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__30947)
& ? [Vvar__3__s2__30948] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__30948)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__30945),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__30946))
& Vvar__1___24Anonymous__30937 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__30946,Vvar__3__s2__30948)
& Vvar__0___24Anonymous__30936 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30945,Vvar__2__s1__30947) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__1127,VX1128] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1127)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__1127,VX1128)
=> ( ? [Vvar__0__n__1129] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1129)
& Vvar__0___24Anonymous__1127 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1129)
& VX1128 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1129) )
| ? [Vvar__0__n__1130] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1130)
& ? [Vvar__1___24Anonymous__1131] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__1130,Vvar__1___24Anonymous__1131)
& Vvar__0___24Anonymous__1127 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1130)
& VX1128 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1130,Vvar__1___24Anonymous__1131) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__3421,Vvar__1___24Anonymous__3422,VX3423] :
( cType___24t(Vvar__0__A__3421)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__3422)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3421,Vvar__1___24Anonymous__3422,VX3423)
=> ( ( Vvar__1___24Anonymous__3422 = cCoq_2eInit_2eDatatypes_2eO
& VX3423 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__3421) )
| ? [Vvar__1__h__3426] :
( t(Vvar__1__h__3426,Vvar__0__A__3421)
& ? [Vvar__2__n__3427] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__3427)
& ? [Vvar__3___24Anonymous__3428] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__3421,Vvar__2__n__3427,Vvar__3___24Anonymous__3428)
& Vvar__1___24Anonymous__3422 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__3427)
& VX3423 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__3421,Vvar__1__h__3426,Vvar__2__n__3427,Vvar__3___24Anonymous__3428) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__24389,Vvar__1__b__24390,Vvar__2__g__24391] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__24389)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__24390)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__24391)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__24389,Vvar__1__b__24390,Vvar__2__g__24391)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__24391,Vvar__0__a__24389)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__24391,Vvar__1__b__24390)
& ! [Vvar__var__var__var__var__5__x__24399__24402__24405__24408__24411] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__24399__24402__24405__24408__24411)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__24399__24402__24405__24408__24411,Vvar__0__a__24389)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__24399__24402__24405__24408__24411,Vvar__1__b__24390)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__24399__24402__24405__24408__24411,Vvar__2__g__24391) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__29268] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__29268)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__29268)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__29268))
& ! [Vvar__var__var__2__n__29273__29275__29277] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__29273__29275__29277)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__29273__29275__29277))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__29273__29275__29277,Vvar__0__p__29268)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__29273__29275__29277,Vvar__0__p__29268) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__25917,VX25918] :
( cType___24t(Vvar__0__C__25917)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,VX25918)
=> ( ? [Vvar__1___24Anonymous__25920] :
( t(Vvar__1___24Anonymous__25920,Vvar__0__C__25917)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__25917,Vvar__1___24Anonymous__25920) )
| ? [Vvar__1___24Anonymous__25922] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25922)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__25917,Vvar__1___24Anonymous__25922) )
| ? [Vvar__1___24Anonymous__25924] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__1___24Anonymous__25924)
& ? [Vvar__2___24Anonymous__25925] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__2___24Anonymous__25925)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__25917,Vvar__1___24Anonymous__25924,Vvar__2___24Anonymous__25925) ) )
| ? [Vvar__1___24Anonymous__25927] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__1___24Anonymous__25927)
& ? [Vvar__2___24Anonymous__25928] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__2___24Anonymous__25928)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__25917,Vvar__1___24Anonymous__25927,Vvar__2___24Anonymous__25928) ) )
| ? [Vvar__1___24Anonymous__25930] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__1___24Anonymous__25930)
& ? [Vvar__2___24Anonymous__25931] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__2___24Anonymous__25931)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__25917,Vvar__1___24Anonymous__25930,Vvar__2___24Anonymous__25931) ) )
| ? [Vvar__1___24Anonymous__25933] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__1___24Anonymous__25933)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__25917,Vvar__1___24Anonymous__25933) )
| ? [Vvar__1___24Anonymous__25935] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__25917,Vvar__1___24Anonymous__25935)
& ? [Vvar__2___24Anonymous__25936] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25936)
& VX25918 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__25917,Vvar__1___24Anonymous__25935,Vvar__2___24Anonymous__25936) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__4951,VX4952] :
( cType___24t(Vvar__0__C__4951)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4951,VX4952)
=> ( ? [Vvar__1___24Anonymous__4954] :
( t(Vvar__1___24Anonymous__4954,Vvar__0__C__4951)
& VX4952 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__4951,Vvar__1___24Anonymous__4954) )
| ? [Vvar__1___24Anonymous__4956] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__4956)
& ? [Vvar__2___24Anonymous__4957] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4951,Vvar__2___24Anonymous__4957)
& VX4952 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__4951,Vvar__1___24Anonymous__4956,Vvar__2___24Anonymous__4957) ) )
| ? [Vvar__1___24Anonymous__4959] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4951,Vvar__1___24Anonymous__4959)
& ? [Vvar__2___24Anonymous__4960] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__4960)
& ? [Vvar__3___24Anonymous__4961] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__4951,Vvar__3___24Anonymous__4961)
& VX4952 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__4951,Vvar__1___24Anonymous__4959,Vvar__2___24Anonymous__4960,Vvar__3___24Anonymous__4961) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376] :
( cType___24t(Vvar__0__R__1345)
=> ( t(Vvar__1__rO__1346,Vvar__0__R__1345)
=> ( t(Vvar__2__rI__1347,Vvar__0__R__1345)
=> ( c_24__type__1777___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__3__rplus__1348)
=> ( c_24__type__1878___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__4__rtimes__1353)
=> ( c_24__type__1979___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__5__rminus__1358)
=> ( c_24__type__2069___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__6__ropp__1363)
=> ( c_24__type__2170___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__7__req__1366)
=> ( c_24__type__2271___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__8__rle__1371)
=> ( c_24__type__2372___24t(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376,Vvar__9__rlt__1376)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366,Vvar__8__rle__1371,Vvar__9__rlt__1376)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__1345,Vvar__7__req__1366)
& ! [Vvar__var__var__var__var__11__x1__1420__1426__1531__1537__1543] :
( t(Vvar__var__var__var__var__11__x1__1420__1426__1531__1537__1543,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__12__x2__1421__1427__1532__1538__1544] :
( t(Vvar__var__var__var__var__12__x2__1421__1427__1532__1538__1544,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__11__x1__1420__1426__1531__1537__1543),Vvar__var__var__var__var__12__x2__1421__1427__1532__1538__1544))
=> ! [Vvar__var__var__var__var__14__y1__1422__1428__1533__1539__1545] :
( t(Vvar__var__var__var__var__14__y1__1422__1428__1533__1539__1545,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__15__y2__1423__1429__1534__1540__1546] :
( t(Vvar__var__var__var__var__15__y2__1423__1429__1534__1540__1546,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__14__y1__1422__1428__1533__1539__1545),Vvar__var__var__var__var__15__y2__1423__1429__1534__1540__1546))
=> p(happ(happ(Vvar__7__req__1366,happ(happ(Vvar__3__rplus__1348,Vvar__var__var__var__var__11__x1__1420__1426__1531__1537__1543),Vvar__var__var__var__var__14__y1__1422__1428__1533__1539__1545)),happ(happ(Vvar__3__rplus__1348,Vvar__var__var__var__var__12__x2__1421__1427__1532__1538__1544),Vvar__var__var__var__var__15__y2__1423__1429__1534__1540__1546))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__1433__1439__1549__1555__1561] :
( t(Vvar__var__var__var__var__12__x1__1433__1439__1549__1555__1561,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__13__x2__1434__1440__1550__1556__1562] :
( t(Vvar__var__var__var__var__13__x2__1434__1440__1550__1556__1562,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__12__x1__1433__1439__1549__1555__1561),Vvar__var__var__var__var__13__x2__1434__1440__1550__1556__1562))
=> ! [Vvar__var__var__var__var__15__y1__1435__1441__1551__1557__1563] :
( t(Vvar__var__var__var__var__15__y1__1435__1441__1551__1557__1563,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__16__y2__1436__1442__1552__1558__1564] :
( t(Vvar__var__var__var__var__16__y2__1436__1442__1552__1558__1564,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__15__y1__1435__1441__1551__1557__1563),Vvar__var__var__var__var__16__y2__1436__1442__1552__1558__1564))
=> p(happ(happ(Vvar__7__req__1366,happ(happ(Vvar__4__rtimes__1353,Vvar__var__var__var__var__12__x1__1433__1439__1549__1555__1561),Vvar__var__var__var__var__15__y1__1435__1441__1551__1557__1563)),happ(happ(Vvar__4__rtimes__1353,Vvar__var__var__var__var__13__x2__1434__1440__1550__1556__1562),Vvar__var__var__var__var__16__y2__1436__1442__1552__1558__1564))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__1446__1449__1567__1570__1573] :
( t(Vvar__var__var__var__var__13__x1__1446__1449__1567__1570__1573,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__14__x2__1447__1450__1568__1571__1574] :
( t(Vvar__var__var__var__var__14__x2__1447__1450__1568__1571__1574,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__13__x1__1446__1449__1567__1570__1573),Vvar__var__var__var__var__14__x2__1447__1450__1568__1571__1574))
=> p(happ(happ(Vvar__7__req__1366,happ(Vvar__6__ropp__1363,Vvar__var__var__var__var__13__x1__1446__1449__1567__1570__1573)),happ(Vvar__6__ropp__1363,Vvar__var__var__var__var__14__x2__1447__1450__1568__1571__1574))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__1453__1459__1576__1582__1588] :
( t(Vvar__var__var__var__var__14__x1__1453__1459__1576__1582__1588,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__15__x2__1454__1460__1577__1583__1589] :
( t(Vvar__var__var__var__var__15__x2__1454__1460__1577__1583__1589,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__14__x1__1453__1459__1576__1582__1588),Vvar__var__var__var__var__15__x2__1454__1460__1577__1583__1589))
=> ! [Vvar__var__var__var__var__17__y1__1455__1461__1578__1584__1590] :
( t(Vvar__var__var__var__var__17__y1__1455__1461__1578__1584__1590,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__18__y2__1456__1462__1579__1585__1591] :
( t(Vvar__var__var__var__var__18__y2__1456__1462__1579__1585__1591,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__17__y1__1455__1461__1578__1584__1590),Vvar__var__var__var__var__18__y2__1456__1462__1579__1585__1591))
=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__var__14__x1__1453__1459__1576__1582__1588),Vvar__var__var__var__var__17__y1__1455__1461__1578__1584__1590))
<=> p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__var__15__x2__1454__1460__1577__1583__1589),Vvar__var__var__var__var__18__y2__1456__1462__1579__1585__1591)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__1466__1472__1594__1600__1606] :
( t(Vvar__var__var__var__var__15__x1__1466__1472__1594__1600__1606,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__16__x2__1467__1473__1595__1601__1607] :
( t(Vvar__var__var__var__var__16__x2__1467__1473__1595__1601__1607,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__15__x1__1466__1472__1594__1600__1606),Vvar__var__var__var__var__16__x2__1467__1473__1595__1601__1607))
=> ! [Vvar__var__var__var__var__18__y1__1468__1474__1596__1602__1608] :
( t(Vvar__var__var__var__var__18__y1__1468__1474__1596__1602__1608,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__19__y2__1469__1475__1597__1603__1609] :
( t(Vvar__var__var__var__var__19__y2__1469__1475__1597__1603__1609,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__18__y1__1468__1474__1596__1602__1608),Vvar__var__var__var__var__19__y2__1469__1475__1597__1603__1609))
=> ( p(happ(happ(Vvar__9__rlt__1376,Vvar__var__var__var__var__15__x1__1466__1472__1594__1600__1606),Vvar__var__var__var__var__18__y1__1468__1474__1596__1602__1608))
<=> p(happ(happ(Vvar__9__rlt__1376,Vvar__var__var__var__var__16__x2__1467__1473__1595__1601__1607),Vvar__var__var__var__var__19__y2__1469__1475__1597__1603__1609)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__1345,Vvar__1__rO__1346,Vvar__2__rI__1347,Vvar__3__rplus__1348,Vvar__4__rtimes__1353,Vvar__5__rminus__1358,Vvar__6__ropp__1363,Vvar__7__req__1366)
& ! [Vvar__var__var__var__17__n__1480__1481__1612__1613] :
( t(Vvar__var__var__var__17__n__1480__1481__1612__1613,Vvar__0__R__1345)
=> p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__17__n__1480__1481__1612__1613),Vvar__var__var__var__17__n__1480__1481__1612__1613)) )
& ! [Vvar__var__var__var__var__18__n__1483__1487__1614__1618__1622] :
( t(Vvar__var__var__var__var__18__n__1483__1487__1614__1618__1622,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__19__m__1484__1488__1615__1619__1623] :
( t(Vvar__var__var__var__var__19__m__1484__1488__1615__1619__1623,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__var__18__n__1483__1487__1614__1618__1622),Vvar__var__var__var__var__19__m__1484__1488__1615__1619__1623))
=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__var__19__m__1484__1488__1615__1619__1623),Vvar__var__var__var__var__18__n__1483__1487__1614__1618__1622))
=> p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__18__n__1483__1487__1614__1618__1622),Vvar__var__var__var__var__19__m__1484__1488__1615__1619__1623)) ) ) ) )
& ! [Vvar__var__var__var__19__n__1492__1497__1626__1631] :
( t(Vvar__var__var__var__19__n__1492__1497__1626__1631,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__20__m__1493__1498__1627__1632] :
( t(Vvar__var__var__var__20__m__1493__1498__1627__1632,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__21__p__1494__1499__1628__1633] :
( t(Vvar__var__var__var__21__p__1494__1499__1628__1633,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__19__n__1492__1497__1626__1631),Vvar__var__var__var__20__m__1493__1498__1627__1632))
=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__20__m__1493__1498__1627__1632),Vvar__var__var__var__21__p__1494__1499__1628__1633))
=> p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__19__n__1492__1497__1626__1631),Vvar__var__var__var__21__p__1494__1499__1628__1633)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__1503__1505__1636__1638__1640__1642] :
( t(Vvar__var__var__var__var__var__20__n__1503__1505__1636__1638__1640__1642,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__var__21__m__1504__1506__1637__1639__1641__1643] :
( t(Vvar__var__var__var__var__var__21__m__1504__1506__1637__1639__1641__1643,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__9__rlt__1376,Vvar__var__var__var__var__var__20__n__1503__1505__1636__1638__1640__1642),Vvar__var__var__var__var__var__21__m__1504__1506__1637__1639__1641__1643))
<=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__var__var__20__n__1503__1505__1636__1638__1640__1642),Vvar__var__var__var__var__var__21__m__1504__1506__1637__1639__1641__1643))
& ~ p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__var__20__n__1503__1505__1636__1638__1640__1642),Vvar__var__var__var__var__var__21__m__1504__1506__1637__1639__1641__1643)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__1508__1510__1644__1646__1648] :
( t(Vvar__var__var__var__var__21__n__1508__1510__1644__1646__1648,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__22__m__1509__1511__1645__1647__1649] :
( t(Vvar__var__var__var__var__22__m__1509__1511__1645__1647__1649,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__9__rlt__1376,Vvar__var__var__var__var__21__n__1508__1510__1644__1646__1648),Vvar__var__var__var__var__22__m__1509__1511__1645__1647__1649))
| p(happ(happ(Vvar__7__req__1366,Vvar__var__var__var__var__21__n__1508__1510__1644__1646__1648),Vvar__var__var__var__var__22__m__1509__1511__1645__1647__1649))
| p(happ(happ(Vvar__9__rlt__1376,Vvar__var__var__var__var__22__m__1509__1511__1645__1647__1649),Vvar__var__var__var__var__21__n__1508__1510__1644__1646__1648)) ) ) )
& ! [Vvar__var__var__var__var__22__n__1513__1517__1650__1654__1658] :
( t(Vvar__var__var__var__var__22__n__1513__1517__1650__1654__1658,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__23__m__1514__1518__1651__1655__1659] :
( t(Vvar__var__var__var__var__23__m__1514__1518__1651__1655__1659,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__24__p__1515__1519__1652__1656__1660] :
( t(Vvar__var__var__var__var__24__p__1515__1519__1652__1656__1660,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__8__rle__1371,Vvar__var__var__var__var__22__n__1513__1517__1650__1654__1658),Vvar__var__var__var__var__23__m__1514__1518__1651__1655__1659))
=> p(happ(happ(Vvar__8__rle__1371,happ(happ(Vvar__3__rplus__1348,Vvar__var__var__var__var__24__p__1515__1519__1652__1656__1660),Vvar__var__var__var__var__22__n__1513__1517__1650__1654__1658)),happ(happ(Vvar__3__rplus__1348,Vvar__var__var__var__var__24__p__1515__1519__1652__1656__1660),Vvar__var__var__var__var__23__m__1514__1518__1651__1655__1659))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__1522__1526__1662__1666__1670__1674] :
( t(Vvar__var__var__var__var__var__23__n__1522__1526__1662__1666__1670__1674,Vvar__0__R__1345)
=> ! [Vvar__var__var__var__var__var__24__m__1523__1527__1663__1667__1671__1675] :
( t(Vvar__var__var__var__var__var__24__m__1523__1527__1663__1667__1671__1675,Vvar__0__R__1345)
=> ( p(happ(happ(Vvar__9__rlt__1376,Vvar__1__rO__1346),Vvar__var__var__var__var__var__23__n__1522__1526__1662__1666__1670__1674))
=> ( p(happ(happ(Vvar__9__rlt__1376,Vvar__1__rO__1346),Vvar__var__var__var__var__var__24__m__1523__1527__1663__1667__1671__1675))
=> p(happ(happ(Vvar__9__rlt__1376,Vvar__1__rO__1346),happ(happ(Vvar__4__rtimes__1353,Vvar__var__var__var__var__var__23__n__1522__1526__1662__1666__1670__1674),Vvar__var__var__var__var__var__24__m__1523__1527__1663__1667__1671__1675))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__1366,Vvar__1__rO__1346),Vvar__2__rI__1347))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__545,VX546] :
( cType___24t(Vvar__0__T__545)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__545,VX546)
=> ? [Vvar__1__Flhs__548] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__545,Vvar__1__Flhs__548)
& ? [Vvar__2__Fop__549] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__549)
& ? [Vvar__3__Frhs__550] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__545,Vvar__3__Frhs__550)
& VX546 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__545,Vvar__1__Flhs__548,Vvar__2__Fop__549,Vvar__3__Frhs__550) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX15708] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX15708)
=> ( VX15708 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX15708 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX15708 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX15708 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX26081] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX26081)
=> ( VX26081 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX26081 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX26081 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX26081 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX26081 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX26081 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176] :
( cType___24t(Vvar__0__R__10107)
=> ( t(Vvar__1__rO__10108,Vvar__0__R__10107)
=> ( t(Vvar__2__rI__10109,Vvar__0__R__10107)
=> ( c_24__type__10640___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__3__rplus__10110)
=> ( c_24__type__10986___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__4__rtimes__10115)
=> ( c_24__type__11332___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__5__rminus__10120)
=> ( c_24__type__11655___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__6__ropp__10125)
=> ( c_24__type__12001___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__7__req__10128)
=> ( c_24__type__12347___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__8__rle__10133)
=> ( cType___24t(Vvar__9__C__10138)
=> ( t(Vvar__10__cO__10139,Vvar__9__C__10138)
=> ( t(Vvar__11__cI__10140,Vvar__9__C__10138)
=> ( c_24__type__12693___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__12__cplus__10141)
=> ( c_24__type__13039___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__13__ctimes__10146)
=> ( c_24__type__13385___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__14__cminus__10151)
=> ( c_24__type__13708___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__15__copp__10156)
=> ( c_24__type__14054___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__16__ceqb__10159)
=> ( c_24__type__14400___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__17__cleb__10164)
=> ( c_24__type__14723___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__18__phi__10169)
=> ( cType___24t(Vvar__19__E__10172)
=> ( c_24__type__15046___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__20__pow__phi__10173)
=> ( c_24__type__15392___24t(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176,Vvar__21__rpow__10176)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__8__rle__10133,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__17__cleb__10164,Vvar__18__phi__10169,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__10107,Vvar__1__rO__10108,Vvar__2__rI__10109,Vvar__3__rplus__10110,Vvar__4__rtimes__10115,Vvar__5__rminus__10120,Vvar__6__ropp__10125,Vvar__7__req__10128,Vvar__9__C__10138,Vvar__10__cO__10139,Vvar__11__cI__10140,Vvar__12__cplus__10141,Vvar__13__ctimes__10146,Vvar__14__cminus__10151,Vvar__15__copp__10156,Vvar__16__ceqb__10159,Vvar__18__phi__10169)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__10107,Vvar__2__rI__10109,Vvar__4__rtimes__10115,Vvar__7__req__10128,Vvar__19__E__10172,Vvar__20__pow__phi__10173,Vvar__21__rpow__10176)
& ! [Vvar__var__var__var__var__var__24__x__10259__10262__10272__10275__10278__10281] :
( t(Vvar__var__var__var__var__var__24__x__10259__10262__10272__10275__10278__10281,Vvar__9__C__10138)
=> ! [Vvar__var__var__var__var__var__25__y__10260__10263__10273__10276__10279__10282] :
( t(Vvar__var__var__var__var__var__25__y__10260__10263__10273__10276__10279__10282,Vvar__9__C__10138)
=> ( happ(happ(Vvar__16__ceqb__10159,Vvar__var__var__var__var__var__24__x__10259__10262__10272__10275__10278__10281),Vvar__var__var__var__var__var__25__y__10260__10263__10273__10276__10279__10282) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__10128,happ(Vvar__18__phi__10169,Vvar__var__var__var__var__var__24__x__10259__10262__10272__10275__10278__10281)),happ(Vvar__18__phi__10169,Vvar__var__var__var__var__var__25__y__10260__10263__10273__10276__10279__10282))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__10266__10269__10284__10287__10290__10293] :
( t(Vvar__var__var__var__var__var__25__x__10266__10269__10284__10287__10290__10293,Vvar__9__C__10138)
=> ! [Vvar__var__var__var__var__var__26__y__10267__10270__10285__10288__10291__10294] :
( t(Vvar__var__var__var__var__var__26__y__10267__10270__10285__10288__10291__10294,Vvar__9__C__10138)
=> ( happ(happ(Vvar__17__cleb__10164,Vvar__var__var__var__var__var__25__x__10266__10269__10284__10287__10290__10293),Vvar__var__var__var__var__var__26__y__10267__10270__10285__10288__10291__10294) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__10133,happ(Vvar__18__phi__10169,Vvar__var__var__var__var__var__25__x__10266__10269__10284__10287__10290__10293)),happ(Vvar__18__phi__10169,Vvar__var__var__var__var__var__26__y__10267__10270__10285__10288__10291__10294))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,VX22595] :
( cType___24t(Vvar__0__TA__22591)
=> ( cType___24t(Vvar__1__TX__22592)
=> ( cType___24t(Vvar__2__AA__22593)
=> ( cType___24t(Vvar__3__AF__22594)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,VX22595)
=> ( VX22595 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594)
| VX22595 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594)
| ? [Vvar__4___24Anonymous__22608] :
( t(Vvar__4___24Anonymous__22608,Vvar__1__TX__22592)
& VX22595 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22608) )
| ? [Vvar__4___24Anonymous__22613] :
( t(Vvar__4___24Anonymous__22613,Vvar__0__TA__22591)
& ? [Vvar__5___24Anonymous__22614] :
( t(Vvar__5___24Anonymous__22614,Vvar__2__AA__22593)
& VX22595 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22613,Vvar__5___24Anonymous__22614) ) )
| ? [Vvar__4___24Anonymous__22619] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22619)
& ? [Vvar__5___24Anonymous__22620] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__5___24Anonymous__22620)
& VX22595 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22619,Vvar__5___24Anonymous__22620) ) )
| ? [Vvar__4___24Anonymous__22625] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22625)
& ? [Vvar__5___24Anonymous__22626] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__5___24Anonymous__22626)
& VX22595 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22625,Vvar__5___24Anonymous__22626) ) )
| ? [Vvar__4___24Anonymous__22631] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22631)
& VX22595 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22631) )
| ? [Vvar__4___24Anonymous__22636] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22636)
& ? [Vvar__5___24Anonymous__22637] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__22594,Vvar__5___24Anonymous__22637)
& ? [Vvar__6___24Anonymous__22638] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__6___24Anonymous__22638)
& VX22595 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22591,Vvar__1__TX__22592,Vvar__2__AA__22593,Vvar__3__AF__22594,Vvar__4___24Anonymous__22636,Vvar__5___24Anonymous__22637,Vvar__6___24Anonymous__22638) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__29282] :
( cProp___24t(Vvar__0___24Anonymous__29282)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__29282)
=> ( ? [Vvar__0__S__29284] :
( cType___24t(Vvar__0__S__29284)
& ? [Vvar__1__x__29285] :
( t(Vvar__1__x__29285,Vvar__0__S__29284)
& ? [Vvar__2__y__29286] :
( t(Vvar__2__y__29286,Vvar__0__S__29284)
& Vvar__0___24Anonymous__29282 = c_24__prop__29306___24a4(Vvar__0___24Anonymous__29282,Vvar__0__S__29284,Vvar__1__x__29285,Vvar__2__y__29286) ) ) )
| ? [Vvar__0__x__29287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__29287)
& ? [Vvar__1__y__29288] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__29288)
& Vvar__0___24Anonymous__29282 = c_24__prop__29307___24a3(Vvar__0___24Anonymous__29282,Vvar__0__x__29287,Vvar__1__y__29288) ) )
| ? [Vvar__0__x__29289] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__29289)
& ? [Vvar__1__s__29290] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__29290)
& Vvar__0___24Anonymous__29282 = c_24__prop__29308___24a3(Vvar__0___24Anonymous__29282,Vvar__0__x__29289,Vvar__1__s__29290) ) )
| Vvar__0___24Anonymous__29282 = c_24True
| Vvar__0___24Anonymous__29282 = c_24False
| ? [Vvar__0__P__29291] :
( cProp___24t(Vvar__0__P__29291)
& ? [Vvar__1__Q__29292] :
( cProp___24t(Vvar__1__Q__29292)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29291)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29292)
& Vvar__0___24Anonymous__29282 = c_24__prop__29309___24a3(Vvar__0___24Anonymous__29282,Vvar__0__P__29291,Vvar__1__Q__29292) ) )
| ? [Vvar__0__P__29295] :
( cProp___24t(Vvar__0__P__29295)
& ? [Vvar__1__Q__29296] :
( cProp___24t(Vvar__1__Q__29296)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29295)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29296)
& Vvar__0___24Anonymous__29282 = c_24__prop__29310___24a3(Vvar__0___24Anonymous__29282,Vvar__0__P__29295,Vvar__1__Q__29296) ) )
| ? [Vvar__0__P__29299] :
( cProp___24t(Vvar__0__P__29299)
& ? [Vvar__1__Q__29300] :
( cProp___24t(Vvar__1__Q__29300)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29299)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29300)
& Vvar__0___24Anonymous__29282 = c_24__prop__29311___24a3(Vvar__0___24Anonymous__29282,Vvar__0__P__29299,Vvar__1__Q__29300) ) )
| ? [Vvar__0__P__29304] :
( cProp___24t(Vvar__0__P__29304)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29304)
& Vvar__0___24Anonymous__29282 = c_24__prop__29312___24a2(Vvar__0___24Anonymous__29282,Vvar__0__P__29304) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__7964,VX7965] :
( cType___24t(Vvar__0__C__7964)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,VX7965)
=> ( VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7964)
| VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7964)
| ? [Vvar__1___24Anonymous__7969] :
( t(Vvar__1___24Anonymous__7969,Vvar__0__C__7964)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7964,Vvar__1___24Anonymous__7969) )
| ? [Vvar__1___24Anonymous__7971] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7971)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7964,Vvar__1___24Anonymous__7971) )
| ? [Vvar__1___24Anonymous__7973] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7973)
& ? [Vvar__2___24Anonymous__7974] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__2___24Anonymous__7974)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7964,Vvar__1___24Anonymous__7973,Vvar__2___24Anonymous__7974) ) )
| ? [Vvar__1___24Anonymous__7976] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7976)
& ? [Vvar__2___24Anonymous__7977] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__2___24Anonymous__7977)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7964,Vvar__1___24Anonymous__7976,Vvar__2___24Anonymous__7977) ) )
| ? [Vvar__1___24Anonymous__7979] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7979)
& ? [Vvar__2___24Anonymous__7980] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__2___24Anonymous__7980)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7964,Vvar__1___24Anonymous__7979,Vvar__2___24Anonymous__7980) ) )
| ? [Vvar__1___24Anonymous__7982] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7982)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7964,Vvar__1___24Anonymous__7982) )
| ? [Vvar__1___24Anonymous__7984] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7984)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7964,Vvar__1___24Anonymous__7984) )
| ? [Vvar__1___24Anonymous__7986] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7986)
& ? [Vvar__2___24Anonymous__7987] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__2___24Anonymous__7987)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7964,Vvar__1___24Anonymous__7986,Vvar__2___24Anonymous__7987) ) )
| ? [Vvar__1___24Anonymous__7989] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7964,Vvar__1___24Anonymous__7989)
& ? [Vvar__2___24Anonymous__7990] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7990)
& VX7965 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7964,Vvar__1___24Anonymous__7989,Vvar__2___24Anonymous__7990) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361] :
( cType___24t(Vvar__0__R__5332)
=> ( t(Vvar__1__rO__5333,Vvar__0__R__5332)
=> ( t(Vvar__2__rI__5334,Vvar__0__R__5332)
=> ( c_24__type__5526___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__3__radd__5335)
=> ( c_24__type__5619___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__4__rmul__5340)
=> ( c_24__type__5712___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__5__rsub__5345)
=> ( c_24__type__5794___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__6__ropp__5350)
=> ( c_24__type__5887___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__7__rdiv__5353)
=> ( c_24__type__5969___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__8__rinv__5358)
=> ( c_24__type__6062___24t(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361,Vvar__9__req__5361)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__7__rdiv__5353,Vvar__8__rinv__5358,Vvar__9__req__5361)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__5332,Vvar__1__rO__5333,Vvar__2__rI__5334,Vvar__3__radd__5335,Vvar__4__rmul__5340,Vvar__5__rsub__5345,Vvar__6__ropp__5350,Vvar__9__req__5361)
& ~ p(happ(happ(Vvar__9__req__5361,Vvar__2__rI__5334),Vvar__1__rO__5333))
& ! [Vvar__var__var__var__var__var__var__12__p__5404__5406__5413__5415__5417__5419__5421] :
( t(Vvar__var__var__var__var__var__var__12__p__5404__5406__5413__5415__5417__5419__5421,Vvar__0__R__5332)
=> ! [Vvar__var__var__var__var__var__var__13__q__5405__5407__5414__5416__5418__5420__5422] :
( t(Vvar__var__var__var__var__var__var__13__q__5405__5407__5414__5416__5418__5420__5422,Vvar__0__R__5332)
=> p(happ(happ(Vvar__9__req__5361,happ(happ(Vvar__7__rdiv__5353,Vvar__var__var__var__var__var__var__12__p__5404__5406__5413__5415__5417__5419__5421),Vvar__var__var__var__var__var__var__13__q__5405__5407__5414__5416__5418__5420__5422)),happ(happ(Vvar__4__rmul__5340,Vvar__var__var__var__var__var__var__12__p__5404__5406__5413__5415__5417__5419__5421),happ(Vvar__8__rinv__5358,Vvar__var__var__var__var__var__var__13__q__5405__5407__5414__5416__5418__5420__5422)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__5409__5411__5423__5425__5427__5429__5431__5433] :
( t(Vvar__var__var__var__var__var__var__var__13__p__5409__5411__5423__5425__5427__5429__5431__5433,Vvar__0__R__5332)
=> ( ~ p(happ(happ(Vvar__9__req__5361,Vvar__var__var__var__var__var__var__var__13__p__5409__5411__5423__5425__5427__5429__5431__5433),Vvar__1__rO__5333))
=> p(happ(happ(Vvar__9__req__5361,happ(happ(Vvar__4__rmul__5340,happ(Vvar__8__rinv__5358,Vvar__var__var__var__var__var__var__var__13__p__5409__5411__5423__5425__5427__5429__5431__5433)),Vvar__var__var__var__var__var__var__var__13__p__5409__5411__5423__5425__5427__5429__5431__5433)),Vvar__2__rI__5334)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784] :
( cType___24t(Vvar__0__R__26755)
=> ( t(Vvar__1__rO__26756,Vvar__0__R__26755)
=> ( t(Vvar__2__rI__26757,Vvar__0__R__26755)
=> ( c_24__type__26949___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__3__radd__26758)
=> ( c_24__type__27042___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__4__rmul__26763)
=> ( c_24__type__27135___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__5__rsub__26768)
=> ( c_24__type__27217___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__6__ropp__26773)
=> ( c_24__type__27310___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__7__rdiv__26776)
=> ( c_24__type__27392___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__8__rinv__26781)
=> ( c_24__type__27485___24t(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784,Vvar__9__req__26784)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__7__rdiv__26776,Vvar__8__rinv__26781,Vvar__9__req__26784)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__26755,Vvar__1__rO__26756,Vvar__2__rI__26757,Vvar__3__radd__26758,Vvar__4__rmul__26763,Vvar__5__rsub__26768,Vvar__6__ropp__26773,Vvar__9__req__26784)
& ~ p(happ(happ(Vvar__9__req__26784,Vvar__2__rI__26757),Vvar__1__rO__26756))
& ! [Vvar__var__var__var__var__var__var__12__p__26827__26829__26836__26838__26840__26842__26844] :
( t(Vvar__var__var__var__var__var__var__12__p__26827__26829__26836__26838__26840__26842__26844,Vvar__0__R__26755)
=> ! [Vvar__var__var__var__var__var__var__13__q__26828__26830__26837__26839__26841__26843__26845] :
( t(Vvar__var__var__var__var__var__var__13__q__26828__26830__26837__26839__26841__26843__26845,Vvar__0__R__26755)
=> p(happ(happ(Vvar__9__req__26784,happ(happ(Vvar__7__rdiv__26776,Vvar__var__var__var__var__var__var__12__p__26827__26829__26836__26838__26840__26842__26844),Vvar__var__var__var__var__var__var__13__q__26828__26830__26837__26839__26841__26843__26845)),happ(happ(Vvar__4__rmul__26763,Vvar__var__var__var__var__var__var__12__p__26827__26829__26836__26838__26840__26842__26844),happ(Vvar__8__rinv__26781,Vvar__var__var__var__var__var__var__13__q__26828__26830__26837__26839__26841__26843__26845)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__26832__26834__26846__26848__26850__26852__26854__26856] :
( t(Vvar__var__var__var__var__var__var__var__13__p__26832__26834__26846__26848__26850__26852__26854__26856,Vvar__0__R__26755)
=> ( ~ p(happ(happ(Vvar__9__req__26784,Vvar__var__var__var__var__var__var__var__13__p__26832__26834__26846__26848__26850__26852__26854__26856),Vvar__1__rO__26756))
=> p(happ(happ(Vvar__9__req__26784,happ(happ(Vvar__4__rmul__26763,happ(Vvar__8__rinv__26781,Vvar__var__var__var__var__var__var__var__13__p__26832__26834__26846__26848__26850__26852__26854__26856)),Vvar__var__var__var__var__var__var__var__13__p__26832__26834__26846__26848__26850__26852__26854__26856)),Vvar__2__rI__26757)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__8576,VX8577] :
( cType___24t(Vvar__0__C__8576)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__8576,VX8577)
=> ? [Vvar__1__num__8579] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8576,Vvar__1__num__8579)
& ? [Vvar__2__denum__8580] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8576,Vvar__2__denum__8580)
& ? [Vvar__3__condition__8581] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__8576),Vvar__3__condition__8581)
& VX8577 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8576,Vvar__1__num__8579,Vvar__2__denum__8580,Vvar__3__condition__8581) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512] :
( cType___24t(Vvar__0__R__27491)
=> ( t(Vvar__1__rO__27492,Vvar__0__R__27491)
=> ( t(Vvar__2__rI__27493,Vvar__0__R__27491)
=> ( c_24__type__27639___24t(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512,Vvar__3__radd__27494)
=> ( c_24__type__27702___24t(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512,Vvar__4__rmul__27499)
=> ( c_24__type__27765___24t(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512,Vvar__5__rdiv__27504)
=> ( c_24__type__27819___24t(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512,Vvar__6__rinv__27509)
=> ( c_24__type__27882___24t(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512,Vvar__7__req__27512)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__5__rdiv__27504,Vvar__6__rinv__27509,Vvar__7__req__27512)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__27491,Vvar__1__rO__27492,Vvar__2__rI__27493,Vvar__3__radd__27494,Vvar__4__rmul__27499,Vvar__7__req__27512)
& ~ p(happ(happ(Vvar__7__req__27512,Vvar__2__rI__27493),Vvar__1__rO__27492))
& ! [Vvar__var__var__var__var__var__var__10__p__27547__27549__27556__27558__27560__27562__27564] :
( t(Vvar__var__var__var__var__var__var__10__p__27547__27549__27556__27558__27560__27562__27564,Vvar__0__R__27491)
=> ! [Vvar__var__var__var__var__var__var__11__q__27548__27550__27557__27559__27561__27563__27565] :
( t(Vvar__var__var__var__var__var__var__11__q__27548__27550__27557__27559__27561__27563__27565,Vvar__0__R__27491)
=> p(happ(happ(Vvar__7__req__27512,happ(happ(Vvar__5__rdiv__27504,Vvar__var__var__var__var__var__var__10__p__27547__27549__27556__27558__27560__27562__27564),Vvar__var__var__var__var__var__var__11__q__27548__27550__27557__27559__27561__27563__27565)),happ(happ(Vvar__4__rmul__27499,Vvar__var__var__var__var__var__var__10__p__27547__27549__27556__27558__27560__27562__27564),happ(Vvar__6__rinv__27509,Vvar__var__var__var__var__var__var__11__q__27548__27550__27557__27559__27561__27563__27565)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__27552__27554__27566__27568__27570__27572__27574__27576] :
( t(Vvar__var__var__var__var__var__var__var__11__p__27552__27554__27566__27568__27570__27572__27574__27576,Vvar__0__R__27491)
=> ( ~ p(happ(happ(Vvar__7__req__27512,Vvar__var__var__var__var__var__var__var__11__p__27552__27554__27566__27568__27570__27572__27574__27576),Vvar__1__rO__27492))
=> p(happ(happ(Vvar__7__req__27512,happ(happ(Vvar__4__rmul__27499,happ(Vvar__6__rinv__27509,Vvar__var__var__var__var__var__var__var__11__p__27552__27554__27566__27568__27570__27572__27574__27576)),Vvar__var__var__var__var__var__var__var__11__p__27552__27554__27566__27568__27570__27572__27574__27576)),Vvar__2__rI__27493)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX17083] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX17083)
=> ( VX17083 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__17084] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17084)
& ? [Vvar__1___24Anonymous__17085] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__17085)
& VX17083 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__17084,Vvar__1___24Anonymous__17085) ) )
| ? [Vvar__0___24Anonymous__17086] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__17086)
& ? [Vvar__1___24Anonymous__17087] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__17087)
& VX17083 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__17086,Vvar__1___24Anonymous__17087) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__17185,VX17186] :
( cType___24t(Vvar__0__C__17185)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,VX17186)
=> ( VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__17185)
| VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__17185)
| ? [Vvar__1___24Anonymous__17190] :
( t(Vvar__1___24Anonymous__17190,Vvar__0__C__17185)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__17185,Vvar__1___24Anonymous__17190) )
| ? [Vvar__1___24Anonymous__17192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17192)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__17185,Vvar__1___24Anonymous__17192) )
| ? [Vvar__1___24Anonymous__17194] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__1___24Anonymous__17194)
& ? [Vvar__2___24Anonymous__17195] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__2___24Anonymous__17195)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__17185,Vvar__1___24Anonymous__17194,Vvar__2___24Anonymous__17195) ) )
| ? [Vvar__1___24Anonymous__17197] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__1___24Anonymous__17197)
& ? [Vvar__2___24Anonymous__17198] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__2___24Anonymous__17198)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__17185,Vvar__1___24Anonymous__17197,Vvar__2___24Anonymous__17198) ) )
| ? [Vvar__1___24Anonymous__17200] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__1___24Anonymous__17200)
& ? [Vvar__2___24Anonymous__17201] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__2___24Anonymous__17201)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__17185,Vvar__1___24Anonymous__17200,Vvar__2___24Anonymous__17201) ) )
| ? [Vvar__1___24Anonymous__17203] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__1___24Anonymous__17203)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__17185,Vvar__1___24Anonymous__17203) )
| ? [Vvar__1___24Anonymous__17205] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__17185,Vvar__1___24Anonymous__17205)
& ? [Vvar__2___24Anonymous__17206] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__17206)
& VX17186 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__17185,Vvar__1___24Anonymous__17205,Vvar__2___24Anonymous__17206) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__16871,VX16872] :
( cType___24t(Vvar__0__C__16871)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__16871,VX16872)
=> ( ? [Vvar__1___24Anonymous__16874] :
( t(Vvar__1___24Anonymous__16874,Vvar__0__C__16871)
& VX16872 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__16871,Vvar__1___24Anonymous__16874) )
| ? [Vvar__1___24Anonymous__16876] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__16876)
& ? [Vvar__2___24Anonymous__16877] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__16871,Vvar__2___24Anonymous__16877)
& VX16872 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__16871,Vvar__1___24Anonymous__16876,Vvar__2___24Anonymous__16877) ) )
| ? [Vvar__1___24Anonymous__16879] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__16871,Vvar__1___24Anonymous__16879)
& ? [Vvar__2___24Anonymous__16880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__16880)
& ? [Vvar__3___24Anonymous__16881] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__16871,Vvar__3___24Anonymous__16881)
& VX16872 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__16871,Vvar__1___24Anonymous__16879,Vvar__2___24Anonymous__16880,Vvar__3___24Anonymous__16881) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536] :
( cType___24t(Vvar__0__R__2515)
=> ( t(Vvar__1__rO__2516,Vvar__0__R__2515)
=> ( t(Vvar__2__rI__2517,Vvar__0__R__2515)
=> ( c_24__type__2764___24t(Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536,Vvar__3__radd__2518)
=> ( c_24__type__2827___24t(Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536,Vvar__4__rmul__2523)
=> ( c_24__type__2890___24t(Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536,Vvar__5__rsub__2528)
=> ( c_24__type__2944___24t(Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536,Vvar__6__ropp__2533)
=> ( c_24__type__3007___24t(Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536,Vvar__7__req__2536)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__2515,Vvar__1__rO__2516,Vvar__2__rI__2517,Vvar__3__radd__2518,Vvar__4__rmul__2523,Vvar__5__rsub__2528,Vvar__6__ropp__2533,Vvar__7__req__2536)
=> ( ! [Vvar__var__var__var__var__var__8__x__2569__2570__2623__2624__2625__2626] :
( t(Vvar__var__var__var__var__var__8__x__2569__2570__2623__2624__2625__2626,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__3__radd__2518,Vvar__1__rO__2516),Vvar__var__var__var__var__var__8__x__2569__2570__2623__2624__2625__2626)),Vvar__var__var__var__var__var__8__x__2569__2570__2623__2624__2625__2626)) )
& ! [Vvar__var__var__var__var__9__x__2572__2574__2627__2629__2631] :
( t(Vvar__var__var__var__var__9__x__2572__2574__2627__2629__2631,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__10__y__2573__2575__2628__2630__2632] :
( t(Vvar__var__var__var__var__10__y__2573__2575__2628__2630__2632,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__9__x__2572__2574__2627__2629__2631),Vvar__var__var__var__var__10__y__2573__2575__2628__2630__2632)),happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__10__y__2573__2575__2628__2630__2632),Vvar__var__var__var__var__9__x__2572__2574__2627__2629__2631))) ) )
& ! [Vvar__var__var__var__var__10__x__2577__2580__2633__2636__2639] :
( t(Vvar__var__var__var__var__10__x__2577__2580__2633__2636__2639,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__11__y__2578__2581__2634__2637__2640] :
( t(Vvar__var__var__var__var__11__y__2578__2581__2634__2637__2640,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__12__z__2579__2582__2635__2638__2641] :
( t(Vvar__var__var__var__var__12__z__2579__2582__2635__2638__2641,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__10__x__2577__2580__2633__2636__2639),happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__11__y__2578__2581__2634__2637__2640),Vvar__var__var__var__var__12__z__2579__2582__2635__2638__2641))),happ(happ(Vvar__3__radd__2518,happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__10__x__2577__2580__2633__2636__2639),Vvar__var__var__var__var__11__y__2578__2581__2634__2637__2640)),Vvar__var__var__var__var__12__z__2579__2582__2635__2638__2641))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__2584__2585__2642__2643__2644__2645] :
( t(Vvar__var__var__var__var__var__11__x__2584__2585__2642__2643__2644__2645,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__4__rmul__2523,Vvar__2__rI__2517),Vvar__var__var__var__var__var__11__x__2584__2585__2642__2643__2644__2645)),Vvar__var__var__var__var__var__11__x__2584__2585__2642__2643__2644__2645)) )
& ! [Vvar__var__var__var__var__var__12__x__2587__2588__2646__2647__2648__2649] :
( t(Vvar__var__var__var__var__var__12__x__2587__2588__2646__2647__2648__2649,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__4__rmul__2523,Vvar__1__rO__2516),Vvar__var__var__var__var__var__12__x__2587__2588__2646__2647__2648__2649)),Vvar__1__rO__2516)) )
& ! [Vvar__var__var__var__var__13__x__2590__2592__2650__2652__2654] :
( t(Vvar__var__var__var__var__13__x__2590__2592__2650__2652__2654,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__14__y__2591__2593__2651__2653__2655] :
( t(Vvar__var__var__var__var__14__y__2591__2593__2651__2653__2655,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__13__x__2590__2592__2650__2652__2654),Vvar__var__var__var__var__14__y__2591__2593__2651__2653__2655)),happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__14__y__2591__2593__2651__2653__2655),Vvar__var__var__var__var__13__x__2590__2592__2650__2652__2654))) ) )
& ! [Vvar__var__var__var__var__14__x__2595__2598__2656__2659__2662] :
( t(Vvar__var__var__var__var__14__x__2595__2598__2656__2659__2662,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__15__y__2596__2599__2657__2660__2663] :
( t(Vvar__var__var__var__var__15__y__2596__2599__2657__2660__2663,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__16__z__2597__2600__2658__2661__2664] :
( t(Vvar__var__var__var__var__16__z__2597__2600__2658__2661__2664,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__14__x__2595__2598__2656__2659__2662),happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__15__y__2596__2599__2657__2660__2663),Vvar__var__var__var__var__16__z__2597__2600__2658__2661__2664))),happ(happ(Vvar__4__rmul__2523,happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__14__x__2595__2598__2656__2659__2662),Vvar__var__var__var__var__15__y__2596__2599__2657__2660__2663)),Vvar__var__var__var__var__16__z__2597__2600__2658__2661__2664))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__2602__2605__2665__2668__2671__2674] :
( t(Vvar__var__var__var__var__var__15__x__2602__2605__2665__2668__2671__2674,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__var__16__y__2603__2606__2666__2669__2672__2675] :
( t(Vvar__var__var__var__var__var__16__y__2603__2606__2666__2669__2672__2675,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__var__17__z__2604__2607__2667__2670__2673__2676] :
( t(Vvar__var__var__var__var__var__17__z__2604__2607__2667__2670__2673__2676,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__4__rmul__2523,happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__var__15__x__2602__2605__2665__2668__2671__2674),Vvar__var__var__var__var__var__16__y__2603__2606__2666__2669__2672__2675)),Vvar__var__var__var__var__var__17__z__2604__2607__2667__2670__2673__2676)),happ(happ(Vvar__3__radd__2518,happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__var__15__x__2602__2605__2665__2668__2671__2674),Vvar__var__var__var__var__var__17__z__2604__2607__2667__2670__2673__2676)),happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__var__16__y__2603__2606__2666__2669__2672__2675),Vvar__var__var__var__var__var__17__z__2604__2607__2667__2670__2673__2676)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__2609__2611__2677__2679__2681__2683] :
( t(Vvar__var__var__var__var__var__16__x__2609__2611__2677__2679__2681__2683,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__var__17__y__2610__2612__2678__2680__2682__2684] :
( t(Vvar__var__var__var__var__var__17__y__2610__2612__2678__2680__2682__2684,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(Vvar__6__ropp__2533,happ(happ(Vvar__4__rmul__2523,Vvar__var__var__var__var__var__16__x__2609__2611__2677__2679__2681__2683),Vvar__var__var__var__var__var__17__y__2610__2612__2678__2680__2682__2684))),happ(happ(Vvar__4__rmul__2523,happ(Vvar__6__ropp__2533,Vvar__var__var__var__var__var__16__x__2609__2611__2677__2679__2681__2683)),Vvar__var__var__var__var__var__17__y__2610__2612__2678__2680__2682__2684))) ) )
& ! [Vvar__var__var__var__var__var__17__x__2614__2616__2685__2687__2689__2691] :
( t(Vvar__var__var__var__var__var__17__x__2614__2616__2685__2687__2689__2691,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__var__18__y__2615__2617__2686__2688__2690__2692] :
( t(Vvar__var__var__var__var__var__18__y__2615__2617__2686__2688__2690__2692,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(Vvar__6__ropp__2533,happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__var__17__x__2614__2616__2685__2687__2689__2691),Vvar__var__var__var__var__var__18__y__2615__2617__2686__2688__2690__2692))),happ(happ(Vvar__3__radd__2518,happ(Vvar__6__ropp__2533,Vvar__var__var__var__var__var__17__x__2614__2616__2685__2687__2689__2691)),happ(Vvar__6__ropp__2533,Vvar__var__var__var__var__var__18__y__2615__2617__2686__2688__2690__2692)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__2619__2621__2693__2695__2697__2699__2701] :
( t(Vvar__var__var__var__var__var__var__18__x__2619__2621__2693__2695__2697__2699__2701,Vvar__0__R__2515)
=> ! [Vvar__var__var__var__var__var__var__19__y__2620__2622__2694__2696__2698__2700__2702] :
( t(Vvar__var__var__var__var__var__var__19__y__2620__2622__2694__2696__2698__2700__2702,Vvar__0__R__2515)
=> p(happ(happ(Vvar__7__req__2536,happ(happ(Vvar__5__rsub__2528,Vvar__var__var__var__var__var__var__18__x__2619__2621__2693__2695__2697__2699__2701),Vvar__var__var__var__var__var__var__19__y__2620__2622__2694__2696__2698__2700__2702)),happ(happ(Vvar__3__radd__2518,Vvar__var__var__var__var__var__var__18__x__2619__2621__2693__2695__2697__2699__2701),happ(Vvar__6__ropp__2533,Vvar__var__var__var__var__var__var__19__y__2620__2622__2694__2696__2698__2700__2702)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649] :
( cType___24t(Vvar__0__R__21629)
=> ( c_24__type__21769___24t(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649,Vvar__1__req__21630)
=> ( cType___24t(Vvar__2__C__21635)
=> ( c_24__type__21819___24t(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649,Vvar__3__cadd__21636)
=> ( c_24__type__21869___24t(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649,Vvar__4__cmul__21641)
=> ( c_24__type__21911___24t(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649,Vvar__5__phi__21646)
=> ( c_24__type__21961___24t(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649,Vvar__6__cdiv__21649)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__21681__21686__21691__21696__21701__21706__21711__21716] :
( t(Vvar__var__var__var__var__var__var__var__7__a__21681__21686__21691__21696__21701__21706__21711__21716,Vvar__2__C__21635)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__21682__21687__21692__21697__21702__21707__21712__21717] :
( t(Vvar__var__var__var__var__var__var__var__8__b__21682__21687__21692__21697__21702__21707__21712__21717,Vvar__2__C__21635)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2422024___24a9(Vvar__0__R__21629,Vvar__1__req__21630,Vvar__2__C__21635,Vvar__3__cadd__21636,Vvar__4__cmul__21641,Vvar__5__phi__21646,Vvar__6__cdiv__21649,Vvar__var__var__var__var__var__var__var__7__a__21681__21686__21691__21696__21701__21706__21711__21716,Vvar__var__var__var__var__var__var__var__8__b__21682__21687__21692__21697__21702__21707__21712__21717) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__3__req__22051,Vvar__4__Cpow__22056,Vvar__5__Cp__phi__22057,Vvar__6__rpow__22060] :
( cType___24t(Vvar__0__R__22044)
=> ( t(Vvar__1__rI__22045,Vvar__0__R__22044)
=> ( c_24__type__22146___24t(Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__3__req__22051,Vvar__4__Cpow__22056,Vvar__5__Cp__phi__22057,Vvar__6__rpow__22060,Vvar__2__rmul__22046)
=> ( c_24__type__22190___24t(Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__3__req__22051,Vvar__4__Cpow__22056,Vvar__5__Cp__phi__22057,Vvar__6__rpow__22060,Vvar__3__req__22051)
=> ( cType___24t(Vvar__4__Cpow__22056)
=> ( c_24__type__22226___24t(Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__3__req__22051,Vvar__4__Cpow__22056,Vvar__5__Cp__phi__22057,Vvar__6__rpow__22060,Vvar__5__Cp__phi__22057)
=> ( c_24__type__22270___24t(Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__3__req__22051,Vvar__4__Cpow__22056,Vvar__5__Cp__phi__22057,Vvar__6__rpow__22060,Vvar__6__rpow__22060)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__3__req__22051,Vvar__4__Cpow__22056,Vvar__5__Cp__phi__22057,Vvar__6__rpow__22060)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__22088__22090__22092__22094__22096__22098__22100__22102] :
( t(Vvar__var__var__var__var__var__var__var__7__r__22088__22090__22092__22094__22096__22098__22100__22102,Vvar__0__R__22044)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__22089__22091__22093__22095__22097__22099__22101__22103] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__22089__22091__22093__22095__22097__22099__22101__22103)
=> p(happ(happ(Vvar__3__req__22051,happ(happ(Vvar__6__rpow__22060,Vvar__var__var__var__var__var__var__var__7__r__22088__22090__22092__22094__22096__22098__22100__22102),happ(Vvar__5__Cp__phi__22057,Vvar__var__var__var__var__var__var__var__8__n__22089__22091__22093__22095__22097__22099__22101__22103))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__22044,Vvar__1__rI__22045,Vvar__2__rmul__22046,Vvar__var__var__var__var__var__var__var__7__r__22088__22090__22092__22094__22096__22098__22100__22102,Vvar__var__var__var__var__var__var__var__8__n__22089__22091__22093__22095__22097__22099__22101__22103))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058] :
( cType___24t(Vvar__0__R__3044)
=> ( c_24__type__3149___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__1__radd__3045)
=> ( c_24__type__3179___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__2__rmul__3050)
=> ( c_24__type__3203___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__3__ropp__3055)
=> ( c_24__type__3233___24t(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058,Vvar__4__req__3058)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3263___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,c_24__type__3287___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),Vvar__4__req__3058,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,Vvar__0__R__3044,Vvar__4__req__3058,Vvar__4__req__3058)),Vvar__1__radd__3045)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3320___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,c_24__type__3344___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),Vvar__4__req__3058,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,Vvar__0__R__3044,Vvar__4__req__3058,Vvar__4__req__3058)),Vvar__2__rmul__3050)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3371___24a5(Vvar__0__R__3044,Vvar__1__radd__3045,Vvar__2__rmul__3050,Vvar__3__ropp__3055,Vvar__4__req__3058),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__3044,Vvar__0__R__3044,Vvar__4__req__3058,Vvar__4__req__3058),Vvar__3__ropp__3055)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029] :
( cType___24t(Vvar__0__R__18977)
=> ( t(Vvar__1__rO__18978,Vvar__0__R__18977)
=> ( t(Vvar__2__rI__18979,Vvar__0__R__18977)
=> ( c_24__type__19373___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__3__radd__18980)
=> ( c_24__type__19586___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__4__rmul__18985)
=> ( c_24__type__19799___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__5__rsub__18990)
=> ( c_24__type__19994___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__6__ropp__18995)
=> ( c_24__type__20207___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__7__req__18998)
=> ( cType___24t(Vvar__8__C__19003)
=> ( t(Vvar__9__cO__19004,Vvar__8__C__19003)
=> ( t(Vvar__10__cI__19005,Vvar__8__C__19003)
=> ( c_24__type__20420___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__11__cadd__19006)
=> ( c_24__type__20633___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__12__cmul__19011)
=> ( c_24__type__20846___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__13__csub__19016)
=> ( c_24__type__21041___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__14__copp__19021)
=> ( c_24__type__21254___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__15__ceqb__19024)
=> ( c_24__type__21449___24t(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029,Vvar__16__phi__19029)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__18977,Vvar__1__rO__18978,Vvar__2__rI__18979,Vvar__3__radd__18980,Vvar__4__rmul__18985,Vvar__5__rsub__18990,Vvar__6__ropp__18995,Vvar__7__req__18998,Vvar__8__C__19003,Vvar__9__cO__19004,Vvar__10__cI__19005,Vvar__11__cadd__19006,Vvar__12__cmul__19011,Vvar__13__csub__19016,Vvar__14__copp__19021,Vvar__15__ceqb__19024,Vvar__16__phi__19029)
=> ( p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,Vvar__9__cO__19004)),Vvar__1__rO__18978))
& p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,Vvar__10__cI__19005)),Vvar__2__rI__18979))
& ! [Vvar__var__var__var__var__var__var__19__x__19091__19093__19115__19117__19119__19121__19123] :
( t(Vvar__var__var__var__var__var__var__19__x__19091__19093__19115__19117__19119__19121__19123,Vvar__8__C__19003)
=> ! [Vvar__var__var__var__var__var__var__20__y__19092__19094__19116__19118__19120__19122__19124] :
( t(Vvar__var__var__var__var__var__var__20__y__19092__19094__19116__19118__19120__19122__19124,Vvar__8__C__19003)
=> p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,happ(happ(Vvar__11__cadd__19006,Vvar__var__var__var__var__var__var__19__x__19091__19093__19115__19117__19119__19121__19123),Vvar__var__var__var__var__var__var__20__y__19092__19094__19116__19118__19120__19122__19124))),happ(happ(Vvar__3__radd__18980,happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__19__x__19091__19093__19115__19117__19119__19121__19123)),happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__20__y__19092__19094__19116__19118__19120__19122__19124)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__19096__19098__19125__19127__19129__19131__19133] :
( t(Vvar__var__var__var__var__var__var__20__x__19096__19098__19125__19127__19129__19131__19133,Vvar__8__C__19003)
=> ! [Vvar__var__var__var__var__var__var__21__y__19097__19099__19126__19128__19130__19132__19134] :
( t(Vvar__var__var__var__var__var__var__21__y__19097__19099__19126__19128__19130__19132__19134,Vvar__8__C__19003)
=> p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,happ(happ(Vvar__13__csub__19016,Vvar__var__var__var__var__var__var__20__x__19096__19098__19125__19127__19129__19131__19133),Vvar__var__var__var__var__var__var__21__y__19097__19099__19126__19128__19130__19132__19134))),happ(happ(Vvar__5__rsub__18990,happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__20__x__19096__19098__19125__19127__19129__19131__19133)),happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__21__y__19097__19099__19126__19128__19130__19132__19134)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__19101__19103__19135__19137__19139__19141__19143] :
( t(Vvar__var__var__var__var__var__var__21__x__19101__19103__19135__19137__19139__19141__19143,Vvar__8__C__19003)
=> ! [Vvar__var__var__var__var__var__var__22__y__19102__19104__19136__19138__19140__19142__19144] :
( t(Vvar__var__var__var__var__var__var__22__y__19102__19104__19136__19138__19140__19142__19144,Vvar__8__C__19003)
=> p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,happ(happ(Vvar__12__cmul__19011,Vvar__var__var__var__var__var__var__21__x__19101__19103__19135__19137__19139__19141__19143),Vvar__var__var__var__var__var__var__22__y__19102__19104__19136__19138__19140__19142__19144))),happ(happ(Vvar__4__rmul__18985,happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__21__x__19101__19103__19135__19137__19139__19141__19143)),happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__22__y__19102__19104__19136__19138__19140__19142__19144)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__19106__19107__19145__19146__19147__19148__19149] :
( t(Vvar__var__var__var__var__var__var__22__x__19106__19107__19145__19146__19147__19148__19149,Vvar__8__C__19003)
=> p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,happ(Vvar__14__copp__19021,Vvar__var__var__var__var__var__var__22__x__19106__19107__19145__19146__19147__19148__19149))),happ(Vvar__6__ropp__18995,happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__var__22__x__19106__19107__19145__19146__19147__19148__19149)))) )
& ! [Vvar__var__var__var__var__var__23__x__19109__19112__19150__19153__19156__19159] :
( t(Vvar__var__var__var__var__var__23__x__19109__19112__19150__19153__19156__19159,Vvar__8__C__19003)
=> ! [Vvar__var__var__var__var__var__24__y__19110__19113__19151__19154__19157__19160] :
( t(Vvar__var__var__var__var__var__24__y__19110__19113__19151__19154__19157__19160,Vvar__8__C__19003)
=> ( happ(happ(Vvar__15__ceqb__19024,Vvar__var__var__var__var__var__23__x__19109__19112__19150__19153__19156__19159),Vvar__var__var__var__var__var__24__y__19110__19113__19151__19154__19157__19160) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__18998,happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__23__x__19109__19112__19150__19153__19156__19159)),happ(Vvar__16__phi__19029,Vvar__var__var__var__var__var__24__y__19110__19113__19151__19154__19157__19160))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103] :
( cType___24t(Vvar__0__R__26082)
=> ( t(Vvar__1__rO__26083,Vvar__0__R__26082)
=> ( t(Vvar__2__rI__26084,Vvar__0__R__26082)
=> ( c_24__type__26306___24t(Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103,Vvar__3__radd__26085)
=> ( c_24__type__26369___24t(Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103,Vvar__4__rmul__26090)
=> ( c_24__type__26432___24t(Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103,Vvar__5__rsub__26095)
=> ( c_24__type__26486___24t(Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103,Vvar__6__ropp__26100)
=> ( c_24__type__26549___24t(Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103,Vvar__7__req__26103)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__26082,Vvar__1__rO__26083,Vvar__2__rI__26084,Vvar__3__radd__26085,Vvar__4__rmul__26090,Vvar__5__rsub__26095,Vvar__6__ropp__26100,Vvar__7__req__26103)
=> ( ! [Vvar__var__var__var__var__var__8__x__26136__26137__26180__26181__26182__26183] :
( t(Vvar__var__var__var__var__var__8__x__26136__26137__26180__26181__26182__26183,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__3__radd__26085,Vvar__1__rO__26083),Vvar__var__var__var__var__var__8__x__26136__26137__26180__26181__26182__26183)),Vvar__var__var__var__var__var__8__x__26136__26137__26180__26181__26182__26183)) )
& ! [Vvar__var__var__var__var__9__x__26139__26141__26184__26186__26188] :
( t(Vvar__var__var__var__var__9__x__26139__26141__26184__26186__26188,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__10__y__26140__26142__26185__26187__26189] :
( t(Vvar__var__var__var__var__10__y__26140__26142__26185__26187__26189,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__9__x__26139__26141__26184__26186__26188),Vvar__var__var__var__var__10__y__26140__26142__26185__26187__26189)),happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__10__y__26140__26142__26185__26187__26189),Vvar__var__var__var__var__9__x__26139__26141__26184__26186__26188))) ) )
& ! [Vvar__var__var__var__var__10__x__26144__26147__26190__26193__26196] :
( t(Vvar__var__var__var__var__10__x__26144__26147__26190__26193__26196,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__11__y__26145__26148__26191__26194__26197] :
( t(Vvar__var__var__var__var__11__y__26145__26148__26191__26194__26197,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__12__z__26146__26149__26192__26195__26198] :
( t(Vvar__var__var__var__var__12__z__26146__26149__26192__26195__26198,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__10__x__26144__26147__26190__26193__26196),happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__11__y__26145__26148__26191__26194__26197),Vvar__var__var__var__var__12__z__26146__26149__26192__26195__26198))),happ(happ(Vvar__3__radd__26085,happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__10__x__26144__26147__26190__26193__26196),Vvar__var__var__var__var__11__y__26145__26148__26191__26194__26197)),Vvar__var__var__var__var__12__z__26146__26149__26192__26195__26198))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__26151__26152__26199__26200__26201__26202] :
( t(Vvar__var__var__var__var__var__11__x__26151__26152__26199__26200__26201__26202,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__4__rmul__26090,Vvar__2__rI__26084),Vvar__var__var__var__var__var__11__x__26151__26152__26199__26200__26201__26202)),Vvar__var__var__var__var__var__11__x__26151__26152__26199__26200__26201__26202)) )
& ! [Vvar__var__var__var__var__12__x__26154__26156__26203__26205__26207] :
( t(Vvar__var__var__var__var__12__x__26154__26156__26203__26205__26207,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__13__y__26155__26157__26204__26206__26208] :
( t(Vvar__var__var__var__var__13__y__26155__26157__26204__26206__26208,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__12__x__26154__26156__26203__26205__26207),Vvar__var__var__var__var__13__y__26155__26157__26204__26206__26208)),happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__13__y__26155__26157__26204__26206__26208),Vvar__var__var__var__var__12__x__26154__26156__26203__26205__26207))) ) )
& ! [Vvar__var__var__var__var__13__x__26159__26162__26209__26212__26215] :
( t(Vvar__var__var__var__var__13__x__26159__26162__26209__26212__26215,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__14__y__26160__26163__26210__26213__26216] :
( t(Vvar__var__var__var__var__14__y__26160__26163__26210__26213__26216,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__15__z__26161__26164__26211__26214__26217] :
( t(Vvar__var__var__var__var__15__z__26161__26164__26211__26214__26217,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__13__x__26159__26162__26209__26212__26215),happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__14__y__26160__26163__26210__26213__26216),Vvar__var__var__var__var__15__z__26161__26164__26211__26214__26217))),happ(happ(Vvar__4__rmul__26090,happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__13__x__26159__26162__26209__26212__26215),Vvar__var__var__var__var__14__y__26160__26163__26210__26213__26216)),Vvar__var__var__var__var__15__z__26161__26164__26211__26214__26217))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__26166__26169__26218__26221__26224__26227] :
( t(Vvar__var__var__var__var__var__14__x__26166__26169__26218__26221__26224__26227,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__var__15__y__26167__26170__26219__26222__26225__26228] :
( t(Vvar__var__var__var__var__var__15__y__26167__26170__26219__26222__26225__26228,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__var__16__z__26168__26171__26220__26223__26226__26229] :
( t(Vvar__var__var__var__var__var__16__z__26168__26171__26220__26223__26226__26229,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__4__rmul__26090,happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__var__14__x__26166__26169__26218__26221__26224__26227),Vvar__var__var__var__var__var__15__y__26167__26170__26219__26222__26225__26228)),Vvar__var__var__var__var__var__16__z__26168__26171__26220__26223__26226__26229)),happ(happ(Vvar__3__radd__26085,happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__var__14__x__26166__26169__26218__26221__26224__26227),Vvar__var__var__var__var__var__16__z__26168__26171__26220__26223__26226__26229)),happ(happ(Vvar__4__rmul__26090,Vvar__var__var__var__var__var__15__y__26167__26170__26219__26222__26225__26228),Vvar__var__var__var__var__var__16__z__26168__26171__26220__26223__26226__26229)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__26173__26175__26230__26232__26234__26236__26238] :
( t(Vvar__var__var__var__var__var__var__15__x__26173__26175__26230__26232__26234__26236__26238,Vvar__0__R__26082)
=> ! [Vvar__var__var__var__var__var__var__16__y__26174__26176__26231__26233__26235__26237__26239] :
( t(Vvar__var__var__var__var__var__var__16__y__26174__26176__26231__26233__26235__26237__26239,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__5__rsub__26095,Vvar__var__var__var__var__var__var__15__x__26173__26175__26230__26232__26234__26236__26238),Vvar__var__var__var__var__var__var__16__y__26174__26176__26231__26233__26235__26237__26239)),happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__var__var__15__x__26173__26175__26230__26232__26234__26236__26238),happ(Vvar__6__ropp__26100,Vvar__var__var__var__var__var__var__16__y__26174__26176__26231__26233__26235__26237__26239)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__26178__26179__26240__26241__26242__26243__26244] :
( t(Vvar__var__var__var__var__var__var__16__x__26178__26179__26240__26241__26242__26243__26244,Vvar__0__R__26082)
=> p(happ(happ(Vvar__7__req__26103,happ(happ(Vvar__3__radd__26085,Vvar__var__var__var__var__var__var__16__x__26178__26179__26240__26241__26242__26243__26244),happ(Vvar__6__ropp__26100,Vvar__var__var__var__var__var__var__16__x__26178__26179__26240__26241__26242__26243__26244))),Vvar__1__rO__26083)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__28312,Vvar__1__rO__28313,Vvar__2__rI__28314,Vvar__3__radd__28315,Vvar__4__rmul__28320,Vvar__5__req__28325] :
( cType___24t(Vvar__0__R__28312)
=> ( t(Vvar__1__rO__28313,Vvar__0__R__28312)
=> ( t(Vvar__2__rI__28314,Vvar__0__R__28312)
=> ( c_24__type__28480___24t(Vvar__0__R__28312,Vvar__1__rO__28313,Vvar__2__rI__28314,Vvar__3__radd__28315,Vvar__4__rmul__28320,Vvar__5__req__28325,Vvar__3__radd__28315)
=> ( c_24__type__28519___24t(Vvar__0__R__28312,Vvar__1__rO__28313,Vvar__2__rI__28314,Vvar__3__radd__28315,Vvar__4__rmul__28320,Vvar__5__req__28325,Vvar__4__rmul__28320)
=> ( c_24__type__28558___24t(Vvar__0__R__28312,Vvar__1__rO__28313,Vvar__2__rI__28314,Vvar__3__radd__28315,Vvar__4__rmul__28320,Vvar__5__req__28325,Vvar__5__req__28325)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__28312,Vvar__1__rO__28313,Vvar__2__rI__28314,Vvar__3__radd__28315,Vvar__4__rmul__28320,Vvar__5__req__28325)
=> ( ! [Vvar__var__var__var__var__var__6__n__28350__28351__28389__28390__28391__28392] :
( t(Vvar__var__var__var__var__var__6__n__28350__28351__28389__28390__28391__28392,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__3__radd__28315,Vvar__1__rO__28313),Vvar__var__var__var__var__var__6__n__28350__28351__28389__28390__28391__28392)),Vvar__var__var__var__var__var__6__n__28350__28351__28389__28390__28391__28392)) )
& ! [Vvar__var__var__var__var__7__n__28353__28355__28393__28395__28397] :
( t(Vvar__var__var__var__var__7__n__28353__28355__28393__28395__28397,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__8__m__28354__28356__28394__28396__28398] :
( t(Vvar__var__var__var__var__8__m__28354__28356__28394__28396__28398,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__3__radd__28315,Vvar__var__var__var__var__7__n__28353__28355__28393__28395__28397),Vvar__var__var__var__var__8__m__28354__28356__28394__28396__28398)),happ(happ(Vvar__3__radd__28315,Vvar__var__var__var__var__8__m__28354__28356__28394__28396__28398),Vvar__var__var__var__var__7__n__28353__28355__28393__28395__28397))) ) )
& ! [Vvar__var__var__var__var__8__n__28358__28361__28399__28402__28405] :
( t(Vvar__var__var__var__var__8__n__28358__28361__28399__28402__28405,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__9__m__28359__28362__28400__28403__28406] :
( t(Vvar__var__var__var__var__9__m__28359__28362__28400__28403__28406,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__10__p__28360__28363__28401__28404__28407] :
( t(Vvar__var__var__var__var__10__p__28360__28363__28401__28404__28407,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__3__radd__28315,Vvar__var__var__var__var__8__n__28358__28361__28399__28402__28405),happ(happ(Vvar__3__radd__28315,Vvar__var__var__var__var__9__m__28359__28362__28400__28403__28406),Vvar__var__var__var__var__10__p__28360__28363__28401__28404__28407))),happ(happ(Vvar__3__radd__28315,happ(happ(Vvar__3__radd__28315,Vvar__var__var__var__var__8__n__28358__28361__28399__28402__28405),Vvar__var__var__var__var__9__m__28359__28362__28400__28403__28406)),Vvar__var__var__var__var__10__p__28360__28363__28401__28404__28407))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__28365__28366__28408__28409__28410__28411] :
( t(Vvar__var__var__var__var__var__9__n__28365__28366__28408__28409__28410__28411,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__4__rmul__28320,Vvar__2__rI__28314),Vvar__var__var__var__var__var__9__n__28365__28366__28408__28409__28410__28411)),Vvar__var__var__var__var__var__9__n__28365__28366__28408__28409__28410__28411)) )
& ! [Vvar__var__var__var__var__var__10__n__28368__28369__28412__28413__28414__28415] :
( t(Vvar__var__var__var__var__var__10__n__28368__28369__28412__28413__28414__28415,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__4__rmul__28320,Vvar__1__rO__28313),Vvar__var__var__var__var__var__10__n__28368__28369__28412__28413__28414__28415)),Vvar__1__rO__28313)) )
& ! [Vvar__var__var__var__var__11__n__28371__28373__28416__28418__28420] :
( t(Vvar__var__var__var__var__11__n__28371__28373__28416__28418__28420,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__12__m__28372__28374__28417__28419__28421] :
( t(Vvar__var__var__var__var__12__m__28372__28374__28417__28419__28421,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__11__n__28371__28373__28416__28418__28420),Vvar__var__var__var__var__12__m__28372__28374__28417__28419__28421)),happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__12__m__28372__28374__28417__28419__28421),Vvar__var__var__var__var__11__n__28371__28373__28416__28418__28420))) ) )
& ! [Vvar__var__var__var__var__12__n__28376__28379__28422__28425__28428] :
( t(Vvar__var__var__var__var__12__n__28376__28379__28422__28425__28428,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__13__m__28377__28380__28423__28426__28429] :
( t(Vvar__var__var__var__var__13__m__28377__28380__28423__28426__28429,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__14__p__28378__28381__28424__28427__28430] :
( t(Vvar__var__var__var__var__14__p__28378__28381__28424__28427__28430,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__12__n__28376__28379__28422__28425__28428),happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__13__m__28377__28380__28423__28426__28429),Vvar__var__var__var__var__14__p__28378__28381__28424__28427__28430))),happ(happ(Vvar__4__rmul__28320,happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__12__n__28376__28379__28422__28425__28428),Vvar__var__var__var__var__13__m__28377__28380__28423__28426__28429)),Vvar__var__var__var__var__14__p__28378__28381__28424__28427__28430))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__28383__28386__28431__28434__28437__28440] :
( t(Vvar__var__var__var__var__var__13__n__28383__28386__28431__28434__28437__28440,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__var__14__m__28384__28387__28432__28435__28438__28441] :
( t(Vvar__var__var__var__var__var__14__m__28384__28387__28432__28435__28438__28441,Vvar__0__R__28312)
=> ! [Vvar__var__var__var__var__var__15__p__28385__28388__28433__28436__28439__28442] :
( t(Vvar__var__var__var__var__var__15__p__28385__28388__28433__28436__28439__28442,Vvar__0__R__28312)
=> p(happ(happ(Vvar__5__req__28325,happ(happ(Vvar__4__rmul__28320,happ(happ(Vvar__3__radd__28315,Vvar__var__var__var__var__var__13__n__28383__28386__28431__28434__28437__28440),Vvar__var__var__var__var__var__14__m__28384__28387__28432__28435__28438__28441)),Vvar__var__var__var__var__var__15__p__28385__28388__28433__28436__28439__28442)),happ(happ(Vvar__3__radd__28315,happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__var__13__n__28383__28386__28431__28434__28437__28440),Vvar__var__var__var__var__var__15__p__28385__28388__28433__28436__28439__28442)),happ(happ(Vvar__4__rmul__28320,Vvar__var__var__var__var__var__14__m__28384__28387__28432__28435__28438__28441),Vvar__var__var__var__var__var__15__p__28385__28388__28433__28436__28439__28442)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_DirectedSets.DirectedSet',axiom,
! [VX285] :
( cDirectedSets_2eDirectedSet___24t(VX285)
=> ? [Vvar__0__DS__set__286] :
( cType___24t(Vvar__0__DS__set__286)
& ? [Vvar__1__DS__ord__287] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__DS__set__286,Vvar__1__DS__ord__287)
& cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__DS__set__286,Vvar__1__DS__ord__287)
& ! [Vvar__var__3__i__290__293] :
( t(Vvar__var__3__i__290__293,Vvar__0__DS__set__286)
=> ! [Vvar__var__4__j__292__295] :
( t(Vvar__var__4__j__292__295,Vvar__0__DS__set__286)
=> ? [Vvar__var__5__k__291__294] :
( t(Vvar__var__5__k__291__294,Vvar__0__DS__set__286)
& p(happ(happ(Vvar__1__DS__ord__287,Vvar__var__3__i__290__293),Vvar__var__5__k__291__294))
& p(happ(happ(Vvar__1__DS__ord__287,Vvar__var__4__j__292__295),Vvar__var__5__k__291__294)) ) ) )
& VX285 = cDirectedSets_2eBuild__DirectedSet___24a2(Vvar__0__DS__set__286,Vvar__1__DS__ord__287) ) ) ) ).
fof('$_lam_15716',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__15716___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_15724',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__15724___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_15732',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__15732___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_15740',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__15740___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_17716',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__17716___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__17644___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_33283',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__33283___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_33291',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__33291___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_33299',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__33299___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_33307',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__33307___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_34337',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__34337___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34338] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34338)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34338)
& c_24__lam__34337___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__34338) ) ) ) ).
fof('$_lam_34344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__34344___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__34345] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34345)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34345)
& c_24__lam__34344___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__34345) ) ) ) ).
fof('$_lam_34348',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__34348___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34349] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34349)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34349)
& c_24__lam__34348___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_lam_34420',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__34420___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
& p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_lam_34547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__34547___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> ~ p(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_lam_34610',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__34610___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( p(happ(Vv__CANONICAL__0,Vv__CANONICAL__2))
=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_lam_34996',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__34996___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_35333',axiom,
! [Vv__CANONICAL__0] :
( c_24__lam__35333___24a1(Vv__CANONICAL__0)
<=> ( ~ ~ p(Vv__CANONICAL__0)
=> p(Vv__CANONICAL__0) ) ) ).
fof('$_lam_35545',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__35545___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24Proof ).
fof('$_lam_37334',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__37334___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_38465',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__0)
=> ( c_24__type__38481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__1)
=> ( c_24__type__38490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),c_24__prop__38493___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))
& c_24__lam__38465___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse )
| ( ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4),c_24__prop__38494___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))
& c_24__lam__38465___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_lam_39314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__39314___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ) ).
fof('$_lam_39316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__39316___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_lam_42991',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__42991___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_46034',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__46034___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
& ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_lam_49406',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__49406___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_lam_9853',axiom,
! [Vv__CANONICAL__0] : c_24__lam__9853___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_9854',axiom,
! [Vv__CANONICAL__0] : c_24__lam__9854___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_prop_24719',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__24719___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_29306',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__S__29284,Vvar__1__x__29285,Vvar__2__y__29286] :
( p(c_24__prop__29306___24a4(Vvar__0___24Anonymous__29282,Vvar__0__S__29284,Vvar__1__x__29285,Vvar__2__y__29286))
<=> Vvar__1__x__29285 = Vvar__2__y__29286 ) ).
fof('$_prop_29307',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__x__29287,Vvar__1__y__29288] :
( p(c_24__prop__29307___24a3(Vvar__0___24Anonymous__29282,Vvar__0__x__29287,Vvar__1__y__29288))
<=> Vvar__0__x__29287 = Vvar__1__y__29288 ) ).
fof('$_prop_29308',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__x__29289,Vvar__1__s__29290] :
( p(c_24__prop__29308___24a3(Vvar__0___24Anonymous__29282,Vvar__0__x__29289,Vvar__1__s__29290))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__29289,Vvar__1__s__29290) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_29309',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__P__29291,Vvar__1__Q__29292] :
( p(c_24__prop__29309___24a3(Vvar__0___24Anonymous__29282,Vvar__0__P__29291,Vvar__1__Q__29292))
<=> ( p(Vvar__0__P__29291)
& p(Vvar__1__Q__29292) ) ) ).
fof('$_prop_29310',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__P__29295,Vvar__1__Q__29296] :
( p(c_24__prop__29310___24a3(Vvar__0___24Anonymous__29282,Vvar__0__P__29295,Vvar__1__Q__29296))
<=> ( p(Vvar__0__P__29295)
| p(Vvar__1__Q__29296) ) ) ).
fof('$_prop_29311',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__P__29299,Vvar__1__Q__29300] :
( p(c_24__prop__29311___24a3(Vvar__0___24Anonymous__29282,Vvar__0__P__29299,Vvar__1__Q__29300))
<=> ( p(Vvar__0__P__29299)
=> p(Vvar__1__Q__29300) ) ) ).
fof('$_prop_29312',axiom,
! [Vvar__0___24Anonymous__29282,Vvar__0__P__29304] :
( p(c_24__prop__29312___24a2(Vvar__0___24Anonymous__29282,Vvar__0__P__29304))
<=> ~ p(Vvar__0__P__29304) ) ).
fof('$_prop_31110',axiom,
! [V7__A] :
( p(c_24__prop__31110___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_34399',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__34399___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_34548',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__34548___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_35096',axiom,
! [V0__C] :
( p(c_24__prop__35096___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_35100',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__35100___24a1(Vv__CANONICAL__0))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_prop_35101',axiom,
! [V0__C] :
( p(c_24__prop__35101___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_35256',axiom,
! [V6__A] :
( p(c_24__prop__35256___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_35329',axiom,
! [V6__A] :
( p(c_24__prop__35329___24a1(V6__A))
<=> ~ ~ p(V6__A) ) ).
fof('$_prop_35330',axiom,
! [V6__A] :
( p(c_24__prop__35330___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_35334',axiom,
! [V0__or,V7__B,V11__A] :
( p(c_24__prop__35334___24a3(V0__or,V7__B,V11__A))
<=> ~ ( c_24Proof != c_24Proof ) ) ).
fof('$_prop_37330',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__37330___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_prop_38391',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__38391___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_38392',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__38347] :
( p(c_24__prop__38392___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__38347))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__38347)) ) ).
fof('$_prop_38393',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__38347] :
( p(c_24__prop__38393___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__38347))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__38347)) ) ).
fof('$_prop_38426',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__38426___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_38439',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__38439___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_38492',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__38492___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_38493',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( p(c_24__prop__38493___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ).
fof('$_prop_38494',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( p(c_24__prop__38494___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ).
fof('$_prop_38507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__38507___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_38516',axiom,
! [V0__C] :
( p(c_24__prop__38516___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_38518',axiom,
! [V0__C] :
( p(c_24__prop__38518___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_38520',axiom,
! [V1__S,V2__x,V3__y] :
( p(c_24__prop__38520___24a3(V1__S,V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_38524',axiom,
! [V2__x,V3__y] :
( p(c_24__prop__38524___24a2(V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_38529',axiom,
! [V6__P,V7__Q] :
( p(c_24__prop__38529___24a2(V6__P,V7__Q))
<=> ( p(V6__P)
& p(V7__Q) ) ) ).
fof('$_prop_38536',axiom,
! [V7__P,V8__Q] :
( p(c_24__prop__38536___24a2(V7__P,V8__Q))
<=> ( p(V7__P)
| p(V8__Q) ) ) ).
fof('$_prop_38543',axiom,
! [V8__P,V9__Q] :
( p(c_24__prop__38543___24a2(V8__P,V9__Q))
<=> ( p(V8__P)
=> p(V9__Q) ) ) ).
fof('$_prop_38551',axiom,
! [V9__P] :
( p(c_24__prop__38551___24a1(V9__P))
<=> ~ p(V9__P) ) ).
fof('$_prop_38555',axiom,
! [V1__S,V2__x,V3__y] :
( p(c_24__prop__38555___24a3(V1__S,V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_38559',axiom,
! [V2__x,V3__y] :
( p(c_24__prop__38559___24a2(V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_38564',axiom,
! [V6__P,V7__Q] :
( p(c_24__prop__38564___24a2(V6__P,V7__Q))
<=> ( p(V6__P)
& p(V7__Q) ) ) ).
fof('$_prop_38571',axiom,
! [V7__P,V8__Q] :
( p(c_24__prop__38571___24a2(V7__P,V8__Q))
<=> ( p(V7__P)
| p(V8__Q) ) ) ).
fof('$_prop_38578',axiom,
! [V8__P,V9__Q] :
( p(c_24__prop__38578___24a2(V8__P,V9__Q))
<=> ( p(V8__P)
=> p(V9__Q) ) ) ).
fof('$_prop_38586',axiom,
! [V9__P] :
( p(c_24__prop__38586___24a1(V9__P))
<=> ~ p(V9__P) ) ).
fof('$_prop_39600',axiom,
! [V0__P,V1__b] :
( p(c_24__prop__39600___24a2(V0__P,V1__b))
<=> ~ p(V0__P) ) ).
fof('$_prop_39601',axiom,
! [V0__P,V1__b] :
( p(c_24__prop__39601___24a2(V0__P,V1__b))
<=> ~ p(V0__P) ) ).
fof('$_prop_39607',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__39607___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_prop_39674',axiom,
! [V6__A] :
( p(c_24__prop__39674___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_39758',axiom,
! [V6__A] :
( p(c_24__prop__39758___24a1(V6__A))
<=> ~ ~ p(V6__A) ) ).
fof('$_prop_39759',axiom,
! [V6__A] :
( p(c_24__prop__39759___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_39762',axiom,
! [V0__or,V7__B,V10__A] :
( p(c_24__prop__39762___24a3(V0__or,V7__B,V10__A))
<=> ~ ( c_24Proof != c_24Proof ) ) ).
fof('$_prop_40058',axiom,
! [V7__A] :
( p(c_24__prop__40058___24a1(V7__A))
<=> ~ ~ p(V7__A) ) ).
fof('$_prop_40059',axiom,
! [V7__A] :
( p(c_24__prop__40059___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_40154',axiom,
! [V0__A] :
( p(c_24__prop__40154___24a1(V0__A))
<=> ~ p(V0__A) ) ).
fof('$_prop_43226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__43226___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_48261',axiom,
! [V0__P] :
( p(c_24__prop__48261___24a1(V0__P))
<=> ~ p(V0__P) ) ).
fof('$_prop_48696',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__48696___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_49205',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__49205___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_49206',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__49206___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_49207',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__49207___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_49395',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__49395___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_49396',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__49396___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_49403',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__49403___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_prop_49404',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__49404___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_49428',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__49428___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_49429',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__49429___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_49430',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__49430___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_49431',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__49431___24a2(V0__x,V1__y))
<=> V0__x != V1__y ) ).
fof('$_prop_49433',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__49433___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_9689',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__9689___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_9690',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__9690___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_9691',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__9691___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_9692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__9692___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_prop_9693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__9693___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 = Vv__CANONICAL__2 ) ).
fof('$_prop_9694',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__9694___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> Vv__CANONICAL__3 != Vv__CANONICAL__2 ) ).
fof('$_type_1',axiom,
! [Vvar__2] :
( c_24__type__1___24t(Vvar__2)
<=> ! [Vv__CANONICAL__0] :
( cDirectedSets_2eDS__set___24t(cI,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10008',axiom,
! [Vvar__10009] :
( c_24__type__10008___24t(Vvar__10009)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__10009,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10042',axiom,
! [Vvar__10043] :
( c_24__type__10042___24t(Vvar__10043)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__10043,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1060',axiom,
! [Vvar__1061] :
( c_24__type__1060___24t(Vvar__1061)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__1061,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10640',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__10641] :
( c_24__type__10640___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__10641)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10641,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1077',axiom,
! [Vvar__1078] :
( c_24__type__1077___24t(Vvar__1078)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1078,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1081',axiom,
! [Vvar__1082] :
( c_24__type__1081___24t(Vvar__1082)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1082,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10986',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__10987] :
( c_24__type__10986___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__10987)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10987,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11332',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11333] :
( c_24__type__11332___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11333)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11333,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11655',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11656] :
( c_24__type__11655___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11656)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__11656,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_12001',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__12002] :
( c_24__type__12001___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__12002)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12002,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_12347',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__12348] :
( c_24__type__12347___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__12348)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12348,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_12693',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__12694] :
( c_24__type__12693___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__12694)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__12694,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_1297',axiom,
! [Vvar__1298] :
( c_24__type__1297___24t(Vvar__1298)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__1298,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_13039',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13040] :
( c_24__type__13039___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13040)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__13040,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_1337',axiom,
! [Vvar__1338] :
( c_24__type__1337___24t(Vvar__1338)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__1338,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_13385',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13386] :
( c_24__type__13385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13386)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__13386,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_13708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13709] :
( c_24__type__13708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13709)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__13709,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_14054',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14055] :
( c_24__type__14054___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14055)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14055,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_14400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14401] :
( c_24__type__14400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14401)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14401,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_14723',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14724] :
( c_24__type__14723___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14724)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__14724,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_15046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15047] :
( c_24__type__15046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15047)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__15047,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_15392',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15393] :
( c_24__type__15392___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15393)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__15393,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15783',axiom,
! [Vvar__15784] :
( c_24__type__15783___24t(Vvar__15784)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__15784,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_169',axiom,
! [Vv__CANONICAL__0,Vvar__170] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vvar__170)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__170,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_17061',axiom,
! [Vvar__17062] :
( c_24__type__17061___24t(Vvar__17062)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__17062,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_171',axiom,
! [Vvar__172] :
( c_24__type__171___24t(Vvar__172)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__172,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17408',axiom,
! [Vvar__17409] :
( c_24__type__17408___24t(Vvar__17409)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__17409,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17411',axiom,
! [Vvar__17412] :
( c_24__type__17411___24t(Vvar__17412)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__17412,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17416',axiom,
! [Vvar__17417] :
( c_24__type__17416___24t(Vvar__17417)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__17417,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17425',axiom,
! [Vvar__17426] :
( c_24__type__17425___24t(Vvar__17426)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__17426,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17618',axiom,
! [Vvar__17619] :
( c_24__type__17618___24t(Vvar__17619)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__800___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__805___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__814___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__17619,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1777',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1778] :
( c_24__type__1777___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1778)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1778,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17848',axiom,
! [Vvar__17849] :
( c_24__type__17848___24t(Vvar__17849)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__17866___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__17849,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_17866',axiom,
! [Vv__CANONICAL__0,Vvar__17867] :
( c_24__type__17866___24t(Vv__CANONICAL__0,Vvar__17867)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__17867,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_180',axiom,
! [Vvar__181] :
( c_24__type__180___24t(Vvar__181)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__181,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18104',axiom,
! [Vvar__18105] :
( c_24__type__18104___24t(Vvar__18105)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__800___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__805___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__814___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8)),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__18105,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_18289',axiom,
! [Vvar__18290] :
( c_24__type__18289___24t(Vvar__18290)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__17866___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__18290,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1878',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1879] :
( c_24__type__1878___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1879)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1879,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18883',axiom,
! [Vvar__18884] :
( c_24__type__18883___24t(Vvar__18884)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__18884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_19373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19374] :
( c_24__type__19373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19374)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19374,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_195',axiom,
! [Vvar__196] :
( c_24__type__195___24t(Vvar__196)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__196,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19586',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19587] :
( c_24__type__19586___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19587)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19587,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1979',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1980] :
( c_24__type__1979___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1980)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1980,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19799',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19800] :
( c_24__type__19799___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19800)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19800,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_198',axiom,
! [Vvar__199] :
( c_24__type__198___24t(Vvar__199)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__199,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19994',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19995] :
( c_24__type__19994___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19995)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__19995,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_202',axiom,
! [Vvar__203] :
( c_24__type__202___24t(Vvar__203)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__203,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20207',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20208] :
( c_24__type__20207___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20208)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20208,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_20420',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20421] :
( c_24__type__20420___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20421)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20421,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20633',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20634] :
( c_24__type__20633___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20634)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20634,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_2069',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2070] :
( c_24__type__2069___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2070)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__2070,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_20846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20847] :
( c_24__type__20846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20847)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20847,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_21041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21042] :
( c_24__type__21041___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21042)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__21042,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_21254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21255] :
( c_24__type__21254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21255)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__21255,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_21449',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21450] :
( c_24__type__21449___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21450)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__21450,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_2170',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2171] :
( c_24__type__2170___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2171)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2171,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_21769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21770] :
( c_24__type__21769___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21770)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21770,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21819',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21820] :
( c_24__type__21819___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21820)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__21820,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_21869',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21870] :
( c_24__type__21869___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21870)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__21870,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_21911',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21912] :
( c_24__type__21911___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21912)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__21912,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_21961',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21962] :
( c_24__type__21961___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21962)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__21962,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_22',axiom,
! [Vv__CANONICAL__0,Vvar__23] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vvar__23)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_22037',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22038] :
( c_24__type__22037___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22038)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__22038,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22147] :
( c_24__type__22146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22147)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22147,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22190',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22191] :
( c_24__type__22190___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22191)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22191,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_22226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22227] :
( c_24__type__22226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22227)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__22227,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_22270',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22271] :
( c_24__type__22270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__22271)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__22271,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22282',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22283] :
( c_24__type__22282___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22283)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__22283,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_22289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22290] :
( c_24__type__22289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22290)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__22290,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_223',axiom,
! [Vvar__224] :
( c_24__type__223___24t(Vvar__224)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__224,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22381',axiom,
! [Vvar__22382] :
( c_24__type__22381___24t(Vvar__22382)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__22382,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22384',axiom,
! [Vvar__22385] :
( c_24__type__22384___24t(Vvar__22385)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22385,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22426',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22427] :
( c_24__type__22426___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22427)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22427,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22466',axiom,
! [Vvar__22467] :
( c_24__type__22466___24t(Vvar__22467)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__22467,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22476',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22477] :
( c_24__type__22476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22477)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__22477,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_22516',axiom,
! [Vvar__22517] :
( c_24__type__22516___24t(Vvar__22517)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22526___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__22476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__22517,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_22526',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22527] :
( c_24__type__22526___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22527)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22527,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22548] :
( c_24__type__22547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22548)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22548,Vv__CANONICAL__2)) ) ) ).
fof('$_type_22551',axiom,
! [Vvar__22552] :
( c_24__type__22551___24t(Vvar__22552)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22552,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22569',axiom,
! [Vvar__22570] :
( c_24__type__22569___24t(Vvar__22570)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__22570,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_22575',axiom,
! [Vvar__22576] :
( c_24__type__22575___24t(Vvar__22576)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__22576,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_22580',axiom,
! [Vvar__22581] :
( c_24__type__22580___24t(Vvar__22581)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__22581,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_22645',axiom,
! [Vvar__22646] :
( c_24__type__22645___24t(Vvar__22646)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__22646,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2271',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2272] :
( c_24__type__2271___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2272)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2272,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_23055',axiom,
! [Vvar__23056] :
( c_24__type__23055___24t(Vvar__23056)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__23056,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_23116',axiom,
! [Vvar__23117] :
( c_24__type__23116___24t(Vvar__23117)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23117,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2373] :
( c_24__type__2372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__2373)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2373,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_24',axiom,
! [Vvar__25] :
( c_24__type__24___24t(Vvar__25)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__25,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24428',axiom,
! [Vvar__24429] :
( c_24__type__24428___24t(Vvar__24429)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__24429,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24568',axiom,
! [Vvar__24569] :
( c_24__type__24568___24t(Vvar__24569)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__24569,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2463',axiom,
! [Vvar__2464] :
( c_24__type__2463___24t(Vvar__2464)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__2464,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24631',axiom,
! [Vvar__24632] :
( c_24__type__24631___24t(Vvar__24632)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__24632,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24639',axiom,
! [Vv__CANONICAL__0,Vvar__24640] :
( c_24__type__24639___24t(Vv__CANONICAL__0,Vvar__24640)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24640,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2465',axiom,
! [Vvar__2466] :
( c_24__type__2465___24t(Vvar__2466)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__2466,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2468',axiom,
! [Vvar__2469] :
( c_24__type__2468___24t(Vvar__2469)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__2469,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24699',axiom,
! [Vvar__24700] :
( c_24__type__24699___24t(Vvar__24700)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__24700,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24728',axiom,
! [Vvar__24729] :
( c_24__type__24728___24t(Vvar__24729)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__9834___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9834___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24729,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2473',axiom,
! [Vvar__2474] :
( c_24__type__2473___24t(Vvar__2474)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__2474,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24757',axiom,
! [Vvar__24758] :
( c_24__type__24757___24t(Vvar__24758)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__24758,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24766',axiom,
! [Vvar__24767] :
( c_24__type__24766___24t(Vvar__24767)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__24767,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24787',axiom,
! [Vvar__24788] :
( c_24__type__24787___24t(Vvar__24788)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__24788,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24810',axiom,
! [Vvar__24811] :
( c_24__type__24810___24t(Vvar__24811)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__24811,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24857',axiom,
! [Vvar__24858] :
( c_24__type__24857___24t(Vvar__24858)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__24858,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2494',axiom,
! [Vvar__2495] :
( c_24__type__2494___24t(Vvar__2495)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__2495,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_24969',axiom,
! [Vvar__24970] :
( c_24__type__24969___24t(Vvar__24970)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__24639___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__24970,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_24977',axiom,
! [Vvar__24978] :
( c_24__type__24977___24t(Vvar__24978)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24978,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24980',axiom,
! [Vvar__24981] :
( c_24__type__24980___24t(Vvar__24981)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24981,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25132',axiom,
! [Vvar__25133] :
( c_24__type__25132___24t(Vvar__25133)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__25133,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25225',axiom,
! [Vvar__25226] :
( c_24__type__25225___24t(Vvar__25226)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__25226,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25240',axiom,
! [Vvar__25241] :
( c_24__type__25240___24t(Vvar__25241)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__25241,Vv__CANONICAL__0)) ) ) ).
fof('$_type_253',axiom,
! [Vvar__254] :
( c_24__type__253___24t(Vvar__254)
<=> ! [Vv__CANONICAL__0] :
( cDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cDirectedSets_2eDS__set___24a1(Vv__CANONICAL__0),happ(Vvar__254,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26306',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26307] :
( c_24__type__26306___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26307)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26307,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26370] :
( c_24__type__26369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26370)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26370,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26432',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26433] :
( c_24__type__26432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26433)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26433,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26486',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26487] :
( c_24__type__26486___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26487)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__26487,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_26549',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26550] :
( c_24__type__26549___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26550)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26550,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_26587',axiom,
! [Vvar__26588] :
( c_24__type__26587___24t(Vvar__26588)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__26588,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26753',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26754] :
( c_24__type__26753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26754)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__26754,Vv__CANONICAL__6)) ) ) ).
fof('$_type_26949',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__26950] :
( c_24__type__26949___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__26950)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26950,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27043] :
( c_24__type__27042___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27043)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27043,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27135',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27136] :
( c_24__type__27135___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27136)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27136,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27217',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27218] :
( c_24__type__27217___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27218)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__27218,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_27310',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27311] :
( c_24__type__27310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27311)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27311,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27392',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27393] :
( c_24__type__27392___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27393)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__27393,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_27485',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27486] :
( c_24__type__27485___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27486)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27486,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_27639',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27640] :
( c_24__type__27639___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27640)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27640,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2764',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2765] :
( c_24__type__2764___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2765)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2765,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27702',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27703] :
( c_24__type__27702___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27703)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27703,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27765',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27766] :
( c_24__type__27765___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27766)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27766,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27819',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27820] :
( c_24__type__27819___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27820)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__27820,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_27882',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27883] :
( c_24__type__27882___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27883)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27883,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_2827',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2828] :
( c_24__type__2827___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2828)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2828,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_283',axiom,
! [Vvar__284] :
( c_24__type__283___24t(Vvar__284)
<=> ! [Vv__CANONICAL__0] :
( cDirectedSets_2eDirectedSet___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__284,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28480',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28481] :
( c_24__type__28480___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28481)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28481,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28520] :
( c_24__type__28519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28520)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28520,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28558',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28559] :
( c_24__type__28558___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28559)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28559,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_2890',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2891] :
( c_24__type__2890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2891)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2891,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29078] :
( c_24__type__29077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29078)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__29078,Vv__CANONICAL__2)) ) ) ).
fof('$_type_29081',axiom,
! [Vvar__29082] :
( c_24__type__29081___24t(Vvar__29082)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29082,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29158',axiom,
! [Vvar__29159] :
( c_24__type__29158___24t(Vvar__29159)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29159,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29339',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29340] :
( c_24__type__29339___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29340)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__29340,Vv__CANONICAL__3)) ) ) ).
fof('$_type_29360',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29361] :
( c_24__type__29360___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29361)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__29361,Vv__CANONICAL__3)) ) ) ).
fof('$_type_2944',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2945] :
( c_24__type__2944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__2945)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__2945,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_29538',axiom,
! [Vvar__29539] :
( c_24__type__29538___24t(Vvar__29539)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__29539,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29570',axiom,
! [Vvar__29571] :
( c_24__type__29570___24t(Vvar__29571)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29571,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3007',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__3008] :
( c_24__type__3007___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__3008)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__3008,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_30629',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30630] :
( c_24__type__30629___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30630)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30630,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30662',axiom,
! [Vvar__30663] :
( c_24__type__30662___24t(Vvar__30663)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__30672___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__22476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__30663,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_30672',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30673] :
( c_24__type__30672___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30673)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30673,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_30955',axiom,
! [Vvar__30956] :
( c_24__type__30955___24t(Vvar__30956)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__30956,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30985',axiom,
! [Vvar__30986] :
( c_24__type__30985___24t(Vvar__30986)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__30986,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_30990',axiom,
! [Vvar__30991] :
( c_24__type__30990___24t(Vvar__30991)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__30991,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31022',axiom,
! [Vvar__31023] :
( c_24__type__31022___24t(Vvar__31023)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31023,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31085',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31086] :
( c_24__type__31085___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31086)
<=> ( p(happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2))
=> cProp___24t(Vvar__31086) ) ) ).
fof('$_type_31150',axiom,
! [Vvar__31151] :
( c_24__type__31150___24t(Vvar__31151)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__31151,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_31196',axiom,
! [Vvar__31197] :
( c_24__type__31196___24t(Vvar__31197)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__31197,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31199',axiom,
! [Vvar__31200] :
( c_24__type__31199___24t(Vvar__31200)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__31200,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31202',axiom,
! [Vvar__31203] :
( c_24__type__31202___24t(Vvar__31203)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__31203,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31207',axiom,
! [Vvar__31208] :
( c_24__type__31207___24t(Vvar__31208)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__31208,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31210',axiom,
! [Vvar__31211] :
( c_24__type__31210___24t(Vvar__31211)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__31211,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31287',axiom,
! [Vvar__31288] :
( c_24__type__31287___24t(Vvar__31288)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__31288,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_31327',axiom,
! [Vvar__31328] :
( c_24__type__31327___24t(Vvar__31328)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__31328,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_31380',axiom,
! [Vvar__31381] :
( c_24__type__31380___24t(Vvar__31381)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__31387___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__31381,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_31387',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31388] :
( c_24__type__31387___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31388)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31388,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3149',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3150] :
( c_24__type__3149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3150)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3150,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31492',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31493] :
( c_24__type__31492___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31493)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31493,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_31514',axiom,
! [Vvar__31515] :
( c_24__type__31514___24t(Vvar__31515)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__31515,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3179',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3180] :
( c_24__type__3179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3180)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3180,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3203',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3204] :
( c_24__type__3203___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3204)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3204,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_32115',axiom,
! [Vvar__32116] :
( c_24__type__32115___24t(Vvar__32116)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__32116,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3234] :
( c_24__type__3233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3234)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__3234,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_3263',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3264] :
( c_24__type__3263___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3264)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3264,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3287',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3288] :
( c_24__type__3287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3288)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3288,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_33',axiom,
! [Vvar__34] :
( c_24__type__33___24t(Vvar__34)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__34,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3320',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3321] :
( c_24__type__3320___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3321)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3321,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33264',axiom,
! [Vvar__33265] :
( c_24__type__33264___24t(Vvar__33265)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__33265,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33344',axiom,
! [Vvar__33345] :
( c_24__type__33344___24t(Vvar__33345)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__33345,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_33359',axiom,
! [Vvar__33360] :
( c_24__type__33359___24t(Vvar__33360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__33360,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33364',axiom,
! [Vvar__33365] :
( c_24__type__33364___24t(Vvar__33365)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__33365,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3344',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3345] :
( c_24__type__3344___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3345)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3345,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_3371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3372] :
( c_24__type__3371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__3372)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__3372,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_33744',axiom,
! [Vvar__33745] :
( c_24__type__33744___24t(Vvar__33745)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__33745,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3375',axiom,
! [Vv__CANONICAL__0,Vvar__3376] :
( c_24__type__3375___24t(Vv__CANONICAL__0,Vvar__3376)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3376,Vv__CANONICAL__1)) ) ) ).
fof('$_type_33818',axiom,
! [Vvar__33819] :
( c_24__type__33818___24t(Vvar__33819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__33819,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33823',axiom,
! [Vvar__33824] :
( c_24__type__33823___24t(Vvar__33824)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__33824,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_33826',axiom,
! [Vvar__33827] :
( c_24__type__33826___24t(Vvar__33827)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__33827,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33834',axiom,
! [Vvar__33835] :
( c_24__type__33834___24t(Vvar__33835)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__33835,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33852',axiom,
! [Vvar__33853] :
( c_24__type__33852___24t(Vvar__33853)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__33853,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_33869',axiom,
! [Vvar__33870] :
( c_24__type__33869___24t(Vvar__33870)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__33870,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3401',axiom,
! [Vvar__3402] :
( c_24__type__3401___24t(Vvar__3402)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3402,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34219',axiom,
! [Vvar__34220] :
( c_24__type__34219___24t(Vvar__34220)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__34220,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3430',axiom,
! [Vvar__3431] :
( c_24__type__3430___24t(Vvar__3431)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3431,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34301',axiom,
! [Vvar__34302] :
( c_24__type__34301___24t(Vvar__34302)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__34302,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34321',axiom,
! [Vvar__34322] :
( c_24__type__34321___24t(Vvar__34322)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34322,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34351',axiom,
! [Vvar__34352] :
( c_24__type__34351___24t(Vvar__34352)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34352,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34387',axiom,
! [Vvar__34388] :
( c_24__type__34387___24t(Vvar__34388)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__34388,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34392',axiom,
! [Vvar__34393] :
( c_24__type__34392___24t(Vvar__34393)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__34393,Vv__CANONICAL__0)) ) ) ).
fof('$_type_345',axiom,
! [Vvar__346] :
( c_24__type__345___24t(Vvar__346)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__346,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34715] :
( c_24__type__34714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34715)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__34715,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34724',axiom,
! [Vvar__34725] :
( c_24__type__34724___24t(Vvar__34725)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3375___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__34725,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_349',axiom,
! [Vvar__350] :
( c_24__type__349___24t(Vvar__350)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__350,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35',axiom,
! [Vvar__36] :
( c_24__type__35___24t(Vvar__36)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__36,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35098',axiom,
! [Vv__CANONICAL__0,Vvar__35099] :
( c_24__type__35098___24t(Vv__CANONICAL__0,Vvar__35099)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__35100___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__35099,Vv__CANONICAL__1)) ) ) ).
fof('$_type_35114',axiom,
! [Vvar__35115] :
( c_24__type__35114___24t(Vvar__35115)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2etrue,happ(Vvar__35115,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_35117',axiom,
! [Vvar__35118] :
( c_24__type__35117___24t(Vvar__35118)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( ~ p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efalse,happ(Vvar__35118,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_35134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35135] :
( c_24__type__35134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35135)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cType___24t(happ(happ(Vvar__35135,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_35159',axiom,
! [Vvar__35160] :
( c_24__type__35159___24t(Vvar__35160)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__35164___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__35170___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__35176___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__35160,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_35164',axiom,
! [Vv__CANONICAL__0,Vvar__35165] :
( c_24__type__35164___24t(Vv__CANONICAL__0,Vvar__35165)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cType___24t(happ(happ(Vvar__35165,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_35170',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35171] :
( c_24__type__35170___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35171)
<=> ( p(Vv__CANONICAL__0)
=> t(Vvar__35171,happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2etrue),cCoq_2eBool_2eBool_2eReflectT___24a1(Vv__CANONICAL__0))) ) ) ).
fof('$_type_35176',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35177] :
( c_24__type__35176___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35177)
<=> ( ~ p(Vv__CANONICAL__0)
=> t(Vvar__35177,happ(happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eBool_2eBool_2eReflectF___24a1(Vv__CANONICAL__0))) ) ) ).
fof('$_type_35181',axiom,
! [Vv__CANONICAL__0,Vvar__35182] :
( c_24__type__35181___24t(Vv__CANONICAL__0,Vvar__35182)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__35182,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_356',axiom,
! [Vvar__357] :
( c_24__type__356___24t(Vvar__357)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__357,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35642',axiom,
! [Vvar__35643] :
( c_24__type__35642___24t(Vvar__35643)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__35645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__35657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__35643,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_35645',axiom,
! [Vv__CANONICAL__0,Vvar__35646] :
( c_24__type__35645___24t(Vv__CANONICAL__0,Vvar__35646)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__35646,Vv__CANONICAL__1)) ) ) ).
fof('$_type_35657',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35658] :
( c_24__type__35657___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35658)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__35658,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_35891',axiom,
! [Vvar__35892] :
( c_24__type__35891___24t(Vvar__35892)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__800___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__805___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__814___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__35892,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_36203',axiom,
! [Vvar__36204] :
( c_24__type__36203___24t(Vvar__36204)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36208___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__36204,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36208',axiom,
! [Vv__CANONICAL__0,Vvar__36209] :
( c_24__type__36208___24t(Vv__CANONICAL__0,Vvar__36209)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__36209,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_36402',axiom,
! [Vvar__36403] :
( c_24__type__36402___24t(Vvar__36403)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__17866___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__10)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__36403,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_37101',axiom,
! [Vvar__37102] :
( c_24__type__37101___24t(Vvar__37102)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3375___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__37102,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__37329] :
( c_24__type__37328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__37329)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__37330___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(Vvar__37329,Vv__CANONICAL__2)) ) ) ).
fof('$_type_376',axiom,
! [Vvar__377] :
( c_24__type__376___24t(Vvar__377)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__377,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3776',axiom,
! [Vvar__3777] :
( c_24__type__3776___24t(Vvar__3777)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3777,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3797',axiom,
! [Vvar__3798] :
( c_24__type__3797___24t(Vvar__3798)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3798,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3805',axiom,
! [Vvar__3806] :
( c_24__type__3805___24t(Vvar__3806)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3806,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3808',axiom,
! [Vvar__3809] :
( c_24__type__3808___24t(Vvar__3809)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3809,Vv__CANONICAL__0)) ) ) ).
fof('$_type_383',axiom,
! [Vvar__384] :
( c_24__type__383___24t(Vvar__384)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__384,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38372] :
( c_24__type__38371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38372)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__38372,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38380',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38381] :
( c_24__type__38380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38381)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__38381,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38389',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38390] :
( c_24__type__38389___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38390)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__38391___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__38390,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38412',axiom,
! [Vvar__38413] :
( c_24__type__38412___24t(Vvar__38413)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__38424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(Vvar__38413,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_38424',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38425] :
( c_24__type__38424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38425)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__38426___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__38425,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38437',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38438] :
( c_24__type__38437___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38438)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__38439___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__38438,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38482] :
( c_24__type__38481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38482)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__38482,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38490',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38491] :
( c_24__type__38490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38491)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__38492___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__38491,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38506] :
( c_24__type__38505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38506)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__38507___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__38506,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38514',axiom,
! [Vvar__38515] :
( c_24__type__38514___24t(Vvar__38515)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> ( ~ p(Vv__CANONICAL__0)
=> t(happ(happ(Vvar__38515,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__1) ) ) ) ) ) ).
fof('$_type_3918',axiom,
! [Vvar__3919] :
( c_24__type__3918___24t(Vvar__3919)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3919,Vv__CANONICAL__0)) ) ) ).
fof('$_type_395',axiom,
! [Vvar__396] :
( c_24__type__395___24t(Vvar__396)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__396,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_39605',axiom,
! [Vvar__39606] :
( c_24__type__39605___24t(Vvar__39606)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__39607___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(Vvar__39606,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40067',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__40068] :
( c_24__type__40067___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__40068)
<=> ( ( p(Vv__CANONICAL__0)
| p(Vv__CANONICAL__1) )
=> cProp___24t(Vvar__40068) ) ) ).
fof('$_type_40129',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__40130] :
( c_24__type__40129___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__40130)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(Vvar__40130,Vv__CANONICAL__2)) ) ) ).
fof('$_type_40839',axiom,
! [Vvar__40840] :
( c_24__type__40839___24t(Vvar__40840)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__40840,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_40945',axiom,
! [Vvar__40946] :
( c_24__type__40945___24t(Vvar__40946)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__40946,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_411',axiom,
! [Vvar__412] :
( c_24__type__411___24t(Vvar__412)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__412,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_414',axiom,
! [Vvar__415] :
( c_24__type__414___24t(Vvar__415)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__415,Vv__CANONICAL__0)) ) ) ).
fof('$_type_41776',axiom,
! [Vvar__41777] :
( c_24__type__41776___24t(Vvar__41777)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__11] :
( c_24__type__5212___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__5212___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( c_24__type__5212___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( c_24__type__5226___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__14)
=> ! [Vv__CANONICAL__15] :
( c_24__type__5233___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__15)
=> ! [Vv__CANONICAL__16] :
( c_24__type__800___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__16)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16)
=> ( ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__19] :
( t(Vv__CANONICAL__19,Vv__CANONICAL__8)
=> ( p(happ(happ(Vv__CANONICAL__7,happ(Vv__CANONICAL__16,Vv__CANONICAL__18)),happ(Vv__CANONICAL__16,Vv__CANONICAL__19)))
=> happ(happ(Vv__CANONICAL__15,Vv__CANONICAL__18),Vv__CANONICAL__19) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
=> ! [Vv__CANONICAL__19] :
( t(Vv__CANONICAL__19,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__20] :
( t(Vv__CANONICAL__20,Vv__CANONICAL__8)
=> cCoq_2eBool_2eBool_2ereflect___24t(happ(happ(Vv__CANONICAL__7,happ(Vv__CANONICAL__16,Vv__CANONICAL__19)),happ(Vv__CANONICAL__16,Vv__CANONICAL__20)),happ(happ(Vv__CANONICAL__15,Vv__CANONICAL__19),Vv__CANONICAL__20),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__41777,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__15),Vv__CANONICAL__16),Vv__CANONICAL__19),Vv__CANONICAL__20)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_421',axiom,
! [Vvar__422] :
( c_24__type__421___24t(Vvar__422)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__422,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43224',axiom,
! [Vvar__43225] :
( c_24__type__43224___24t(Vvar__43225)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__43226___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__43225,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_43783',axiom,
! [Vvar__43784] :
( c_24__type__43783___24t(Vvar__43784)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__43784,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_43861',axiom,
! [Vvar__43862] :
( c_24__type__43861___24t(Vvar__43862)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__43862,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44501',axiom,
! [Vvar__44502] :
( c_24__type__44501___24t(Vvar__44502)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__44502,Vv__CANONICAL__0)) ) ) ).
fof('$_type_44521',axiom,
! [Vvar__44522] :
( c_24__type__44521___24t(Vvar__44522)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(happ(Vvar__44522,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_44616',axiom,
! [Vvar__44617] :
( c_24__type__44616___24t(Vvar__44617)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__44617,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_44643',axiom,
! [Vvar__44644] :
( c_24__type__44643___24t(Vvar__44644)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__44644,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_44756',axiom,
! [Vvar__44757] :
( c_24__type__44756___24t(Vvar__44757)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__9770___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__44761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__44757,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_44761',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44762] :
( c_24__type__44761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__44762)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__44762,Vv__CANONICAL__2)) ) ) ).
fof('$_type_44765',axiom,
! [Vvar__44766] :
( c_24__type__44765___24t(Vvar__44766)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__44766,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_45373',axiom,
! [Vvar__45374] :
( c_24__type__45373___24t(Vvar__45374)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__45380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__45374,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_45380',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__45381] :
( c_24__type__45380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__45381)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__45381,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_45404',axiom,
! [Vvar__45405] :
( c_24__type__45404___24t(Vvar__45405)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__45380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2eclause___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__45405,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_45433',axiom,
! [Vvar__45434] :
( c_24__type__45433___24t(Vvar__45434)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__45380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__45434,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_4591',axiom,
! [Vvar__4592] :
( c_24__type__4591___24t(Vvar__4592)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__383___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4592,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4593',axiom,
! [Vvar__4594] :
( c_24__type__4593___24t(Vvar__4594)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__383___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4594,Vv__CANONICAL__0)) ) ) ).
fof('$_type_46043',axiom,
! [Vvar__46044] :
( c_24__type__46043___24t(Vvar__46044)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9770___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__46044,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_461',axiom,
! [Vvar__462] :
( c_24__type__461___24t(Vvar__462)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__462,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4663',axiom,
! [Vvar__4664] :
( c_24__type__4663___24t(Vvar__4664)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__4664,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4665',axiom,
! [Vvar__4666] :
( c_24__type__4665___24t(Vvar__4666)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__4666,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4713',axiom,
! [Vvar__4714] :
( c_24__type__4713___24t(Vvar__4714)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__4714,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_4733',axiom,
! [Vvar__4734] :
( c_24__type__4733___24t(Vvar__4734)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__4734,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4738',axiom,
! [Vvar__4739] :
( c_24__type__4738___24t(Vvar__4739)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4739,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4741',axiom,
! [Vv__CANONICAL__0,Vvar__4742] :
( c_24__type__4741___24t(Vv__CANONICAL__0,Vvar__4742)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__4742,Vv__CANONICAL__1)) ) ) ).
fof('$_type_4754',axiom,
! [Vvar__4755] :
( c_24__type__4754___24t(Vvar__4755)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__4755,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4766',axiom,
! [Vvar__4767] :
( c_24__type__4766___24t(Vvar__4767)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4767,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4769',axiom,
! [Vvar__4770] :
( c_24__type__4769___24t(Vvar__4770)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__4770,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4771',axiom,
! [Vvar__4772] :
( c_24__type__4771___24t(Vvar__4772)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4772,Vv__CANONICAL__0)) ) ) ).
fof('$_type_483',axiom,
! [Vvar__484] :
( c_24__type__483___24t(Vvar__484)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__484,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_48693',axiom,
! [Vvar__48694] :
( c_24__type__48693___24t(Vvar__48694)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__48694,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_48725',axiom,
! [Vvar__48726] :
( c_24__type__48725___24t(Vvar__48726)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(happ(Vvar__48726,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_49203',axiom,
! [Vvar__49204] :
( c_24__type__49203___24t(Vvar__49204)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__49205___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__49206___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__49204,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_49215',axiom,
! [Vvar__49216] :
( c_24__type__49215___24t(Vvar__49216)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(Vvar__49216,Vv__CANONICAL__0)) ) ) ).
fof('$_type_49292',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__49293] :
( c_24__type__49292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__49293)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__49293) ) ) ).
fof('$_type_49309',axiom,
! [Vvar__49310] :
( c_24__type__49309___24t(Vvar__49310)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__49310,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_49326',axiom,
! [Vvar__49327] :
( c_24__type__49326___24t(Vvar__49327)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__49330___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__49327,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_49330',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__49331] :
( c_24__type__49330___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__49331)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__49331,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_49390',axiom,
! [Vv__CANONICAL__0,Vvar__49391] :
( c_24__type__49390___24t(Vv__CANONICAL__0,Vvar__49391)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__49391,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_49393',axiom,
! [Vvar__49394] :
( c_24__type__49393___24t(Vvar__49394)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__49395___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__49396___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__49394,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_49398',axiom,
! [Vvar__49399] :
( c_24__type__49398___24t(Vvar__49399)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(Vvar__49399,Vv__CANONICAL__0)) ) ) ).
fof('$_type_49401',axiom,
! [Vvar__49402] :
( c_24__type__49401___24t(Vvar__49402)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__49403___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__49404___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__49402,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_49410',axiom,
! [Vvar__49411] :
( c_24__type__49410___24t(Vvar__49411)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__49411,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4999',axiom,
! [Vvar__5000] :
( c_24__type__4999___24t(Vvar__5000)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__5000,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5004',axiom,
! [Vvar__5005] :
( c_24__type__5004___24t(Vvar__5005)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__5005,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5012',axiom,
! [Vvar__5013] :
( c_24__type__5012___24t(Vvar__5013)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__5013,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_503',axiom,
! [Vvar__504] :
( c_24__type__503___24t(Vvar__504)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__504,Vv__CANONICAL__0)) ) ) ).
fof('$_type_508',axiom,
! [Vvar__509] :
( c_24__type__508___24t(Vvar__509)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__509,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5134',axiom,
! [Vv__CANONICAL__0,Vvar__5135] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vvar__5135)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5135,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_521',axiom,
! [Vvar__522] :
( c_24__type__521___24t(Vvar__522)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__522,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5212',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5213] :
( c_24__type__5212___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5213)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__5213,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_5226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5227] :
( c_24__type__5226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5227)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__5227,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_5233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5234] :
( c_24__type__5233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5234)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5234,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_531',axiom,
! [Vvar__532] :
( c_24__type__531___24t(Vvar__532)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__532,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5321',axiom,
! [Vv__CANONICAL__0,Vvar__5322] :
( c_24__type__5321___24t(Vv__CANONICAL__0,Vvar__5322)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5322,Vv__CANONICAL__1)) ) ) ).
fof('$_type_534',axiom,
! [Vvar__535] :
( c_24__type__534___24t(Vvar__535)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__535,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_539',axiom,
! [Vvar__540] :
( c_24__type__539___24t(Vvar__540)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__540,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5526',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5527] :
( c_24__type__5526___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5527)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5527,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5619',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5620] :
( c_24__type__5619___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5620)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5620,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5712',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5713] :
( c_24__type__5712___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5713)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5713,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5794',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5795] :
( c_24__type__5794___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5795)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5795,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_5887',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5888] :
( c_24__type__5887___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5888)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5888,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5969',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5970] :
( c_24__type__5969___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5970)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5970,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_6062',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6063] :
( c_24__type__6062___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6063)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__6063,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_780',axiom,
! [Vv__CANONICAL__0,Vvar__781] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vvar__781)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__781,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7831',axiom,
! [Vvar__7832] :
( c_24__type__7831___24t(Vvar__7832)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__7832,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__801] :
( c_24__type__800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__801)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__801,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_805',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__806] :
( c_24__type__805___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__806)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__806,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_814',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__815] :
( c_24__type__814___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__815)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__815,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8599',axiom,
! [Vvar__8600] :
( c_24__type__8599___24t(Vvar__8600)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__8600,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8619',axiom,
! [Vvar__8620] :
( c_24__type__8619___24t(Vvar__8620)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__8620,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8838',axiom,
! [Vvar__8839] :
( c_24__type__8838___24t(Vvar__8839)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__169___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__800___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__805___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__814___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__8839,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_9157',axiom,
! [Vvar__9158] :
( c_24__type__9157___24t(Vvar__9158)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__9158,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9205',axiom,
! [Vvar__9206] :
( c_24__type__9205___24t(Vvar__9206)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__780___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5134___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(Vvar__9206,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_9609',axiom,
! [Vvar__9610] :
( c_24__type__9609___24t(Vvar__9610)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__9610,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9687',axiom,
! [Vv__CANONICAL__0,Vvar__9688] :
( c_24__type__9687___24t(Vv__CANONICAL__0,Vvar__9688)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__9689___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__9690___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__9688,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_9704',axiom,
! [Vvar__9705] :
( c_24__type__9704___24t(Vvar__9705)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9687___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__9705,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_9767',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9768] :
( c_24__type__9767___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9768)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9768,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9770',axiom,
! [Vv__CANONICAL__0,Vvar__9771] :
( c_24__type__9770___24t(Vv__CANONICAL__0,Vvar__9771)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9771,Vv__CANONICAL__1)) ) ) ).
fof('$_type_9804',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9805] :
( c_24__type__9804___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9805)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9805,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9834',axiom,
! [Vvar__9835] :
( c_24__type__9834___24t(Vvar__9835)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__9835,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9851',axiom,
! [Vvar__9852] :
( c_24__type__9851___24t(Vvar__9852)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__9852,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9960',axiom,
! [Vvar__9961] :
( c_24__type__9960___24t(Vvar__9961)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__9961,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9965',axiom,
! [Vvar__9966] :
( c_24__type__9965___24t(Vvar__9966)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__9966,Vv__CANONICAL__0)) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__30990___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__521___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__521___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.Wf_nat.has_unique_least_element',axiom,
c_24__type__46043___24t(cCoq_2eArith_2eWf__nat_2ehas__unique__least__element) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__1081___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.ReflectF',axiom,
c_24__type__35117___24t(cCoq_2eBool_2eBool_2eReflectF) ).
fof('$_typeof_Coq.Bool.Bool.ReflectT',axiom,
c_24__type__35114___24t(cCoq_2eBool_2eBool_2eReflectT) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__349___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__26587___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bool.reflect_dec',axiom,
c_24__type__39605___24t(cCoq_2eBool_2eBool_2ereflect__dec) ).
fof('$_typeof_Coq.Bool.Bool.reflect_rec',axiom,
c_24__type__35159___24t(cCoq_2eBool_2eBool_2ereflect__rec) ).
fof('$_typeof_Coq.Bool.Bool.reflect_rect',axiom,
c_24__type__35159___24t(cCoq_2eBool_2eBool_2ereflect__rect) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__9834___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Empty',axiom,
c_24__type__24568___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__24980___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__24977___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__24787___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__24980___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.add',axiom,
c_24__type__24810___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
c_24__type__24980___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.fold',axiom,
c_24__type__24969___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.inter',axiom,
c_24__type__24857___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__1060___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.remove',axiom,
c_24__type__24810___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.singleton',axiom,
c_24__type__49215___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.union',axiom,
c_24__type__24857___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__4769___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__4665___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__356___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__4663___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__349___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__4766___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_typeof_Coq.Init.Datatypes.bool',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_typeof_Coq.Init.Datatypes.comparison',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2ecomparison) ).
fof('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__4738___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__31150___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__4754___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__24___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__35642___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.list_rect',axiom,
c_24__type__35642___24t(cCoq_2eInit_2eDatatypes_2elist__rect) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__1077___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__4733___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__24___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__349___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__411___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__395___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__4713___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).
fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__31514___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2ediv) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__9851___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__9834___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__9851___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__9834___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__356___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__508___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__9851___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__521___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__521___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__521___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.absurd_set',axiom,
c_24__type__38514___24t(cCoq_2eInit_2eSpecif_2eabsurd__set) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__22569___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__33744___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__33818___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__33823___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__22575___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__22580___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__22551___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__29081___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__3401___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__29158___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__23116___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__9609___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.count_occ',axiom,
c_24__type__9704___24t(cCoq_2eLists_2eList_2ecount__occ) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__37101___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__31380___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__31327___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__49326___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__22516___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__43783___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.findA',axiom,
c_24__type__34724___24t(cCoq_2eLists_2eSetoidList_2efindA) ).
fof('$_typeof_Coq.Lists.SetoidList.removeA',axiom,
c_24__type__38412___24t(cCoq_2eLists_2eSetoidList_2eremoveA) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__22466___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__22466___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__30662___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__30662___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.Minimal',axiom,
c_24__type__4591___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimal) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.Minimization_Property',axiom,
c_24__type__4593___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.weak_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__4771___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
c_24__type__29538___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__3805___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__3805___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__3805___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__34219___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__48693___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__414___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__24699___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__3797___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.gcd',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.leb',axiom,
c_24__type__24699___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eleb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__414___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__3797___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__414___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__421___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__414___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__24699___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__30955___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__24728___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__503___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_typeof_Coq.Numbers.BinNums.Z',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_typeof_Coq.Numbers.BinNums.Z0',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__35___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__35___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_typeof_Coq.Numbers.BinNums.positive',axiom,
cType___24t(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_typeof_Coq.Numbers.BinNums.xH',axiom,
cCoq_2eNumbers_2eBinNums_2epositive___24t(cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__345___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__345___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.ge',axiom,
c_24__type__3776___24t(cCoq_2ePArith_2eBinPos_2ePos_2ege) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__3776___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__3776___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__461___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__34301___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare_cont',axiom,
c_24__type__48725___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__34321___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.leb',axiom,
c_24__type__34321___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__461___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__24757___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__24757___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred',axiom,
c_24__type__345___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred_double',axiom,
c_24__type__345___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__461___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__345___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__34351___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__171___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__9965___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qeq',axiom,
c_24__type__534___24t(cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('$_typeof_Coq.QArith.QArith_base.Qle',axiom,
c_24__type__534___24t(cCoq_2eQArith_2eQArith__base_2eQle) ).
fof('$_typeof_Coq.QArith.QArith_base.Qlt',axiom,
c_24__type__534___24t(cCoq_2eQArith_2eQArith__base_2eQlt) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__531___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmult',axiom,
c_24__type__539___24t(cCoq_2eQArith_2eQArith__base_2eQmult) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__9960___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Req_EM_T',axiom,
c_24__type__49393___24t(cCoq_2eReals_2eRIneq_2eReq__EM__T) ).
fof('$_typeof_Coq.Reals.RIneq.Rle_dec',axiom,
c_24__type__43224___24t(cCoq_2eReals_2eRIneq_2eRle__dec) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__2465___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.Raxioms.INR',axiom,
c_24__type__10008___24t(cCoq_2eReals_2eRaxioms_2eINR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__2473___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__2463___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__2468___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__2468___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__2465___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__2468___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__2468___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__2463___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__2463___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__2465___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__2463___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__29570___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__24428___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rfunctions.intP',axiom,
c_24__type__49398___24t(cCoq_2eReals_2eRfunctions_2eintP) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__22381___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__24___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__22384___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__30985___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__33826___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.length',axiom,
c_24__type__44501___24t(cCoq_2eStrings_2eString_2elength) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Strings.String.substring',axiom,
c_24__type__44521___24t(cCoq_2eStrings_2eString_2esubstring) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__521___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__521___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__3776___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__3776___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__49203___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__3776___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__3776___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__3776___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
c_24__type__34387___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__34387___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__376___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__3430___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__25132___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.eqb',axiom,
c_24__type__483___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__25240___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__483___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
c_24__type__483___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__25240___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__3918___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__33___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
c_24__type__25225___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__195___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.testbit',axiom,
c_24__type__483___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__34392___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.ZArith_dec.Z_noteq_dec',axiom,
c_24__type__49401___24t(cCoq_2eZArith_2eZArith__dec_2eZ__noteq__dec) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__483___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__202___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__202___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__24766___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
c_24__type__521___24t(cCoq_2eZArith_2eZnat_2eneq) ).
fof('$_typeof_Coq.ZArith.Znumtheory.rel_prime',axiom,
c_24__type__198___24t(cCoq_2eZArith_2eZnumtheory_2erel__prime) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__24___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__5012___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__4999___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__5004___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__24___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__32115___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__10042___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__24___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
c_24__type__24___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__24___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__24___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__33264___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__15783___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__33344___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__33869___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.Cj',axiom,
c_24__type__44616___24t(cCoq_2emicromega_2eTauto_2eCj) ).
fof('$_typeof_Coq.micromega.Tauto.D',axiom,
c_24__type__44616___24t(cCoq_2emicromega_2eTauto_2eD) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__33834___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__22645___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__23055___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.Tauto.N',axiom,
c_24__type__44643___24t(cCoq_2emicromega_2eTauto_2eN) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__33834___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__33852___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__395___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__395___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
c_24__type__44765___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).
fof('$_typeof_Coq.micromega.Tauto.eval_clause',axiom,
c_24__type__45404___24t(cCoq_2emicromega_2eTauto_2eeval__clause) ).
fof('$_typeof_Coq.micromega.Tauto.eval_cnf',axiom,
c_24__type__45433___24t(cCoq_2emicromega_2eTauto_2eeval__cnf) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__44756___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__45373___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
c_24__type__31287___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.Add',axiom,
c_24__type__24631___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb',axiom,
c_24__type__34321___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb) ).
fof('$_typeof_Coq.micromega.ZMicromega.Zeval_op2',axiom,
c_24__type__49410___24t(cCoq_2emicromega_2eZMicromega_2eZeval__op2) ).
fof('$_typeof_Coq.micromega.ZMicromega.isZ0',axiom,
c_24__type__25240___24t(cCoq_2emicromega_2eZMicromega_2eisZ0) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__31196___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__31196___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__31202___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEadd',axiom,
c_24__type__31207___24t(cCoq_2esetoid__ring_2eField__theory_2eFEadd) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__31199___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEdiv',axiom,
c_24__type__31207___24t(cCoq_2esetoid__ring_2eField__theory_2eFEdiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__31210___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__31207___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEopp',axiom,
c_24__type__31210___24t(cCoq_2esetoid__ring_2eField__theory_2eFEopp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEpow',axiom,
c_24__type__40839___24t(cCoq_2esetoid__ring_2eField__theory_2eFEpow) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEsub',axiom,
c_24__type__31207___24t(cCoq_2esetoid__ring_2eField__theory_2eFEsub) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__24___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__36203___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons00',axiom,
c_24__type__36402___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons00) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fcons2',axiom,
c_24__type__36402___24t(cCoq_2esetoid__ring_2eField__theory_2eFcons2) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__35891___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEmul',axiom,
c_24__type__7831___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__8838___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.absurd_PCond',axiom,
c_24__type__40945___24t(cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.ceqb_spec\'',axiom,
c_24__type__41776___24t(cCoq_2esetoid__ring_2eField__theory_2eceqb__spec_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__8619___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__8599___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__24___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__49309___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__8599___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__9157___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__9157___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__9157___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.split',axiom,
c_24__type__9205___24t(cCoq_2esetoid__ring_2eField__theory_2esplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__414___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__421___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__1337___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__1297___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__1297___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__31287___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__33359___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__33359___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__17411___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__17416___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__17408___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__17618___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__17416___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__17425___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__33364___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__17416___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__24___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__17061___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__24___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.interp_PElist',axiom,
c_24__type__18104___24t(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
c_24__type__18289___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__17848___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__18883___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__2494___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_DirectedSets.DS_ord',axiom,
c_24__type__253___24t(cDirectedSets_2eDS__ord) ).
fof('$_typeof_DirectedSets.DS_set',axiom,
c_24__type__283___24t(cDirectedSets_2eDS__set) ).
fof('$_typeof_DirectedSets.DirectedSet',axiom,
cType___24t(cDirectedSets_2eDirectedSet) ).
fof('$_typeof_DirectedSets.for_large.eventually',axiom,
c_24__type__223___24t(cDirectedSets_2efor__large_2eeventually) ).
fof('$_typeof_DirectedSets.for_large.exists_arbitrarily_large',axiom,
c_24__type__223___24t(cDirectedSets_2efor__large_2eexists__arbitrarily__large) ).
fof('$_typeof_I',axiom,
cDirectedSets_2eDirectedSet___24t(cI) ).
fof('Coq.Arith.Between.between_ind',axiom,
! [V0__P] :
( c_24__type__383___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__P] :
( c_24__type__383___24t(V2__P)
=> ( p(happ(V2__P,V1__k))
=> ( ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V4__l)
=> ( p(happ(V2__P,V4__l))
=> ( p(happ(V0__P,V4__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__l))) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V5__n)
=> p(happ(V2__P,V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.between_not_exists',axiom,
! [V0__P] :
( c_24__type__383___24t(V0__P)
=> ! [V1__Q] :
( c_24__type__383___24t(V1__Q)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V2__k,V3__l)
=> ( ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V2__k,V3__l,V5__n)
=> ( p(happ(V0__P,V5__n))
=> ~ p(happ(V1__Q,V5__n)) ) ) )
=> ~ cCoq_2eArith_2eBetween_2eexists__between___24a3(V1__Q,V2__k,V3__l) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.exists_S_le',axiom,
! [V0__Q] :
( c_24__type__383___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__l))
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V2__l) ) ) ) ) ).
fof('Coq.Arith.Between.exists_in_int',axiom,
! [V0__Q] :
( c_24__type__383___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l)
=> cCoq_2eInit_2eLogic_2eex2___24a3(cCoq_2eInit_2eDatatypes_2enat,c_24__lam__39314___24a2(V1__k,V2__l),c_24__lam__39316___24a1(V0__Q)) ) ) ) ) ).
fof('Coq.Arith.Between.exists_le_S',axiom,
! [V0__Q] :
( c_24__type__383___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),V2__l) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_S',axiom,
! [V0__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__r)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
=> cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__q),V2__r) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_exists',axiom,
! [V0__Q] :
( c_24__type__383___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ! [V3__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__r)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V1__k,V2__l,V3__r)
=> ( p(happ(V0__Q,V3__r))
=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_intro',axiom,
! [V0__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__r)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q)
=> cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r) ) ) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_asym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Gt.gt_irrefl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Gt.le_not_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.le_not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Lt.lt_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_Sm_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.lt_not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.Lt.nat_total_order',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Parity.Odd_0',axiom,
~ cCoq_2eArith_2ePeanoNat_2eNat_2eOdd___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_le_mono',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__q)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__p,V3__q)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V2__p),cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V3__q)) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__508,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__356,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2eadd) ).
fof('Coq.Arith.PeanoNat.Nat.case_analysis',axiom,
! [V0__A] :
( c_24__type__383___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__383,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n))) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__24719___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_dne',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_mul_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eO
<=> ( V0__n = cCoq_2eInit_2eDatatypes_2eO
| V1__m = cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
& V0__n != V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ngt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__521,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__383,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_asymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> V0__n != V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_nge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__521,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__383,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2elt) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__508,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__356,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2emul) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0',axiom,
~ ! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.PeanoNat.Nat.nle_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.nlt_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pow_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__508,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__356,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2epow) ).
fof('Coq.Arith.PeanoNat.Nat.pred_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.pred_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__356,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eNat_2epred) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj_wd_neg',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)
<=> V0__n != V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__356,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2eS) ).
fof('Coq.Arith.PeanoNat.Nat.two_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.Arith.Plus.n_SSSSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)))) ) ).
fof('Coq.Arith.Plus.n_SSSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.Plus.n_SSn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.Plus.succ_plus_discr',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n)) ) ) ).
fof('Coq.Arith.Wf_nat.dec_inh_nat_subset_has_unique_least_element',axiom,
! [V0__P] :
( c_24__type__383___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(happ(V0__P,V1__n))
| ~ p(happ(V0__P,V1__n)) ) )
=> ( ? [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
& p(happ(V0__P,V2__n)) )
=> cCoq_2eArith_2eWf__nat_2ehas__unique__least__element___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele,V0__P) ) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( p(c_24False)
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Bool.Bool.diff_true_false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('Coq.Bool.Bool.no_fixpoint_negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) != V0__b ) ).
fof('Coq.Bool.Bool.not_true_iff_false',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2etrue
<=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.not_true_is_false',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2etrue
=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.reflect_ind',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__P] :
( c_24__type__35181___24t(V0__P,V1__P)
=> ( ( p(V0__P)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2etrue),cCoq_2eBool_2eBool_2eReflectT___24a1(V0__P))) )
=> ( ( ~ p(V0__P)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eBool_2eBool_2eReflectF___24a1(V0__P))) )
=> ! [V4__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b)
=> ! [V5__r] :
( cCoq_2eBool_2eBool_2ereflect___24t(V0__P,V4__b,V5__r)
=> p(happ(happ(V1__P,V4__b),V5__r)) ) ) ) ) ) ) ).
fof('Coq.Bool.Bool.reflect_sind',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__P] :
( c_24__type__35181___24t(V0__P,V1__P)
=> ( ( p(V0__P)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2etrue),cCoq_2eBool_2eBool_2eReflectT___24a1(V0__P))) )
=> ( ( ~ p(V0__P)
=> p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eBool_2eBool_2eReflectF___24a1(V0__P))) )
=> ! [V4__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V4__b)
=> ! [V5__r] :
( cCoq_2eBool_2eBool_2ereflect___24t(V0__P,V4__b,V5__r)
=> p(happ(happ(V1__P,V4__b),V5__r)) ) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.comparison_eq_stable',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ~ ( V0__c != V1__c_27 )
=> V0__c = V1__c_27 ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4741___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__383___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.O_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__49390___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_0_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.n_Sn',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n != cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) ) ).
fof('Coq.Init.Peano.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__521___24t(V0__R)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.not_eq_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Init.Tactics.decide_left',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ! [V1__decide] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__C,c_24__prop__35096___24a1(V0__C),V1__decide)
=> ( p(V0__C)
=> ! [V3__P] :
( c_24__type__35098___24t(V0__C,V3__P)
=> ( ( p(V0__C)
=> p(happ(V3__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__C,c_24__prop__35101___24a1(V0__C)))) )
=> p(happ(V3__P,V1__decide)) ) ) ) ) ) ).
fof('Coq.Init.Tactics.decide_right',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ! [V1__decide] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__C,c_24__prop__38516___24a1(V0__C),V1__decide)
=> ( ~ p(V0__C)
=> ! [V3__P] :
( c_24__type__35098___24t(V0__C,V3__P)
=> ( ( ~ p(V0__C)
=> p(happ(V3__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__C,c_24__prop__38518___24a1(V0__C)))) )
=> p(happ(V3__P,V1__decide)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_Forall_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
| ~ p(happ(V1__P,V3__x)) ) )
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,c_24__lam__34996___24a2(V0__A,V1__P),V2__l)
<=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.Exists_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_exists',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V2__l)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l)
& p(happ(V1__P,V3__x)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_Exists_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,c_24__lam__42991___24a2(V0__A,V1__P),V2__l)
<=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V2__l) ) ) ) ) ).
fof('Coq.Lists.List.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l_27)
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l)
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.in_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__a] :
( t(V1__a,V0__A)
=> ~ cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__a,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.neg_Forall_Exists_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3___24Anonymous] :
( c_24__type__37328___24t(V0__A,V1__P,V3___24Anonymous)
=> ( ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,c_24__lam__37334___24a2(V0__A,V1__P),V2__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_eqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__eqA,V4__x),V5__y))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__y,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqasym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__eqA) ) ) ) ).
fof('Coq.Lists.SetoidList.removeA_InA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__eqA__dec] :
( c_24__type__38505___24t(V0__A,V1__eqA,V3__eqA__dec)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V3__eqA__dec,V5__x,V4__l))
<=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V6__y,V4__l)
& ~ p(happ(happ(V1__eqA,V5__x),V6__y)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.removeA_filter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__22___24t(V0__A,V1__eqA)
=> ! [V2__eqA__dec] :
( c_24__type__38437___24t(V0__A,V1__eqA,V2__eqA__dec)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V3__x,V4__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,c_24__lam__38465___24a4(V0__A,V1__eqA,V2__eqA__dec,V3__x),V4__l) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.excluded_middle_entails_unrestricted_minimization',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__P] :
( c_24__type__383___24t(V1__P)
=> cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V1__P) ) ) ).
fof('Coq.Logic.ClassicalFacts.or_indd',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__40067___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eLogic_2eor__introl___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eLogic_2eor__intror___24a2(V0__A,V1__B))) )
=> ( ( p(V0__A)
| p(V1__B) )
=> p(V2__P) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.p2p1',axiom,
! [V0__or] :
( c_24__type__31022___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__P] :
( c_24__type__31085___24t(V0__or,V5__A,V6__B,V7__P)
=> ( ( p(V5__A)
=> p(V7__P) )
=> ( ( p(V6__B)
=> p(V7__P) )
=> ( p(happ(happ(V0__or,V5__A),V6__B))
=> p(V7__P) ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> p(happ(happ(V0__or,V6__A),c_24__prop__35256___24a1(V6__A))) )
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ( p(V7__B)
=> ( p(V7__B)
=> ! [V10__A] :
( cProp___24t(V10__A)
=> ( p(V10__A)
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.p2p2',axiom,
! [V0__or] :
( c_24__type__31022___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V5__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__P] :
( c_24__type__31085___24t(V0__or,V5__A,V6__B,V7__P)
=> ( ( p(V5__A)
=> p(V7__P) )
=> ( ( p(V6__B)
=> p(V7__P) )
=> ( p(happ(happ(V0__or,V5__A),V6__B))
=> p(V7__P) ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> p(happ(happ(V0__or,V6__A),c_24__prop__39674___24a1(V6__A))) )
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ( p(V7__B)
=> ( p(V7__B)
=> ( c_24Proof != c_24Proof
=> ! [V11__A] :
( cProp___24t(V11__A)
=> ( c_24Proof = c_24Proof
=> p(V11__A) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__31022___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__C] :
( cProp___24t(V7__C)
=> ( ( p(V5__A)
=> p(V7__C) )
=> ( ( p(V6__B)
=> p(V7__C) )
=> ( p(V6__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ! [V8__P] :
( c_24__type__31085___24t(V0__or,V6__A,V7__B,V8__P)
=> ( ( p(V6__A)
=> p(V8__P) )
=> ( ( p(V7__B)
=> p(V8__P) )
=> ( p(happ(happ(V0__or,V6__A),V7__B))
=> p(V8__P) ) ) ) ) ) )
=> ( ! [V7__A] :
( cProp___24t(V7__A)
=> p(happ(happ(V0__or,V7__A),c_24__prop__31110___24a1(V7__A))) )
=> ! [V8__B] :
( cProp___24t(V8__B)
=> ( p(V8__B)
=> ( p(V8__B)
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cci',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V1__B)
=> ( p(V1__B)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.unrestricted_minimization_entails_excluded_middle',axiom,
( ! [V0__P] :
( c_24__type__383___24t(V0__P)
=> cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V0__P) )
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ( p(V1__A)
| ~ p(V1__A) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wem_proof_irrelevance_cci',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( ~ ~ p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V1__B)
=> ( p(V1__B)
=> ~ ( c_24Proof != c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wp2p1',axiom,
! [V0__or] :
( c_24__type__31022___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__P] :
( c_24__type__31085___24t(V0__or,V5__A,V6__B,V7__P)
=> ( ( p(V5__A)
=> p(V7__P) )
=> ( ( p(V6__B)
=> p(V7__P) )
=> ( p(happ(happ(V0__or,V5__A),V6__B))
=> p(V7__P) ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> p(happ(happ(V0__or,c_24__prop__39758___24a1(V6__A)),c_24__prop__39759___24a1(V6__A))) )
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ( p(V7__B)
=> ( p(V7__B)
=> ! [V10__A] :
( cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eNProp___24t(V10__A)
=> ( cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eEl___24a1(V10__A)
=> cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eEl___24a1(cCoq_2eInit_2eSpecif_2eexist___24a4(cProp,c_24__lam__35333,c_24__prop__39762___24a3(V0__or,V7__B,V10__A),c_24__lam__35545___24a3(V0__or,V7__B,V10__A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wp2p2',axiom,
! [V0__or] :
( c_24__type__31022___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V5__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__P] :
( c_24__type__31085___24t(V0__or,V5__A,V6__B,V7__P)
=> ( ( p(V5__A)
=> p(V7__P) )
=> ( ( p(V6__B)
=> p(V7__P) )
=> ( p(happ(happ(V0__or,V5__A),V6__B))
=> p(V7__P) ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> p(happ(happ(V0__or,c_24__prop__35329___24a1(V6__A)),c_24__prop__35330___24a1(V6__A))) )
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ( p(V7__B)
=> ( p(V7__B)
=> ( c_24Proof != c_24Proof
=> ! [V11__A] :
( cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eNProp___24t(V11__A)
=> ( cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eEl___24a1(cCoq_2eInit_2eSpecif_2eexist___24a4(cProp,c_24__lam__35333,c_24__prop__35334___24a3(V0__or,V7__B,V11__A),c_24__lam__35545___24a3(V0__or,V7__B,V11__A)))
=> cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eEl___24a1(V11__A) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wproof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__31022___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__C] :
( cProp___24t(V7__C)
=> ( ( p(V5__A)
=> p(V7__C) )
=> ( ( p(V6__B)
=> p(V7__C) )
=> ( p(V6__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ! [V8__P] :
( c_24__type__31085___24t(V0__or,V6__A,V7__B,V8__P)
=> ( ( p(V6__A)
=> p(V8__P) )
=> ( ( p(V7__B)
=> p(V8__P) )
=> ( p(happ(happ(V0__or,V6__A),V7__B))
=> p(V8__P) ) ) ) ) ) )
=> ( ! [V7__A] :
( cProp___24t(V7__A)
=> p(happ(happ(V0__or,c_24__prop__40058___24a1(V7__A)),c_24__prop__40059___24a1(V7__A))) )
=> ! [V8__B] :
( cProp___24t(V8__B)
=> ( p(V8__B)
=> ( p(V8__B)
=> ~ ( c_24Proof != c_24Proof ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.all_not_not_ex',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__U,V1__P)
=> ( ! [V2__n] :
( t(V2__n,V0__U)
=> ~ p(happ(V1__P,V2__n)) )
=> ~ ? [V3__n] :
( t(V3__n,V0__U)
& p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.ex_not_not_all',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__U,V1__P)
=> ( ? [V2__n] :
( t(V2__n,V0__U)
& ~ p(happ(V1__P,V2__n)) )
=> ~ ! [V3__n] :
( t(V3__n,V0__U)
=> p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_not_ex',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> ~ p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_ex_all_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__U,V1__P)
=> ( ~ ? [V2__n] :
( t(V2__n,V0__U)
& p(happ(V1__P,V2__n)) )
=> ! [V3__n] :
( t(V3__n,V0__U)
=> ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_ex_not_all',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9770___24t(V0__U,V1__P)
=> ( ~ ? [V2__n] :
( t(V2__n,V0__U)
& ~ p(happ(V1__P,V2__n)) )
=> ! [V3__n] :
( t(V3__n,V0__U)
=> p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.and_not_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
& ~ p(V1__Q) )
=> ~ ( p(V0__P)
| p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ( p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ~ p(V0__P)
| p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_and_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
& p(V1__Q) )
=> ( ~ p(V0__P)
| ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ~ p(V1__Q) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_or_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
| p(V1__Q) )
=> ( ~ p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.or_not_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
| ~ p(V1__Q) )
=> ~ ( p(V0__P)
& p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.or_to_imply',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
| p(V1__Q) )
=> ( p(V0__P)
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Decidable.contrapositive',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> ( p(V1__B)
=> p(c_24False) ) )
<=> ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__34548___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__40154___24a1(V0__A)) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.imp_not_l',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> p(V1__B) )
<=> ( p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
& p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
=> ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> ( ~ ( p(V0__A)
<=> p(V1__B) )
=> ( ( p(V0__A)
& ~ p(V1__B) )
| ( ~ p(V0__A)
& p(V1__B) ) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_imp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
=> p(V1__B) )
=> ( p(V0__A)
& ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_imp_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ~ ~ p(V0__P)
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.not_not_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> p(c_24False) )
<=> p(V0__A) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_l_iff_1',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
| p(V1__B) )
<=> ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_l_iff_2',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> ( ( ( p(V0__A)
=> p(c_24False) )
| p(V1__B) )
<=> ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_r_iff_1',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
| ( p(V1__B)
=> p(c_24False) ) )
<=> ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_r_iff_2',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> ( ( p(V0__A)
| ( p(V1__B)
=> p(c_24False) ) )
<=> ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__49292___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__P] :
( c_24__type__49292___24t(V0__A,V1__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ( V1__x = V1__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.UIP_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__9687___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V1__x = V3__y
=> ( V1__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PropExt_imp_RefutPropExt',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) )
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ( ~ p(V1__A)
=> V1__A = c_24False ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.case_analysis',axiom,
! [V0__A] :
( c_24__type__3808___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3808,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ( p(happ(V0__A,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n))) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> p(happ(V0__A,V4__n)) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__48696___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.eq_dne',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3805,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__3808,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.lt_asymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
<=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> V0__n != V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V1__m))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0',axiom,
~ ! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_succ_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) != V0__n ) ).
fof('Coq.NArith.BinNat.N.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> V0__n != cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) ) ).
fof('Coq.NArith.BinNat.N.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.nle_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.nlt_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) ) ).
fof('Coq.NArith.BinNat.N.nlt_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V0__n) ) ).
fof('Coq.NArith.BinNat.N.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.sub_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__24766___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x)
=> p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x))
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.add_no_neutral',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) != V0__p ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__49207___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x),cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.PArith.BinPos.Pos.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.PArith.BinPos.Pos.lt_total',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q))
| V0__p = V1__q
| p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p)) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.nlt_1_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ~ p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,cCoq_2eNumbers_2eBinNums_2exH)) ) ).
fof('Coq.PArith.BinPos.Pos.sub_add',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p))
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__p,V1__q),V1__q) = V0__p ) ) ) ).
fof('Coq.PArith.BinPos.Pos.succ_discr',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> V0__p != cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V0__p) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.QArith.QArith_base.Qeq_sym',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y)
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.QArith.QArith_base.Qlt_irrefl',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ~ cCoq_2eQArith_2eQArith__base_2eQlt___24a2(V0__x,V0__x) ) ).
fof('Coq.QArith.QArith_base.Qlt_not_eq',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( cCoq_2eQArith_2eQArith__base_2eQlt___24a2(V0__x,V1__y)
=> ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.QArith.QArith_base.Qnot_eq_sym',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V1__y)
=> ( ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V1__y)
=> ~ cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V1__y,V0__x) ) ) ) ).
fof('Coq.QArith.Qreals.IZR_nz',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_dec',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
| V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_not_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r)) ) ).
fof('Coq.Reals.RIneq.Rgt_asym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
=> ~ cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r,V0__r) ) ).
fof('Coq.Reals.RIneq.Rgt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rle_not_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1))
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_dichotomy_converse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2) )
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> ~ cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_not_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1)
=> ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_eq_contra',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 != V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.Reals.RIneq.Rminus_not_eq_right',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V1__r2,V0__r1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_le_gt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_le_lt',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2))
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rnot_lt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> p(cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_0_r',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)) = V0__r ) ).
fof('Coq.Reals.RIneq.eq_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.lt_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n),cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m)) ) ) ) ).
fof('Coq.Reals.RIneq.not_0_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.Reals.RIneq.not_INR',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eReals_2eRaxioms_2eINR___24a1(V0__n) != cCoq_2eReals_2eRaxioms_2eINR___24a1(V1__m) ) ) ) ).
fof('Coq.Reals.Raxioms.R1_neq_R0',axiom,
cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.Reals.Raxioms.Rlt_asym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Reals.Raxioms.Rplus_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Strings.String.string_ind',axiom,
! [V0__P] :
( c_24__type__43861___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eStrings_2eString_2eEmptyString))
=> ( ! [V2__a] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V2__a)
=> ! [V3__s] :
( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> ( p(happ(V0__P,V3__s))
=> p(happ(V0__P,cCoq_2eStrings_2eString_2eString___24a2(V2__a,V3__s))) ) ) )
=> ! [V3__s] :
( cCoq_2eStrings_2eString_2estring___24t(V3__s)
=> p(happ(V0__P,V3__s)) ) ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.N_as_OT.lt_not_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> V0__n != V1__m ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_antirefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V0__x,V0__x) ) ).
fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_sym',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.Z_as_OT.lt_not_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> V0__x != V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_0_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__p,V3__q))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q))) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2eEq ) ).
fof('Coq.ZArith.BinInt.Z.divide_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ).
fof('Coq.ZArith.BinInt.Z.divide_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__34399___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_dne',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ ( V0__n != V1__m )
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ge_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.ge_le_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.gt_lt_iff',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ngt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__198,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__202,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.ZArith.BinInt.Z.lt_asymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> V0__n != V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_nge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n))) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_lt_mono_pos_r',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__p)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__p))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__n,V0__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__m,V0__p))) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__195,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__180,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2eeq,cCoq_2eZArith_2eBinInt_2eZ_2eeq)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('Coq.ZArith.BinInt.Z.neg_pos_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
& V1__m != cCoq_2eNumbers_2eBinNums_2eZ0 )
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_pred_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n) != V0__n ) ).
fof('Coq.ZArith.BinInt.Z.neq_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) != V0__n ) ).
fof('Coq.ZArith.BinInt.Z.neq_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> V0__n != cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.nle_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.nle_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.nlt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.nlt_square_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V0__n),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ).
fof('Coq.ZArith.BinInt.Z.nlt_succ_diag_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V0__n)) ) ).
fof('Coq.ZArith.BinInt.Z.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.ZArith.BinInt.Z.opp_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_involutive',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.opp_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.ZArith.BinInt.Z.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__b))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.sgn_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__180,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)),cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('Coq.ZArith.BinInt.Z.sub_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.two_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.ZArith.Zbool.Zeq_bool_if',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_2449414___24a2(V0__x,V1__y) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
=> V0__x != V1__y ) ) ) ).
fof('Coq.ZArith.Zlogarithm.Is_power_or',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V0__p)
| ~ cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V0__p) ) ) ).
fof('Coq.ZArith.Znumtheory.Zis_gcd_intro',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ! [V2__g] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__g)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__g,V1__b)
=> ( ! [V5__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V0__a)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V1__b)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V5__x,V2__g) ) ) )
=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,V2__g) ) ) ) ) ) ) ).
fof('Coq.ZArith.Znumtheory.not_prime_0',axiom,
~ cCoq_2eZArith_2eZnumtheory_2eprime___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.ZArith.Zorder.Zgt_asym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.Zorder.Zgt_irrefl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.Zorder.Zgt_not_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Zle_not_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Zle_not_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.Zorder.Zlt_not_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_ge_lt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_gt_le',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V0__n)) ) ).
fof('Coq.ZArith.Zorder.Znot_lt_ge',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.not_Zeq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.OrderedRing.Req_dne',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ~ ~ p(happ(happ(V7__req,V11__n),V12__m))
<=> p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Req_em',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V7__req,V11__n),V12__m))
| ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_gt_cases',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_le_minus',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
<=> p(happ(happ(V8__rle,V1__rO),happ(happ(V5__rminus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_lt_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_ngt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
<=> ~ p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_neq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
<=> ( p(happ(happ(V8__rle,V11__n),V12__m))
& ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_lt_minus',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
<=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V5__rminus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_neq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_nge',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
<=> ~ p(happ(happ(V8__rle,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trichotomy',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rminus_eq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V7__req,happ(happ(V5__rminus,V11__n),V12__m)),V1__rO))
<=> p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rneq_0_1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ~ p(happ(happ(V7__req,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rneq_symm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ~ p(happ(happ(V7__req,V11__n),V12__m))
=> ~ p(happ(happ(V7__req,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V1__rO))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ( ~ p(happ(happ(V7__req,V11__n),V1__rO))
& ~ p(happ(happ(V7__req,V12__m),V1__rO)) )
=> ~ p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORle_antisymm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V11__n))
=> p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORle_refl',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V11__n),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORle_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V8__rle,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORle_wd',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> ! [V14__y1] :
( t(V14__y1,V0__R)
=> ! [V15__y2] :
( t(V15__y2,V0__R)
=> ( p(happ(happ(V7__req,V14__y1),V15__y2))
=> ( p(happ(happ(V8__rle,V11__x1),V14__y1))
<=> p(happ(happ(V8__rle,V12__x2),V15__y2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORlt_le_neq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
<=> ( p(happ(happ(V8__rle,V11__n),V12__m))
& ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORlt_trichotomy',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORlt_wd',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> ! [V14__y1] :
( t(V14__y1,V0__R)
=> ! [V15__y2] :
( t(V15__y2,V0__R)
=> ( p(happ(happ(V7__req,V14__y1),V15__y2))
=> ( p(happ(happ(V9__rlt,V11__x1),V14__y1))
<=> p(happ(happ(V9__rlt,V12__x2),V15__y2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORneq_0_1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ~ p(happ(happ(V7__req,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORopp_wd',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> p(happ(happ(V7__req,happ(V6__ropp,V11__x1)),happ(V6__ropp,V12__x2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORplus_le_mono_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> p(happ(happ(V8__rle,happ(happ(V3__rplus,V13__p),V11__n)),happ(happ(V3__rplus,V13__p),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORplus_wd',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> ! [V14__y1] :
( t(V14__y1,V0__R)
=> ! [V15__y2] :
( t(V15__y2,V0__R)
=> ( p(happ(happ(V7__req,V14__y1),V15__y2))
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__x1),V14__y1)),happ(happ(V3__rplus,V12__x2),V15__y2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORrt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORsetoid',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORtimes_pos_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.SORtimes_wd',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> ! [V14__y1] :
( t(V14__y1,V0__R)
=> ! [V15__y2] :
( t(V15__y2,V0__R)
=> ( p(happ(happ(V7__req,V14__y1),V15__y2))
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__x1),V14__y1)),happ(happ(V4__rtimes,V12__x2),V15__y2))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.mk_SOR_theory',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req)
=> ( ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> ! [V14__y1] :
( t(V14__y1,V0__R)
=> ! [V15__y2] :
( t(V15__y2,V0__R)
=> ( p(happ(happ(V7__req,V14__y1),V15__y2))
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__x1),V14__y1)),happ(happ(V3__rplus,V12__x2),V15__y2))) ) ) ) ) ) )
=> ( ! [V12__x1] :
( t(V12__x1,V0__R)
=> ! [V13__x2] :
( t(V13__x2,V0__R)
=> ( p(happ(happ(V7__req,V12__x1),V13__x2))
=> ! [V15__y1] :
( t(V15__y1,V0__R)
=> ! [V16__y2] :
( t(V16__y2,V0__R)
=> ( p(happ(happ(V7__req,V15__y1),V16__y2))
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V12__x1),V15__y1)),happ(happ(V4__rtimes,V13__x2),V16__y2))) ) ) ) ) ) )
=> ( ! [V13__x1] :
( t(V13__x1,V0__R)
=> ! [V14__x2] :
( t(V14__x2,V0__R)
=> ( p(happ(happ(V7__req,V13__x1),V14__x2))
=> p(happ(happ(V7__req,happ(V6__ropp,V13__x1)),happ(V6__ropp,V14__x2))) ) ) )
=> ( ! [V14__x1] :
( t(V14__x1,V0__R)
=> ! [V15__x2] :
( t(V15__x2,V0__R)
=> ( p(happ(happ(V7__req,V14__x1),V15__x2))
=> ! [V17__y1] :
( t(V17__y1,V0__R)
=> ! [V18__y2] :
( t(V18__y2,V0__R)
=> ( p(happ(happ(V7__req,V17__y1),V18__y2))
=> ( p(happ(happ(V8__rle,V14__x1),V17__y1))
<=> p(happ(happ(V8__rle,V15__x2),V18__y2)) ) ) ) ) ) ) )
=> ( ! [V15__x1] :
( t(V15__x1,V0__R)
=> ! [V16__x2] :
( t(V16__x2,V0__R)
=> ( p(happ(happ(V7__req,V15__x1),V16__x2))
=> ! [V18__y1] :
( t(V18__y1,V0__R)
=> ! [V19__y2] :
( t(V19__y2,V0__R)
=> ( p(happ(happ(V7__req,V18__y1),V19__y2))
=> ( p(happ(happ(V9__rlt,V15__x1),V18__y1))
<=> p(happ(happ(V9__rlt,V16__x2),V19__y2)) ) ) ) ) ) ) )
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req)
=> ( ! [V17__n] :
( t(V17__n,V0__R)
=> p(happ(happ(V8__rle,V17__n),V17__n)) )
=> ( ! [V18__n] :
( t(V18__n,V0__R)
=> ! [V19__m] :
( t(V19__m,V0__R)
=> ( p(happ(happ(V8__rle,V18__n),V19__m))
=> ( p(happ(happ(V8__rle,V19__m),V18__n))
=> p(happ(happ(V7__req,V18__n),V19__m)) ) ) ) )
=> ( ! [V19__n] :
( t(V19__n,V0__R)
=> ! [V20__m] :
( t(V20__m,V0__R)
=> ! [V21__p] :
( t(V21__p,V0__R)
=> ( p(happ(happ(V8__rle,V19__n),V20__m))
=> ( p(happ(happ(V8__rle,V20__m),V21__p))
=> p(happ(happ(V8__rle,V19__n),V21__p)) ) ) ) ) )
=> ( ! [V20__n] :
( t(V20__n,V0__R)
=> ! [V21__m] :
( t(V21__m,V0__R)
=> ( p(happ(happ(V9__rlt,V20__n),V21__m))
<=> ( p(happ(happ(V8__rle,V20__n),V21__m))
& ~ p(happ(happ(V7__req,V20__n),V21__m)) ) ) ) )
=> ( ! [V21__n] :
( t(V21__n,V0__R)
=> ! [V22__m] :
( t(V22__m,V0__R)
=> ( p(happ(happ(V9__rlt,V21__n),V22__m))
| p(happ(happ(V7__req,V21__n),V22__m))
| p(happ(happ(V9__rlt,V22__m),V21__n)) ) ) )
=> ( ! [V22__n] :
( t(V22__n,V0__R)
=> ! [V23__m] :
( t(V23__m,V0__R)
=> ! [V24__p] :
( t(V24__p,V0__R)
=> ( p(happ(happ(V8__rle,V22__n),V23__m))
=> p(happ(happ(V8__rle,happ(happ(V3__rplus,V24__p),V22__n)),happ(happ(V3__rplus,V24__p),V23__m))) ) ) ) )
=> ( ! [V23__n] :
( t(V23__n,V0__R)
=> ! [V24__m] :
( t(V24__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V23__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V24__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V23__n),V24__m))) ) ) ) )
=> ( ~ p(happ(happ(V7__req,V1__rO),V2__rI))
=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rlt_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__9770___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.sor_setoid_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__9770___24t(V0__A,V1__eval)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
<=> ( p(happ(V1__eval,V2__a))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V3__l) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__t)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__9770___24t(V0__A,V3__eval)
=> ( ! [V4__d] :
( t(V4__d,V0__A)
=> ( p(happ(V3__eval,V4__d))
| ~ p(happ(V3__eval,V4__d)) ) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__t,V2__a))
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V1__t)
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( t(V1__t,V0__A)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__9770___24t(V0__A,V3__eval)
=> ( ( p(happ(V3__eval,V1__t))
| ~ p(happ(V3__eval,V1__t)) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__t,V2__a))
=> ( ~ p(happ(V3__eval,V1__t))
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORcleb_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__5212___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__5212___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__5212___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__5226___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__5233___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__5233___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__800___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__805___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> ! [V23__x] :
( t(V23__x,V9__C)
=> ! [V24__y] :
( t(V24__y,V9__C)
=> ( happ(happ(V17__cleb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V8__rle,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORcneqb_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__5212___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__5212___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__5212___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__5226___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__5233___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__5233___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__800___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__805___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> ! [V23__x] :
( t(V23__x,V9__C)
=> ! [V24__y] :
( t(V24__y,V9__C)
=> ( happ(happ(V16__ceqb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORpower',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__5212___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__5212___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__5212___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__5226___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__5233___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__5233___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__800___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__805___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rtimes,V7__req,V19__E,V20__pow__phi,V21__rpow) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.SORrm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__5212___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__5212___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__5212___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__5226___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__5233___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__5233___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__800___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__805___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.cneqb_sound',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__5212___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__5212___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__5212___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__5226___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__5233___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__5233___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__800___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__805___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
=> ! [V23__x] :
( t(V23__x,V9__C)
=> ! [V24__y] :
( t(V24__y,V9__C)
=> ( cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V9__C,V16__ceqb,V23__x,V24__y) = cCoq_2eInit_2eDatatypes_2etrue
=> ~ p(happ(happ(V7__req,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.mk_SOR_addon',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__5212___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__5212___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__5212___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__5226___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__5233___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__5233___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__800___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__805___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rtimes,V7__req,V19__E,V20__pow__phi,V21__rpow)
=> ( ! [V24__x] :
( t(V24__x,V9__C)
=> ! [V25__y] :
( t(V25__y,V9__C)
=> ( happ(happ(V16__ceqb,V24__x),V25__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,happ(V18__phi,V24__x)),happ(V18__phi,V25__y))) ) ) )
=> ( ! [V25__x] :
( t(V25__x,V9__C)
=> ! [V26__y] :
( t(V26__y,V9__C)
=> ( happ(happ(V17__cleb,V25__x),V26__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V8__rle,happ(V18__phi,V25__x)),happ(V18__phi,V26__y))) ) ) )
=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Tauto.no_middle_eval_tt',axiom,
! [V0__Env] :
( cType___24t(V0__Env)
=> ! [V1__Term_27] :
( cType___24t(V1__Term_27)
=> ! [V2__Annot] :
( cType___24t(V2__Annot)
=> ! [V3__eval_27] :
( c_24__type__45380___24t(V0__Env,V1__Term_27,V3__eval_27)
=> ( ! [V4__env] :
( t(V4__env,V0__Env)
=> ! [V5__d] :
( t(V5__d,V1__Term_27)
=> ( p(happ(happ(V3__eval_27,V4__env),V5__d))
| ~ p(happ(happ(V3__eval_27,V4__env),V5__d)) ) ) )
=> ! [V5__env] :
( t(V5__env,V0__Env)
=> ! [V6__a] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V1__Term_27,V2__Annot,V6__a)
=> ( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V5__env,V6__a)
| ~ cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V5__env,V6__a) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.Zcneqb_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V11__x)
=> ! [V12__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V12__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V11__x,V12__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V11__x)),cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V12__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.clt_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__780___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__780___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__780___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__22___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__22___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V11__x)
=> ! [V12__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V12__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V11__x,V12__y))
=> p(happ(happ(V9__rlt,cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V11__x)),cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V6__ropp,V12__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.add_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__y)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V1__x,V0__s)))
<=> ( V1__x = V2__y
| p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.diff_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ! [V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__x)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ediff___24a2(V0__s,V1__s_27)))
<=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s))
& ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V1__s_27)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.inter_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ! [V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__x)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V0__s,V1__s_27)))
<=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s))
& p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V1__s_27)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.remove_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__x)
=> ! [V2__y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__y)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V1__x,V0__s)))
<=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__y,V0__s))
& V1__x != V2__y ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.union_iff',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ! [V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__x)
=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V0__s,V1__s_27)))
<=> ( p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s))
| p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V1__s_27)) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_ind',axiom,
! [V0__P] :
( c_24__type__4771___24t(V0__P)
=> ( ! [V1__S] :
( cType___24t(V1__S)
=> ! [V2__x] :
( t(V2__x,V1__S)
=> ! [V3__y] :
( t(V3__y,V1__S)
=> p(happ(V0__P,c_24__prop__38520___24a3(V1__S,V2__x,V3__y))) ) ) )
=> ( ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> p(happ(V0__P,c_24__prop__38524___24a2(V2__x,V3__y))) ) )
=> ( ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ! [V4__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V4__s)
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V3__x,V4__s))) ) )
=> ( p(happ(V0__P,c_24True))
=> ( p(happ(V0__P,c_24False))
=> ( ! [V6__P] :
( cProp___24t(V6__P)
=> ! [V7__Q] :
( cProp___24t(V7__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V6__P)
=> ( p(happ(V0__P,V6__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__Q)
=> ( p(happ(V0__P,V7__Q))
=> p(happ(V0__P,c_24__prop__38529___24a2(V6__P,V7__Q))) ) ) ) ) ) )
=> ( ! [V7__P] :
( cProp___24t(V7__P)
=> ! [V8__Q] :
( cProp___24t(V8__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__P)
=> ( p(happ(V0__P,V7__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__Q)
=> ( p(happ(V0__P,V8__Q))
=> p(happ(V0__P,c_24__prop__38536___24a2(V7__P,V8__Q))) ) ) ) ) ) )
=> ( ! [V8__P] :
( cProp___24t(V8__P)
=> ! [V9__Q] :
( cProp___24t(V9__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__P)
=> ( p(happ(V0__P,V8__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__Q)
=> ( p(happ(V0__P,V9__Q))
=> p(happ(V0__P,c_24__prop__38543___24a2(V8__P,V9__Q))) ) ) ) ) ) )
=> ( ! [V9__P] :
( cProp___24t(V9__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__P)
=> ( p(happ(V0__P,V9__P))
=> p(happ(V0__P,c_24__prop__38551___24a1(V9__P))) ) ) )
=> ! [V10__P] :
( cProp___24t(V10__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V10__P)
=> p(happ(V0__P,V10__P)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_sind',axiom,
! [V0__P] :
( c_24__type__4771___24t(V0__P)
=> ( ! [V1__S] :
( cType___24t(V1__S)
=> ! [V2__x] :
( t(V2__x,V1__S)
=> ! [V3__y] :
( t(V3__y,V1__S)
=> p(happ(V0__P,c_24__prop__38555___24a3(V1__S,V2__x,V3__y))) ) ) )
=> ( ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> p(happ(V0__P,c_24__prop__38559___24a2(V2__x,V3__y))) ) )
=> ( ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ! [V4__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V4__s)
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V3__x,V4__s))) ) )
=> ( p(happ(V0__P,c_24True))
=> ( p(happ(V0__P,c_24False))
=> ( ! [V6__P] :
( cProp___24t(V6__P)
=> ! [V7__Q] :
( cProp___24t(V7__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V6__P)
=> ( p(happ(V0__P,V6__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__Q)
=> ( p(happ(V0__P,V7__Q))
=> p(happ(V0__P,c_24__prop__38564___24a2(V6__P,V7__Q))) ) ) ) ) ) )
=> ( ! [V7__P] :
( cProp___24t(V7__P)
=> ! [V8__Q] :
( cProp___24t(V8__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__P)
=> ( p(happ(V0__P,V7__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__Q)
=> ( p(happ(V0__P,V8__Q))
=> p(happ(V0__P,c_24__prop__38571___24a2(V7__P,V8__Q))) ) ) ) ) ) )
=> ( ! [V8__P] :
( cProp___24t(V8__P)
=> ! [V9__Q] :
( cProp___24t(V9__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__P)
=> ( p(happ(V0__P,V8__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__Q)
=> ( p(happ(V0__P,V9__Q))
=> p(happ(V0__P,c_24__prop__38578___24a2(V8__P,V9__Q))) ) ) ) ) ) )
=> ( ! [V9__P] :
( cProp___24t(V9__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__P)
=> ( p(happ(V0__P,V9__P))
=> p(happ(V0__P,c_24__prop__38586___24a1(V9__P))) ) ) )
=> ! [V10__P] :
( cProp___24t(V10__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V10__P)
=> p(happ(V0__P,V10__P)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.In_elt_prop',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ! [V1__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s)
=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__x,V1__s)) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_In',axiom,
! [V0__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V0__x)
=> ! [V1__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__x,V1__s)) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__49433___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_refl_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( V0__x = V0__x
<=> p(c_24True) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.not_elt_prop',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V0__P)
=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(c_24__prop__48261___24a1(V0__P)) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetLogicalFacts.test_pull',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__Q)
=> ( ~ p(c_24True)
=> ( ~ p(c_24False)
=> ( ~ ~ p(V0__P)
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
=> ~ p(V2__R) )
=> ( ( ( p(V0__P)
& p(V1__Q) )
| ~ p(V2__R) )
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
| p(V2__R) )
=> ( ( p(V2__R)
| ~ ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V2__R)
| ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V0__P)
=> p(V2__R) )
=> ( ( ~ ( p(V2__R)
=> p(V0__P) )
& ~ ( p(V1__Q)
=> p(V2__R) ) )
=> ( ( ~ p(V0__P)
| ~ p(V2__R) )
=> ( ( p(V0__P)
& ~ p(V2__R) )
=> ( ( ~ p(V2__R)
& p(V0__P) )
=> p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetLogicalFacts.test_push',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__Q)
=> ( ~ p(c_24True)
=> ( ~ p(c_24False)
=> ( ~ ~ p(V0__P)
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
=> ~ p(V2__R) )
=> ( ( ( p(V0__P)
& p(V1__Q) )
| ~ p(V2__R) )
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
| p(V2__R) )
=> ( ( p(V2__R)
| ~ ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V2__R)
| ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V0__P)
=> p(V2__R) )
=> ( ~ ( ( p(V2__R)
=> p(V0__P) )
| ( p(V1__Q)
=> p(V2__R) ) )
=> ( ~ ( p(V0__P)
& p(V2__R) )
=> ( ~ ( p(V0__P)
=> p(V2__R) )
=> p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.not_in_union',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> ! [V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V1__s_27)
=> ! [V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__x)
=> ( ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V0__s))
=> ( ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,V1__s_27))
=> ~ p(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__x,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V0__s,V1__s_27))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__P] :
( c_24__type__202___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__202___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__202___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__202___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__202___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.new_var',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& V0__x = V1__y ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_1_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ~ p(happ(happ(V9__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_AR',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFdiv_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ! [V12__q] :
( t(V12__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V11__p),V12__q)),happ(happ(V4__rmul,V11__p),happ(V8__rinv,V12__q)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFinv_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_1_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ~ p(happ(happ(V9__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_R',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.Fdiv_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ! [V12__q] :
( t(V12__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V11__p),V12__q)),happ(happ(V4__rmul,V11__p),happ(V8__rinv,V12__q)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.Finv_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.NPEequiv_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__phi] :
( c_24__type__800___24t(V0__R,V9__C,V10__phi)
=> ! [V11__Cpow] :
( cType___24t(V11__Cpow)
=> ! [V12__Cp__phi] :
( c_24__type__805___24t(V0__R,V9__C,V11__Cpow,V12__Cp__phi)
=> ! [V13__rpow] :
( c_24__type__814___24t(V0__R,V9__C,V11__Cpow,V13__rpow)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V9__C),cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a13(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V9__C,V10__phi,V11__Cpow,V12__Cp__phi,V13__rpow)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_cons',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__800___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__805___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__814___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__a] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,V14__a)
=> ! [V15__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__l1)
=> ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__l,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__a,V15__l1))
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__l,V14__a)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__l,V15__l1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PCond_cons_inv_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__phi] :
( c_24__type__800___24t(V0__R,V8__C,V9__phi)
=> ! [V10__Cpow] :
( cType___24t(V10__Cpow)
=> ! [V11__Cp__phi] :
( c_24__type__805___24t(V0__R,V8__C,V10__Cpow,V11__Cp__phi)
=> ! [V12__rpow] :
( c_24__type__814___24t(V0__R,V8__C,V10__Cpow,V12__rpow)
=> ! [V13__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V13__l)
=> ! [V14__a] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,V14__a)
=> ! [V15__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__l1)
=> ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__l,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V14__a,V15__l1))
=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__l,V14__a)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.PEpow_nz',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__C] :
( cType___24t(V13__C)
=> ! [V14__phi] :
( c_24__type__800___24t(V0__R,V13__C,V14__phi)
=> ! [V15__Cpow] :
( cType___24t(V15__Cpow)
=> ! [V16__Cp__phi] :
( c_24__type__805___24t(V0__R,V13__C,V15__Cpow,V16__Cp__phi)
=> ! [V17__rpow] :
( c_24__type__814___24t(V0__R,V13__C,V15__Cpow,V17__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rmul,V9__req,V15__Cpow,V16__Cp__phi,V17__rpow)
=> ! [V19__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V19__l)
=> ! [V20__e] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V13__C,V20__e)
=> ! [V21__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V21__n)
=> ( ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V13__C,V14__phi,V15__Cpow,V16__Cp__phi,V17__rpow,V19__l,V20__e)),V1__rO))
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V13__C,V14__phi,V15__Cpow,V16__Cp__phi,V17__rpow,V19__l,cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V13__C,V20__e,V21__n))),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__22___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__22___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3_Symmetric',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__22___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3_Transitive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__22___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SF_1_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__780___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__169___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> ~ p(happ(happ(V7__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SF_SR',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__780___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__169___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SFdiv_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__780___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__169___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> ! [V9__p] :
( t(V9__p,V0__R)
=> ! [V10__q] :
( t(V10__q,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rdiv,V9__p),V10__q)),happ(happ(V4__rmul,V9__p),happ(V6__rinv,V10__q)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SFinv_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__780___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__169___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> ! [V9__p] :
( t(V9__p,V0__R)
=> ( ~ p(happ(happ(V7__req,V9__p),V1__rO))
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(V6__rinv,V9__p)),V9__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.absurd_PCond_bottom',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5212___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5212___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5212___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5226___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5233___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__800___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__Cpow] :
( cType___24t(V18__Cpow)
=> ! [V19__Cp__phi] :
( c_24__type__805___24t(V0__R,V8__C,V18__Cpow,V19__Cp__phi)
=> ! [V20__rpow] :
( c_24__type__814___24t(V0__R,V8__C,V18__Cpow,V20__rpow)
=> ! [V21__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V21__l)
=> ~ cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V16__phi,V18__Cpow,V19__Cp__phi,V20__rpow,V21__l,cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond___24a2(V8__C,V9__cO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.cross_product_eq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V15__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V17__d),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b)))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V14__a),V15__b)),happ(happ(V7__rdiv,V16__c),V17__d))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.field_is_integral_domain',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r1] :
( t(V13__r1,V0__R)
=> ! [V14__r2] :
( t(V14__r2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__r1),V1__rO))
=> ( ~ p(happ(happ(V9__req,V14__r2),V1__rO))
=> ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V13__r1),V14__r2)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.gen_phiPOS_discr_sgn',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ( ! [V13__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V13__p)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V13__p)),V1__rO)) )
=> ! [V14__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__x)
=> ! [V15__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V15__y)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V14__x)),happ(V6__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V15__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_afield',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req)
=> ( ~ p(happ(happ(V9__req,V2__rI),V1__rO))
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__p),V13__q)),happ(happ(V4__rmul,V12__p),happ(V8__rinv,V13__q)))) ) )
=> ( ! [V13__p] :
( t(V13__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V13__p)),V13__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_field',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req)
=> ( ~ p(happ(happ(V9__req,V2__rI),V1__rO))
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__p),V13__q)),happ(happ(V4__rmul,V12__p),happ(V8__rinv,V13__q)))) ) )
=> ( ! [V13__p] :
( t(V13__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V13__p)),V13__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_sfield',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__780___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__169___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req)
=> ( ~ p(happ(happ(V7__req,V2__rI),V1__rO))
=> ( ! [V10__p] :
( t(V10__p,V0__R)
=> ! [V11__q] :
( t(V11__q,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rdiv,V10__p),V11__q)),happ(happ(V4__rmul,V10__p),happ(V6__rinv,V11__q)))) ) )
=> ( ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V7__req,V11__p),V1__rO))
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(V6__rinv,V11__p)),V11__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.pow_pos_div',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V15__p)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,happ(happ(V7__rdiv,V13__a),V14__b),V15__p)),happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__a,V15__p)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V14__b,V15__p)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.pow_pos_nz',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__p)
=> ( ~ p(happ(happ(V9__req,V13__x),V1__rO))
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__x,V14__p)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__780___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__780___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__169___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__22___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__780___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__169___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv2',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V16__d),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V3__radd,happ(happ(V7__rdiv,V13__a),V14__b)),happ(happ(V7__rdiv,V15__c),V16__d))),happ(happ(V7__rdiv,happ(happ(V3__radd,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V15__c),V14__b))),happ(happ(V4__rmul,V14__b),V16__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv2b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ! [V17__e] :
( t(V17__e,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V14__b),V17__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V16__d),V17__e)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V3__radd,happ(happ(V7__rdiv,V13__a),happ(happ(V4__rmul,V14__b),V17__e))),happ(happ(V7__rdiv,V15__c),happ(happ(V4__rmul,V16__d),V17__e)))),happ(happ(V7__rdiv,happ(happ(V3__radd,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V15__c),V14__b))),happ(happ(V4__rmul,V14__b),happ(happ(V4__rmul,V16__d),V17__e))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv3b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V18__e)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V5__rsub,happ(happ(V7__rdiv,V14__a),happ(happ(V4__rmul,V15__b),V18__e))),happ(happ(V7__rdiv,V16__c),happ(happ(V4__rmul,V17__d),V18__e)))),happ(happ(V7__rdiv,happ(happ(V5__rsub,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b))),happ(happ(V4__rmul,V15__b),happ(happ(V4__rmul,V17__d),V18__e))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv4',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V16__d),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(happ(V7__rdiv,V13__a),V14__b)),happ(happ(V7__rdiv,V15__c),V16__d))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V13__a),V15__c)),happ(happ(V4__rmul,V14__b),V16__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv4b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ! [V19__f] :
( t(V19__f,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V19__f)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V19__f)),happ(happ(V4__rmul,V15__b),V18__e))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V16__c),V18__e)),happ(happ(V4__rmul,V17__d),V19__f)))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V16__c)),happ(happ(V4__rmul,V15__b),V17__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv5',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> p(happ(happ(V9__req,happ(V6__ropp,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,happ(V6__ropp,V13__a)),V14__b))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv6',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> p(happ(happ(V9__req,happ(V8__rinv,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,V14__b),V13__a))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv7',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V15__c),V1__rO))
=> ( ~ p(happ(happ(V9__req,V16__d),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,happ(happ(V7__rdiv,V13__a),V14__b)),happ(happ(V7__rdiv,V15__c),V16__d))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V14__b),V15__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv7b',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ! [V19__f] :
( t(V19__f,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V19__f)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V16__c),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V19__f)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V18__e)),happ(happ(V4__rmul,V15__b),V19__f))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V16__c),V18__e)),happ(happ(V4__rmul,V17__d),V19__f)))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V15__b),V16__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv8',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( p(happ(happ(V9__req,V13__a),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V13__a),V14__b)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_r_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V12__r] :
( t(V12__r,V0__R)
=> ( ~ p(happ(happ(V9__req,V12__r),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__r),V12__r)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_simpl',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__q),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,V14__q),happ(happ(V7__rdiv,V13__p),V14__q))),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ring_S_inj',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ( p(happ(happ(V9__req,happ(happ(V3__radd,V2__rI),V13__x)),happ(happ(V3__radd,V2__rI),V14__y)))
=> p(happ(happ(V9__req,V13__x),V14__y)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rinv_nz',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V8__rinv,V13__a)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__780___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__780___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__169___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__22___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__780___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__169___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_reg_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q1] :
( t(V14__q1,V0__R)
=> ! [V15__q2] :
( t(V15__q2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V13__p),V14__q1)),happ(happ(V4__rmul,V13__p),V15__q2)))
=> p(happ(happ(V9__req,V14__q1),V15__q2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext3_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__780___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__780___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__169___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__22___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__169___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__780___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__780___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__169___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__22___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__169___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__780___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__169___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__22___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r] :
( t(V13__r,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(V6__ropp,V2__rI)),V1__rO))
=> ( ~ p(happ(happ(V9__req,V13__r),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V6__ropp,V13__r)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.ARgen_phiPOS_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V11__x)
=> ! [V12__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V12__y)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V11__x,V12__y))),happ(happ(V3__radd,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V11__x)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.InitialRing.same_gen',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V11__x)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V11__x)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V11__x))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),V1__rO)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__z),happ(happ(V3__radd,V11__x),V12__y))),happ(happ(V3__radd,happ(happ(V4__rmul,V13__z),V11__x)),happ(happ(V4__rmul,V13__z),V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V2__rI)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_zero',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__780___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__780___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__169___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__22___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__780___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__169___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Ropp_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(V6__ropp,V9__x))),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Ropp_opp',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(V6__ropp,V11__x))),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5212___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5212___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5212___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5226___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5233___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__800___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5212___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5212___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5212___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5226___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5233___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__800___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph_opp',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__780___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__780___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__780___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__169___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__22___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__5212___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__5212___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__5212___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__5226___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__5233___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__800___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> ! [V18__x] :
( t(V18__x,V8__C)
=> p(happ(happ(V7__req,happ(V16__phi,happ(V14__copp,V18__x))),happ(V6__ropp,happ(V16__phi,V18__x)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__780___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__22___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__22282___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__22289___24t(V0__R,V4__Cpow,V6__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow)
=> ! [V8__r] :
( t(V8__r,V0__R)
=> ! [V9__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V9__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V8__r),happ(V5__Cp__phi,V9__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V8__r,V9__n))) ) ) ) ) ) ) ) ) ) ) ).
fof('DirectedSets.DS_join_cond',axiom,
! [V0__d] :
( cDirectedSets_2eDirectedSet___24t(V0__d)
=> ! [V1__i] :
( cDirectedSets_2eDS__set___24t(V0__d,V1__i)
=> ! [V2__j] :
( cDirectedSets_2eDS__set___24t(V0__d,V2__j)
=> ? [V3__k] :
( cDirectedSets_2eDS__set___24t(V0__d,V3__k)
& cDirectedSets_2eDS__ord___24a3(V0__d,V1__i,V3__k)
& cDirectedSets_2eDS__ord___24a3(V0__d,V2__j,V3__k) ) ) ) ) ).
fof('DirectedSets.DS_ord_cond',axiom,
! [V0__d] :
( cDirectedSets_2eDirectedSet___24t(V0__d)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(cDirectedSets_2eDS__set___24a1(V0__d),cDirectedSets_2eDS__ord___24a1(V0__d)) ) ).
fof('DirectedSets.for_large.eventually_and',axiom,
! [V0__P] :
( c_24__type__1___24t(V0__P)
=> ! [V1__Q] :
( c_24__type__1___24t(V1__Q)
=> ( cDirectedSets_2efor__large_2eeventually___24a1(V0__P)
=> ( cDirectedSets_2efor__large_2eeventually___24a1(V1__Q)
=> cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34420___24a2(V0__P,V1__Q)) ) ) ) ) ).
fof('DirectedSets.for_large.eventually_impl',axiom,
! [V0__P] :
( c_24__type__1___24t(V0__P)
=> ! [V1__Q] :
( c_24__type__1___24t(V1__Q)
=> ( cDirectedSets_2efor__large_2eeventually___24a1(V0__P)
=> ( cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34610___24a2(V0__P,V1__Q))
=> cDirectedSets_2efor__large_2eeventually___24a1(V1__Q) ) ) ) ) ).
fof('DirectedSets.for_large.eventually_impl_base',axiom,
! [V0__P] :
( c_24__type__1___24t(V0__P)
=> ! [V1__Q] :
( c_24__type__1___24t(V1__Q)
=> ( ! [V2__i] :
( cDirectedSets_2eDS__set___24t(cI,V2__i)
=> ( p(happ(V0__P,V2__i))
=> p(happ(V1__Q,V2__i)) ) )
=> ( cDirectedSets_2efor__large_2eeventually___24a1(V0__P)
=> cDirectedSets_2efor__large_2eeventually___24a1(V1__Q) ) ) ) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xfold_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfold___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.QArith.QArith_base.Qlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQlt,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEmul_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEmul,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEmul___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_38520_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__38520,V_24X1),V_24X2),V_24X3) = c_24__prop__38520___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_34547_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34547,V_24X1) = c_24__lam__34547___24a1(V_24X1) ).
fof('$adef_$_lam_34337_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34337,V_24X1) = c_24__lam__34337___24a1(V_24X1) ).
fof('$adef_$_prop_9693_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__9693,V_24X1),V_24X2),V_24X3) = c_24__prop__9693___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_34420_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__34420,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__34420___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33291_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33291,V_24X1),V_24X2) = c_24__lam__33291___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.ex2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eLogic_2eex2,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eLogic_2eex2___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Lists.List.count_occ_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecount__occ,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecount__occ___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.inter_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2einter___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__tt___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_49431_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49431,V_24X1),V_24X2) = c_24__prop__49431___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_37334_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__37334,V_24X1),V_24X2) = c_24__lam__37334___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_37330_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37330,V_24X1),V_24X2),V_24X3) = c_24__prop__37330___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_39607_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__39607,V_24X1),V_24X2) = c_24__prop__39607___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35096_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35096,V_24X1) = c_24__prop__35096___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.False_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eLogic_2eFalse__rec,V_24X1) = cCoq_2eInit_2eLogic_2eFalse__rec___24a1(V_24X1) ).
fof('$adef_$_lam_35545_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__35545,V_24X1),V_24X2),V_24X3) = c_24__lam__35545___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_$_prop_49206_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49206,V_24X1),V_24X2) = c_24__prop__49206___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.eval_f_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_15716_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15716,V_24X1),V_24X2),V_24X3) = c_24__lam__15716___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.singleton_$a1',axiom,
! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2esingleton___24a1(V_24X1) ).
fof('$adef_$_prop_35330_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35330,V_24X1) = c_24__prop__35330___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_9690_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__9690,V_24X1),V_24X2),V_24X3) = c_24__prop__9690___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_49404_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49404,V_24X1),V_24X2) = c_24__prop__49404___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38439_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38439,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38439___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_$_prop_35100_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35100,V_24X1) = c_24__prop__35100___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_37334_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__37334,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__37334___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_35333_$a1',axiom,
! [V_24X1] :
( p(happ(c_24__lam__35333,V_24X1))
<=> c_24__lam__35333___24a1(V_24X1) ) ).
fof('$adef_$_lam_34344_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34344,V_24X1),V_24X2) = c_24__lam__34344___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_49395_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49395,V_24X1),V_24X2) = c_24__prop__49395___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_33291_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__33291,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__33291___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_DirectedSets.DS_set_$a1',axiom,
! [V_24X1] : happ(cDirectedSets_2eDS__set,V_24X1) = cDirectedSets_2eDS__set___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.or_intror_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eor__intror,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eor__intror___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_prop_29309_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29309,V_24X1),V_24X2),V_24X3) = c_24__prop__29309___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ediv,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Raxioms.INR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRaxioms_2eINR,V_24X1) = cCoq_2eReals_2eRaxioms_2eINR___24a1(V_24X1) ).
fof('$adef_$_prop_49403_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49403,V_24X1),V_24X2) = c_24__prop__49403___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_$_fix_431_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__431__1__add__carry,V_24X1),V_24X2) = c_24__fix__431__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$28268_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428268,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428268___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35334_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35334,V_24X1),V_24X2),V_24X3) = c_24__prop__35334___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_2482_2484_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__2482__2484,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__2482__2484___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_34996_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__34996,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__34996___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38426_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38426,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38426___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2esplit___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_39758_$a1',axiom,
! [V_24X1] : happ(c_24__prop__39758,V_24X1) = c_24__prop__39758___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.eval_cnf_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__cnf,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__cnf___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.interp_PElist_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eRing__polynom_2einterp__PElist___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_$_lam_39314_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__39314,V_24X1),V_24X2) = c_24__lam__39314___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQle,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Strings.String.length_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eString_2elength,V_24X1) = cCoq_2eStrings_2eString_2elength___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons2_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons2___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_9854_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9854,V_24X1) = c_24__lam__9854___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.Hurkens.NoRetractToNegativeProp.El_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eEl,V_24X1))
<=> cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eEl___24a1(V_24X1) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_$_prop_34548_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__34548,V_24X1),V_24X2) = c_24__prop__34548___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_38465_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__38465,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__38465___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$28273_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2428273___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2enode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.PEsimp_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePEsimp,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eField__theory_2ePEsimp___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons1_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons1___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_34547_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__34547,V_24X1),V_24X2))
<=> c_24__lam__34547___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_15716_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__15716,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__15716___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_DirectedSets.DS_ord_$a1',axiom,
! [V_24X1] : happ(cDirectedSets_2eDS__ord,V_24X1) = cDirectedSets_2eDS__ord___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$22024_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2422024,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
<=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2422024___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.ltb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_29307_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29307,V_24X1),V_24X2),V_24X3) = c_24__prop__29307___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$28251_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2428251,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2428251___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_38551_$a1',axiom,
! [V_24X1] : happ(c_24__prop__38551,V_24X1) = c_24__prop__38551___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_49428_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49428,V_24X1),V_24X2) = c_24__prop__49428___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Init.Specif.absurd_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eabsurd__set,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eabsurd__set___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_34996_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34996,V_24X1),V_24X2) = c_24__lam__34996___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35256_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35256,V_24X1) = c_24__prop__35256___24a1(V_24X1) ).
fof('$adef_$_prop_38586_$a1',axiom,
! [V_24X1] : happ(c_24__prop__38586,V_24X1) = c_24__prop__38586___24a1(V_24X1) ).
fof('$adef_$_prop_39759_$a1',axiom,
! [V_24X1] : happ(c_24__prop__39759,V_24X1) = c_24__prop__39759___24a1(V_24X1) ).
fof('$adef_$_prop_49205_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49205,V_24X1),V_24X2) = c_24__prop__49205___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_DirectedSets.for_large.exists_arbitrarily_large_$a1',axiom,
! [V_24X1] :
( p(happ(cDirectedSets_2efor__large_2eexists__arbitrarily__large,V_24X1))
<=> cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(V_24X1) ) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.unique_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eunique,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eunique___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_var_7_n_9644_9648_9657_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__var__7__n__9644__9648__9657,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__var__7__n__9644__9648__9657___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_24719_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__24719,V_24X1),V_24X2) = c_24__prop__24719___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_46034_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__46034,V_24X1),V_24X2),V_24X3) = c_24__lam__46034___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.ClassicalFacts.Minimization_Property_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property,V_24X1))
<=> cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec,V_24X1),V_24X2) = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38494_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38494,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38494___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_49430_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49430,V_24X1),V_24X2) = c_24__prop__49430___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_$_lam_42991_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__42991,V_24X1),V_24X2) = c_24__lam__42991___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eF_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Specif.sumbool$9675_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_249675,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_249675___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_15732_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__15732,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__15732___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_38578_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38578,V_24X1),V_24X2) = c_24__prop__38578___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_$_lam_34337_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34337,V_24X1),V_24X2) = c_24__lam__34337___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_prop_39601_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__39601,V_24X1),V_24X2) = c_24__prop__39601___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_38536_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38536,V_24X1),V_24X2) = c_24__prop__38536___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ege,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_$_prop_38529_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38529,V_24X1),V_24X2) = c_24__prop__38529___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.absurd_PCond_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eabsurd__PCond___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.reflect_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect__rec,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_Coq.Lists.SetoidList.findA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2efindA,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eSetoidList_2efindA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_9689_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__9689,V_24X1),V_24X2),V_24X3) = c_24__prop__9689___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_$_prop_9692_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__9692,V_24X1),V_24X2),V_24X3) = c_24__prop__9692___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Logic.or_introl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eor__introl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eor__introl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Empty_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty,V_24X1))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEmpty___24a1(V_24X1) ) ).
fof('$adef_$_prop_39600_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__39600,V_24X1),V_24X2) = c_24__prop__39600___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38507_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38507,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38507___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.eval_clause_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eeval__clause___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.exist_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_38518_$a1',axiom,
! [V_24X1] : happ(c_24__prop__38518,V_24X1) = c_24__prop__38518___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_34610_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__34610,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__34610___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_38392_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38392,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38392___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.QArith.QArith_base.Qmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmult,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_prop_35329_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35329,V_24X1) = c_24__prop__35329___24a1(V_24X1) ).
fof('$adef_$_prop_38393_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38393,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38393___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_46034_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__46034,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__46034___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_35101_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35101,V_24X1) = c_24__prop__35101___24a1(V_24X1) ).
fof('$adef_$_lam_39316_$a1',axiom,
! [V_24X1] : happ(c_24__lam__39316,V_24X1) = c_24__lam__39316___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.ZMicromega.Zeval_op2_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZeval__op2,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZeval__op2___24a1(V_24X1) ).
fof('$adef_$_lam_33283_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33283,V_24X1),V_24X2) = c_24__lam__33283___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_40154_$a1',axiom,
! [V_24X1] : happ(c_24__prop__40154,V_24X1) = c_24__prop__40154___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_prop_38555_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__38555,V_24X1),V_24X2),V_24X3) = c_24__prop__38555___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_29310_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29310,V_24X1),V_24X2),V_24X3) = c_24__prop__29310___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.ex_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eLogic_2eex,V_24X1),V_24X2))
<=> cCoq_2eInit_2eLogic_2eex___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_33283_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__33283,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__33283___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_34348_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34348,V_24X1) = c_24__lam__34348___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_DirectedSets.Build_DirectedSet_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cDirectedSets_2eBuild__DirectedSet,V_24X1),V_24X2) = cDirectedSets_2eBuild__DirectedSet___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_9853_$a1',axiom,
! [V_24X1] : happ(c_24__lam__9853,V_24X1) = c_24__lam__9853___24a1(V_24X1) ).
fof('$adef_$_lam_15740_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__15740,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__15740___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_lam_39314_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__39314,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__39314___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.shiftl_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eshiftl,V_24X1) = cCoq_2eInit_2eNat_2eshiftl___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_42991_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__42991,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__42991___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34344_$a1',axiom,
! [V_24X1] : happ(c_24__lam__34344,V_24X1) = c_24__lam__34344___24a1(V_24X1) ).
fof('$adef_$_prop_48261_$a1',axiom,
! [V_24X1] : happ(c_24__prop__48261,V_24X1) = c_24__prop__48261___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2egcd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33307_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33307,V_24X1),V_24X2) = c_24__lam__33307___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.compat_op_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__op,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2egcd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.isZ0_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eisZ0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_15724_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15724,V_24X1),V_24X2),V_24X3) = c_24__lam__15724___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_33299_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__33299,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__33299___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons0_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons0,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons0___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.NArith.BinNatDef.N.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eleb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_39316_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__39316,V_24X1),V_24X2))
<=> c_24__lam__39316___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_49433_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49433,V_24X1),V_24X2) = c_24__prop__49433___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_39674_$a1',axiom,
! [V_24X1] : happ(c_24__prop__39674,V_24X1) = c_24__prop__39674___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.split_aux_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esplit__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2esetoid__ring_2eField__theory_2esplit__aux___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.reflect_dec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2ereflect__dec,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2ereflect__dec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_38492_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38492,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38492___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_40059_$a1',axiom,
! [V_24X1] : happ(c_24__prop__40059,V_24X1) = c_24__prop__40059___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_49207_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49207,V_24X1),V_24X2) = c_24__prop__49207___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_49429_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49429,V_24X1),V_24X2) = c_24__prop__49429___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38543_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38543,V_24X1),V_24X2) = c_24__prop__38543___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_9694_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__9694,V_24X1),V_24X2),V_24X3) = c_24__prop__9694___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_38465_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__38465,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__38465___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.list_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2elist__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEpow_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEpow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eField__theory_2eNPEpow___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_$_prop_38516_$a1',axiom,
! [V_24X1] : happ(c_24__prop__38516,V_24X1) = c_24__prop__38516___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_49396_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__49396,V_24X1),V_24X2) = c_24__prop__49396___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34610_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34610,V_24X1),V_24X2) = c_24__lam__34610___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_$_lam_49406_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__49406,V_24X1),V_24X2))
<=> c_24__lam__49406___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.Odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eOdd,V_24X1))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eOdd___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_38564_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38564,V_24X1),V_24X2) = c_24__prop__38564___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13) = cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_DirectedSets.for_large.eventually_$a1',axiom,
! [V_24X1] :
( p(happ(cDirectedSets_2efor__large_2eeventually,V_24X1))
<=> cDirectedSets_2efor__large_2eeventually___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2elog2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_DirectedSets.DS_ord_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cDirectedSets_2eDS__ord,V_24X1),V_24X2),V_24X3))
<=> cDirectedSets_2eDS__ord___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.diff_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ediff,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ediff___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Init.Datatypes.bool$49414_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2449414,V_24X1),V_24X2))
<=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_2449414___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_38493_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38493,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38493___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.cnf_tt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.union_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eunion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_15732_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15732,V_24X1),V_24X2),V_24X3) = c_24__lam__15732___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Wf_nat.has_unique_least_element_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eWf__nat_2ehas__unique__least__element,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eWf__nat_2ehas__unique__least__element___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_$_let_var_6_p_2480_2483_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__2480__2483,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__2480__2483___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_9691_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__9691,V_24X1),V_24X2),V_24X3) = c_24__prop__9691___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_$_prop_34399_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__34399,V_24X1),V_24X2) = c_24__prop__34399___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_29312_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__29312,V_24X1),V_24X2) = c_24__prop__29312___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38559_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38559,V_24X1),V_24X2) = c_24__prop__38559___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.removeA_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eremoveA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fcons00_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFcons00,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eField__theory_2eFcons00___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_prop_39762_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__39762,V_24X1),V_24X2),V_24X3) = c_24__prop__39762___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_43226_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__43226,V_24X1),V_24X2) = c_24__prop__43226___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_17716_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__17716,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__17716___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bool.reflect_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect__rect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Bool.Bool.reflect_rect_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eBool_2eBool_2ereflect__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eBool_2eBool_2ereflect__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.ClassicalFacts.Minimal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eClassicalFacts_2eMinimal,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_40058_$a1',axiom,
! [V_24X1] : happ(c_24__prop__40058,V_24X1) = c_24__prop__40058___24a1(V_24X1) ).
fof('$adef_$_prop_48696_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__48696,V_24X1),V_24X2) = c_24__prop__48696___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_15740_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__15740,V_24X1),V_24X2),V_24X3) = c_24__lam__15740___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_11_subst_l_17644_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__17644,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__17644___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.Strings.String.substring_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eStrings_2eString_2esubstring,V_24X1),V_24X2),V_24X3) = cCoq_2eStrings_2eString_2esubstring___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_29308_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29308,V_24X1),V_24X2),V_24X3) = c_24__prop__29308___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_31110_$a1',axiom,
! [V_24X1] : happ(c_24__prop__31110,V_24X1) = c_24__prop__31110___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Add_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.remove_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eremove___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38524_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38524,V_24X1),V_24X2) = c_24__prop__38524___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epow,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_$_lam_15724_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__15724,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__15724___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.eval_clause_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__clause,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__clause___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_17716_$a12',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__17716,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__17716___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_$_prop_29311_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29311,V_24X1),V_24X2),V_24X3) = c_24__prop__29311___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_29306_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__29306,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__29306___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33307_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__33307,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__33307___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.fold_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efold___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38391_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__38391,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__38391___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34420_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__34420,V_24X1),V_24X2) = c_24__lam__34420___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_33299_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33299,V_24X1),V_24X2) = c_24__lam__33299___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_38571_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__38571,V_24X1),V_24X2) = c_24__prop__38571___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.divmod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_31210',axiom,
! [V_24Y] :
( c_24__type__31210___24t(V_24Y)
<=> t(V_24Y,c_24__type__31210) ) ).
fof('$tdef_$_type_11332',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__11332___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__11332___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_38437',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38437___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38437___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27485',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27485___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27485___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_383',axiom,
! [V_24Y] :
( c_24__type__383___24t(V_24Y)
<=> t(V_24Y,c_24__type__383) ) ).
fof('$tdef_$_type_3344',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3344___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3344___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_12693',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__12693___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__12693___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_22426',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22426___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22426___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_34724',axiom,
! [V_24Y] :
( c_24__type__34724___24t(V_24Y)
<=> t(V_24Y,c_24__type__34724) ) ).
fof('$tdef_$_type_13039',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__13039___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__13039___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_180',axiom,
! [V_24Y] :
( c_24__type__180___24t(V_24Y)
<=> t(V_24Y,c_24__type__180) ) ).
fof('$tdef_$_type_531',axiom,
! [V_24Y] :
( c_24__type__531___24t(V_24Y)
<=> t(V_24Y,c_24__type__531) ) ).
fof('$tdef_$_type_5619',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5619___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5619___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_45380',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__45380___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__45380___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4733',axiom,
! [V_24Y] :
( c_24__type__4733___24t(V_24Y)
<=> t(V_24Y,c_24__type__4733) ) ).
fof('$tdef_$_type_22476',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22476___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22476___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_45433',axiom,
! [V_24Y] :
( c_24__type__45433___24t(V_24Y)
<=> t(V_24Y,c_24__type__45433) ) ).
fof('$tdef_$_type_35642',axiom,
! [V_24Y] :
( c_24__type__35642___24t(V_24Y)
<=> t(V_24Y,c_24__type__35642) ) ).
fof('$tdef_$_type_24969',axiom,
! [V_24Y] :
( c_24__type__24969___24t(V_24Y)
<=> t(V_24Y,c_24__type__24969) ) ).
fof('$tdef_$_type_11655',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__11655___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__11655___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_508',axiom,
! [V_24Y] :
( c_24__type__508___24t(V_24Y)
<=> t(V_24Y,c_24__type__508) ) ).
fof('$tdef_$_type_37101',axiom,
! [V_24Y] :
( c_24__type__37101___24t(V_24Y)
<=> t(V_24Y,c_24__type__37101) ) ).
fof('$tdef_$_type_22569',axiom,
! [V_24Y] :
( c_24__type__22569___24t(V_24Y)
<=> t(V_24Y,c_24__type__22569) ) ).
fof('$tdef_$_type_40839',axiom,
! [V_24Y] :
( c_24__type__40839___24t(V_24Y)
<=> t(V_24Y,c_24__type__40839) ) ).
fof('$tdef_$_type_26486',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26486___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26486___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_9687',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9687___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9687___24a1(V_24X1)) ) ).
fof('$tdef_$_type_356',axiom,
! [V_24Y] :
( c_24__type__356___24t(V_24Y)
<=> t(V_24Y,c_24__type__356) ) ).
fof('$tdef_$_type_25225',axiom,
! [V_24Y] :
( c_24__type__25225___24t(V_24Y)
<=> t(V_24Y,c_24__type__25225) ) ).
fof('$tdef_$_type_29339',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29339___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29339___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_35159',axiom,
! [V_24Y] :
( c_24__type__35159___24t(V_24Y)
<=> t(V_24Y,c_24__type__35159) ) ).
fof('$tdef_$_type_28480',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28480___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28480___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29081',axiom,
! [V_24Y] :
( c_24__type__29081___24t(V_24Y)
<=> t(V_24Y,c_24__type__29081) ) ).
fof('$tdef_$_type_24568',axiom,
! [V_24Y] :
( c_24__type__24568___24t(V_24Y)
<=> t(V_24Y,c_24__type__24568) ) ).
fof('$tdef_$_type_503',axiom,
! [V_24Y] :
( c_24__type__503___24t(V_24Y)
<=> t(V_24Y,c_24__type__503) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_$_type_5226',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5226___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5226___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31287',axiom,
! [V_24Y] :
( c_24__type__31287___24t(V_24Y)
<=> t(V_24Y,c_24__type__31287) ) ).
fof('$tdef_$_type_195',axiom,
! [V_24Y] :
( c_24__type__195___24t(V_24Y)
<=> t(V_24Y,c_24__type__195) ) ).
fof('$tdef_$_type_18289',axiom,
! [V_24Y] :
( c_24__type__18289___24t(V_24Y)
<=> t(V_24Y,c_24__type__18289) ) ).
fof('$tdef_$_type_15783',axiom,
! [V_24Y] :
( c_24__type__15783___24t(V_24Y)
<=> t(V_24Y,c_24__type__15783) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_171',axiom,
! [V_24Y] :
( c_24__type__171___24t(V_24Y)
<=> t(V_24Y,c_24__type__171) ) ).
fof('$tdef_$_type_9609',axiom,
! [V_24Y] :
( c_24__type__9609___24t(V_24Y)
<=> t(V_24Y,c_24__type__9609) ) ).
fof('$tdef_$_type_35176',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35176___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35176___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27702',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27702___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27702___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_44761',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__44761___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__44761___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22381',axiom,
! [V_24Y] :
( c_24__type__22381___24t(V_24Y)
<=> t(V_24Y,c_24__type__22381) ) ).
fof('$tdef_$_type_10986',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__10986___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__10986___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_1979',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1979___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1979___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_17866',axiom,
! [V_24X1,V_24Y] :
( c_24__type__17866___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__17866___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Logic.Hurkens.NoRetractToNegativeProp.NProp',axiom,
! [V_24Y] :
( cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eNProp___24t(V_24Y)
<=> t(V_24Y,cCoq_2eLogic_2eHurkens_2eNoRetractToNegativeProp_2eNProp) ) ).
fof('$tdef_$_type_5887',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5887___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5887___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12347',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__12347___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__12347___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_43861',axiom,
! [V_24Y] :
( c_24__type__43861___24t(V_24Y)
<=> t(V_24Y,c_24__type__43861) ) ).
fof('$tdef_$_type_2271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2271___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31514',axiom,
! [V_24Y] :
( c_24__type__31514___24t(V_24Y)
<=> t(V_24Y,c_24__type__31514) ) ).
fof('$tdef_$_type_4999',axiom,
! [V_24Y] :
( c_24__type__4999___24t(V_24Y)
<=> t(V_24Y,c_24__type__4999) ) ).
fof('$tdef_$_type_4754',axiom,
! [V_24Y] :
( c_24__type__4754___24t(V_24Y)
<=> t(V_24Y,c_24__type__4754) ) ).
fof('$tdef_$_type_21869',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21869___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21869___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).
fof('$tdef_$_type_49292',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__49292___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__49292___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10640',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__10640___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__10640___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_349',axiom,
! [V_24Y] :
( c_24__type__349___24t(V_24Y)
<=> t(V_24Y,c_24__type__349) ) ).
fof('$tdef_$_type_22551',axiom,
! [V_24Y] :
( c_24__type__22551___24t(V_24Y)
<=> t(V_24Y,c_24__type__22551) ) ).
fof('$tdef_$_type_805',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__805___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__805___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_19994',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19994___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19994___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_49401',axiom,
! [V_24Y] :
( c_24__type__49401___24t(V_24Y)
<=> t(V_24Y,c_24__type__49401) ) ).
fof('$tdef_$_type_3808',axiom,
! [V_24Y] :
( c_24__type__3808___24t(V_24Y)
<=> t(V_24Y,c_24__type__3808) ) ).
fof('$tdef_$_type_30955',axiom,
! [V_24Y] :
( c_24__type__30955___24t(V_24Y)
<=> t(V_24Y,c_24__type__30955) ) ).
fof('$tdef_$_type_24631',axiom,
! [V_24Y] :
( c_24__type__24631___24t(V_24Y)
<=> t(V_24Y,c_24__type__24631) ) ).
fof('$tdef_$_type_780',axiom,
! [V_24X1,V_24Y] :
( c_24__type__780___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__780___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26949',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__26949___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__26949___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_534',axiom,
! [V_24Y] :
( c_24__type__534___24t(V_24Y)
<=> t(V_24Y,c_24__type__534) ) ).
fof('$tdef_$_type_24757',axiom,
! [V_24Y] :
( c_24__type__24757___24t(V_24Y)
<=> t(V_24Y,c_24__type__24757) ) ).
fof('$tdef_$_type_5526',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5526___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5526___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33344',axiom,
! [V_24Y] :
( c_24__type__33344___24t(V_24Y)
<=> t(V_24Y,c_24__type__33344) ) ).
fof('$tdef_$_type_31022',axiom,
! [V_24Y] :
( c_24__type__31022___24t(V_24Y)
<=> t(V_24Y,c_24__type__31022) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_29158',axiom,
! [V_24Y] :
( c_24__type__29158___24t(V_24Y)
<=> t(V_24Y,c_24__type__29158) ) ).
fof('$tdef_$_type_49398',axiom,
! [V_24Y] :
( c_24__type__49398___24t(V_24Y)
<=> t(V_24Y,c_24__type__49398) ) ).
fof('$tdef_$_type_25132',axiom,
! [V_24Y] :
( c_24__type__25132___24t(V_24Y)
<=> t(V_24Y,c_24__type__25132) ) ).
fof('$tdef_$_type_198',axiom,
! [V_24Y] :
( c_24__type__198___24t(V_24Y)
<=> t(V_24Y,c_24__type__198) ) ).
fof('$tdef_$_type_539',axiom,
! [V_24Y] :
( c_24__type__539___24t(V_24Y)
<=> t(V_24Y,c_24__type__539) ) ).
fof('$tdef_$_type_46043',axiom,
! [V_24Y] :
( c_24__type__46043___24t(V_24Y)
<=> t(V_24Y,c_24__type__46043) ) ).
fof('$tdef_$_type_414',axiom,
! [V_24Y] :
( c_24__type__414___24t(V_24Y)
<=> t(V_24Y,c_24__type__414) ) ).
fof('$tdef_$_type_22516',axiom,
! [V_24Y] :
( c_24__type__22516___24t(V_24Y)
<=> t(V_24Y,c_24__type__22516) ) ).
fof('$tdef_$_type_22',axiom,
! [V_24X1,V_24Y] :
( c_24__type__22___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__22___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8599',axiom,
! [V_24Y] :
( c_24__type__8599___24t(V_24Y)
<=> t(V_24Y,c_24__type__8599) ) ).
fof('$tdef_Coq.Init.Specif.sumbool',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3007',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__3007___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__3007___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_3918',axiom,
! [V_24Y] :
( c_24__type__3918___24t(V_24Y)
<=> t(V_24Y,c_24__type__3918) ) ).
fof('$tdef_$_type_4665',axiom,
! [V_24Y] :
( c_24__type__4665___24t(V_24Y)
<=> t(V_24Y,c_24__type__4665) ) ).
fof('$tdef_$_type_48725',axiom,
! [V_24Y] :
( c_24__type__48725___24t(V_24Y)
<=> t(V_24Y,c_24__type__48725) ) ).
fof('$tdef_$_type_49393',axiom,
! [V_24Y] :
( c_24__type__49393___24t(V_24Y)
<=> t(V_24Y,c_24__type__49393) ) ).
fof('$tdef_$_type_9834',axiom,
! [V_24Y] :
( c_24__type__9834___24t(V_24Y)
<=> t(V_24Y,c_24__type__9834) ) ).
fof('$tdef_$_type_23116',axiom,
! [V_24Y] :
( c_24__type__23116___24t(V_24Y)
<=> t(V_24Y,c_24__type__23116) ) ).
fof('$tdef_$_type_461',axiom,
! [V_24Y] :
( c_24__type__461___24t(V_24Y)
<=> t(V_24Y,c_24__type__461) ) ).
fof('$tdef_$_type_41776',axiom,
! [V_24Y] :
( c_24__type__41776___24t(V_24Y)
<=> t(V_24Y,c_24__type__41776) ) ).
fof('$tdef_$_type_22226',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__22226___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__22226___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_49390',axiom,
! [V_24X1,V_24Y] :
( c_24__type__49390___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__49390___24a1(V_24X1)) ) ).
fof('$tdef_$_type_30985',axiom,
! [V_24Y] :
( c_24__type__30985___24t(V_24Y)
<=> t(V_24Y,c_24__type__30985) ) ).
fof('$tdef_$_type_20207',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20207___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20207___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_1',axiom,
! [V_24Y] :
( c_24__type__1___24t(V_24Y)
<=> t(V_24Y,c_24__type__1) ) ).
fof('$tdef_$_type_202',axiom,
! [V_24Y] :
( c_24__type__202___24t(V_24Y)
<=> t(V_24Y,c_24__type__202) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_345',axiom,
! [V_24Y] :
( c_24__type__345___24t(V_24Y)
<=> t(V_24Y,c_24__type__345) ) ).
fof('$tdef_$_type_22270',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__22270___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__22270___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_35181',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35181___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35181___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33',axiom,
! [V_24Y] :
( c_24__type__33___24t(V_24Y)
<=> t(V_24Y,c_24__type__33) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_27882',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27882___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27882___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4766',axiom,
! [V_24Y] :
( c_24__type__4766___24t(V_24Y)
<=> t(V_24Y,c_24__type__4766) ) ).
fof('$tdef_$_type_6062',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6062___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6062___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_44756',axiom,
! [V_24Y] :
( c_24__type__44756___24t(V_24Y)
<=> t(V_24Y,c_24__type__44756) ) ).
fof('$tdef_$_type_33818',axiom,
! [V_24Y] :
( c_24__type__33818___24t(V_24Y)
<=> t(V_24Y,c_24__type__33818) ) ).
fof('$tdef_$_type_34351',axiom,
! [V_24Y] :
( c_24__type__34351___24t(V_24Y)
<=> t(V_24Y,c_24__type__34351) ) ).
fof('$tdef_$_type_24857',axiom,
! [V_24Y] :
( c_24__type__24857___24t(V_24Y)
<=> t(V_24Y,c_24__type__24857) ) ).
fof('$tdef_$_type_3149',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3149___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3149___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20846',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20846___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20846___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_44765',axiom,
! [V_24Y] :
( c_24__type__44765___24t(V_24Y)
<=> t(V_24Y,c_24__type__44765) ) ).
fof('$tdef_$_type_15392',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__15392___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__15392___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_40067',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__40067___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__40067___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21961',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21961___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21961___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_38514',axiom,
! [V_24Y] :
( c_24__type__38514___24t(V_24Y)
<=> t(V_24Y,c_24__type__38514) ) ).
fof('$tdef_$_type_27217',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27217___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27217___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5969',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5969___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5969___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4713',axiom,
! [V_24Y] :
( c_24__type__4713___24t(V_24Y)
<=> t(V_24Y,c_24__type__4713) ) ).
fof('$tdef_$_type_421',axiom,
! [V_24Y] :
( c_24__type__421___24t(V_24Y)
<=> t(V_24Y,c_24__type__421) ) ).
fof('$tdef_$_type_34301',axiom,
! [V_24Y] :
( c_24__type__34301___24t(V_24Y)
<=> t(V_24Y,c_24__type__34301) ) ).
fof('$tdef_$_type_25240',axiom,
! [V_24Y] :
( c_24__type__25240___24t(V_24Y)
<=> t(V_24Y,c_24__type__25240) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_24766',axiom,
! [V_24Y] :
( c_24__type__24766___24t(V_24Y)
<=> t(V_24Y,c_24__type__24766) ) ).
fof('$tdef_$_type_1077',axiom,
! [V_24Y] :
( c_24__type__1077___24t(V_24Y)
<=> t(V_24Y,c_24__type__1077) ) ).
fof('$tdef_$_type_2170',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2170___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2170___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29360',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29360___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29360___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_9704',axiom,
! [V_24Y] :
( c_24__type__9704___24t(V_24Y)
<=> t(V_24Y,c_24__type__9704) ) ).
fof('$tdef_$_type_9770',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9770___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9770___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2764',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2764___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__2764___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33869',axiom,
! [V_24Y] :
( c_24__type__33869___24t(V_24Y)
<=> t(V_24Y,c_24__type__33869) ) ).
fof('$tdef_$_type_23055',axiom,
! [V_24Y] :
( c_24__type__23055___24t(V_24Y)
<=> t(V_24Y,c_24__type__23055) ) ).
fof('$tdef_$_type_21819',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21819___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21819___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_19586',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19586___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19586___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_38389',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38389___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38389___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8838',axiom,
! [V_24Y] :
( c_24__type__8838___24t(V_24Y)
<=> t(V_24Y,c_24__type__8838) ) ).
fof('$tdef_$_type_34219',axiom,
! [V_24Y] :
( c_24__type__34219___24t(V_24Y)
<=> t(V_24Y,c_24__type__34219) ) ).
fof('$tdef_$_type_33823',axiom,
! [V_24Y] :
( c_24__type__33823___24t(V_24Y)
<=> t(V_24Y,c_24__type__33823) ) ).
fof('$tdef_$_type_18104',axiom,
! [V_24Y] :
( c_24__type__18104___24t(V_24Y)
<=> t(V_24Y,c_24__type__18104) ) ).
fof('$tdef_$_type_31150',axiom,
! [V_24Y] :
( c_24__type__31150___24t(V_24Y)
<=> t(V_24Y,c_24__type__31150) ) ).
fof('$tdef_$_type_223',axiom,
! [V_24Y] :
( c_24__type__223___24t(V_24Y)
<=> t(V_24Y,c_24__type__223) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.linear',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35657',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35657___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35657___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30629',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30629___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30629___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_49203',axiom,
! [V_24Y] :
( c_24__type__49203___24t(V_24Y)
<=> t(V_24Y,c_24__type__49203) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_49326',axiom,
! [V_24Y] :
( c_24__type__49326___24t(V_24Y)
<=> t(V_24Y,c_24__type__49326) ) ).
fof('$tdef_$_type_49410',axiom,
! [V_24Y] :
( c_24__type__49410___24t(V_24Y)
<=> t(V_24Y,c_24__type__49410) ) ).
fof('$tdef_$_type_9157',axiom,
! [V_24Y] :
( c_24__type__9157___24t(V_24Y)
<=> t(V_24Y,c_24__type__9157) ) ).
fof('$tdef_$_type_48693',axiom,
! [V_24Y] :
( c_24__type__48693___24t(V_24Y)
<=> t(V_24Y,c_24__type__48693) ) ).
fof('$tdef_DirectedSets.DS_set',axiom,
! [V_24X1,V_24Y] :
( cDirectedSets_2eDS__set___24t(V_24X1,V_24Y)
<=> t(V_24Y,cDirectedSets_2eDS__set___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2473',axiom,
! [V_24Y] :
( c_24__type__2473___24t(V_24Y)
<=> t(V_24Y,c_24__type__2473) ) ).
fof('$tdef_$_type_5012',axiom,
! [V_24Y] :
( c_24__type__5012___24t(V_24Y)
<=> t(V_24Y,c_24__type__5012) ) ).
fof('$tdef_$_type_43224',axiom,
! [V_24Y] :
( c_24__type__43224___24t(V_24Y)
<=> t(V_24Y,c_24__type__43224) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_26306',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26306___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26306___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_38505',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38505___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38505___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22384',axiom,
! [V_24Y] :
( c_24__type__22384___24t(V_24Y)
<=> t(V_24Y,c_24__type__22384) ) ).
fof('$tdef_$_type_14723',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__14723___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__14723___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_169',axiom,
! [V_24X1,V_24Y] :
( c_24__type__169___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__169___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2944',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2944___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__2944___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_34714',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34714___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34714___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27310',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27310___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27310___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27765',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27765___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27765___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_22289',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22289___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22289___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_35164',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35164___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35164___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33359',axiom,
! [V_24Y] :
( c_24__type__33359___24t(V_24Y)
<=> t(V_24Y,c_24__type__33359) ) ).
fof('$tdef_$_type_49330',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__49330___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__49330___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34321',axiom,
! [V_24Y] :
( c_24__type__34321___24t(V_24Y)
<=> t(V_24Y,c_24__type__34321) ) ).
fof('$tdef_$_type_24810',axiom,
! [V_24Y] :
( c_24__type__24810___24t(V_24Y)
<=> t(V_24Y,c_24__type__24810) ) ).
fof('$tdef_$_type_24787',axiom,
! [V_24Y] :
( c_24__type__24787___24t(V_24Y)
<=> t(V_24Y,c_24__type__24787) ) ).
fof('$tdef_$_type_1878',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1878___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1878___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27135',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27135___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27135___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_395',axiom,
! [V_24Y] :
( c_24__type__395___24t(V_24Y)
<=> t(V_24Y,c_24__type__395) ) ).
fof('$tdef_$_type_283',axiom,
! [V_24Y] :
( c_24__type__283___24t(V_24Y)
<=> t(V_24Y,c_24__type__283) ) ).
fof('$tdef_$_type_21254',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__21254___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__21254___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_13708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__13708___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__13708___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_253',axiom,
! [V_24Y] :
( c_24__type__253___24t(V_24Y)
<=> t(V_24Y,c_24__type__253) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_7831',axiom,
! [V_24Y] :
( c_24__type__7831___24t(V_24Y)
<=> t(V_24Y,c_24__type__7831) ) ).
fof('$tdef_$_type_38424',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38424___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38424___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24977',axiom,
! [V_24Y] :
( c_24__type__24977___24t(V_24Y)
<=> t(V_24Y,c_24__type__24977) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35114',axiom,
! [V_24Y] :
( c_24__type__35114___24t(V_24Y)
<=> t(V_24Y,c_24__type__35114) ) ).
fof('$tdef_$_type_1060',axiom,
! [V_24Y] :
( c_24__type__1060___24t(V_24Y)
<=> t(V_24Y,c_24__type__1060) ) ).
fof('$tdef_$_type_26432',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26432___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26432___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_44616',axiom,
! [V_24Y] :
( c_24__type__44616___24t(V_24Y)
<=> t(V_24Y,c_24__type__44616) ) ).
fof('$tdef_$_type_22282',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22282___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22282___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12001',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__12001___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__12001___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_3263',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3263___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3263___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_38380',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38380___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38380___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3797',axiom,
! [V_24Y] :
( c_24__type__3797___24t(V_24Y)
<=> t(V_24Y,c_24__type__3797) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22146',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__22146___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__22146___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_39605',axiom,
! [V_24Y] :
( c_24__type__39605___24t(V_24Y)
<=> t(V_24Y,c_24__type__39605) ) ).
fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_40945',axiom,
! [V_24Y] :
( c_24__type__40945___24t(V_24Y)
<=> t(V_24Y,c_24__type__40945) ) ).
fof('$tdef_$_type_35645',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35645___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35645___24a1(V_24X1)) ) ).
fof('$tdef_DirectedSets.DirectedSet',axiom,
! [V_24Y] :
( cDirectedSets_2eDirectedSet___24t(V_24Y)
<=> t(V_24Y,cDirectedSets_2eDirectedSet) ) ).
fof('$tdef_$_type_9965',axiom,
! [V_24Y] :
( c_24__type__9965___24t(V_24Y)
<=> t(V_24Y,c_24__type__9965) ) ).
fof('$tdef_$_type_49215',axiom,
! [V_24Y] :
( c_24__type__49215___24t(V_24Y)
<=> t(V_24Y,c_24__type__49215) ) ).
fof('$tdef_$_type_17425',axiom,
! [V_24Y] :
( c_24__type__17425___24t(V_24Y)
<=> t(V_24Y,c_24__type__17425) ) ).
fof('$tdef_$_type_3203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3203___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3203___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_31492',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31492___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31492___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24639',axiom,
! [V_24X1,V_24Y] :
( c_24__type__24639___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__24639___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5134',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5134___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5134___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31327',axiom,
! [V_24Y] :
( c_24__type__31327___24t(V_24Y)
<=> t(V_24Y,c_24__type__31327) ) ).
fof('$tdef_$_type_24428',axiom,
! [V_24Y] :
( c_24__type__24428___24t(V_24Y)
<=> t(V_24Y,c_24__type__24428) ) ).
fof('$tdef_$_type_27392',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27392___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27392___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_22526',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22526___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22526___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1297',axiom,
! [V_24Y] :
( c_24__type__1297___24t(V_24Y)
<=> t(V_24Y,c_24__type__1297) ) ).
fof('$tdef_$_type_14054',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__14054___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__14054___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_5321',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5321___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5321___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4741',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4741___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4741___24a1(V_24X1)) ) ).
fof('$tdef_$_type_44521',axiom,
! [V_24Y] :
( c_24__type__44521___24t(V_24Y)
<=> t(V_24Y,c_24__type__44521) ) ).
fof('$tdef_$_type_5233',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5233___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5233___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9851',axiom,
! [V_24Y] :
( c_24__type__9851___24t(V_24Y)
<=> t(V_24Y,c_24__type__9851) ) ).
fof('$tdef_$_type_3401',axiom,
! [V_24Y] :
( c_24__type__3401___24t(V_24Y)
<=> t(V_24Y,c_24__type__3401) ) ).
fof('$tdef_$_type_35170',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__35170___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__35170___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27042',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27042___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27042___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35891',axiom,
! [V_24Y] :
( c_24__type__35891___24t(V_24Y)
<=> t(V_24Y,c_24__type__35891) ) ).
fof('$tdef_$_type_3375',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3375___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3375___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1337',axiom,
! [V_24Y] :
( c_24__type__1337___24t(V_24Y)
<=> t(V_24Y,c_24__type__1337) ) ).
fof('$tdef_$_type_28519',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28519___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28519___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_28558',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28558___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28558___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_21769',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21769___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21769___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_20420',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20420___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20420___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_31387',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31387___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31387___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_1777',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1777___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1777___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33852',axiom,
! [V_24Y] :
( c_24__type__33852___24t(V_24Y)
<=> t(V_24Y,c_24__type__33852) ) ).
fof('$tdef_$_type_376',axiom,
! [V_24Y] :
( c_24__type__376___24t(V_24Y)
<=> t(V_24Y,c_24__type__376) ) ).
fof('$tdef_$_type_3320',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3320___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3320___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22645',axiom,
! [V_24Y] :
( c_24__type__22645___24t(V_24Y)
<=> t(V_24Y,c_24__type__22645) ) ).
fof('$tdef_$_type_22466',axiom,
! [V_24Y] :
( c_24__type__22466___24t(V_24Y)
<=> t(V_24Y,c_24__type__22466) ) ).
fof('$tdef_$_type_13385',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__13385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__13385___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_483',axiom,
! [V_24Y] :
( c_24__type__483___24t(V_24Y)
<=> t(V_24Y,c_24__type__483) ) ).
fof('$tdef_$_type_22580',axiom,
! [V_24Y] :
( c_24__type__22580___24t(V_24Y)
<=> t(V_24Y,c_24__type__22580) ) ).
fof('$tdef_$_type_800',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__800___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__800___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3179',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3179___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3179___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_36208',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36208___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36208___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2827',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2827___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__2827___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2494',axiom,
! [V_24Y] :
( c_24__type__2494___24t(V_24Y)
<=> t(V_24Y,c_24__type__2494) ) ).
fof('$tdef_Coq.micromega.Tauto.cnf',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17411',axiom,
! [V_24Y] :
( c_24__type__17411___24t(V_24Y)
<=> t(V_24Y,c_24__type__17411) ) ).
fof('$tdef_$_type_4771',axiom,
! [V_24Y] :
( c_24__type__4771___24t(V_24Y)
<=> t(V_24Y,c_24__type__4771) ) ).
fof('$tdef_$_type_3805',axiom,
! [V_24Y] :
( c_24__type__3805___24t(V_24Y)
<=> t(V_24Y,c_24__type__3805) ) ).
fof('$tdef_$_type_814',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__814___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__814___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_45404',axiom,
! [V_24Y] :
( c_24__type__45404___24t(V_24Y)
<=> t(V_24Y,c_24__type__45404) ) ).
fof('$tdef_$_type_17618',axiom,
! [V_24Y] :
( c_24__type__17618___24t(V_24Y)
<=> t(V_24Y,c_24__type__17618) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_15046',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__15046___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__15046___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4593',axiom,
! [V_24Y] :
( c_24__type__4593___24t(V_24Y)
<=> t(V_24Y,c_24__type__4593) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_33744',axiom,
! [V_24Y] :
( c_24__type__33744___24t(V_24Y)
<=> t(V_24Y,c_24__type__33744) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_5004',axiom,
! [V_24Y] :
( c_24__type__5004___24t(V_24Y)
<=> t(V_24Y,c_24__type__5004) ) ).
fof('$tdef_$_type_4591',axiom,
! [V_24Y] :
( c_24__type__4591___24t(V_24Y)
<=> t(V_24Y,c_24__type__4591) ) ).
fof('$tdef_$_type_29538',axiom,
! [V_24Y] :
( c_24__type__29538___24t(V_24Y)
<=> t(V_24Y,c_24__type__29538) ) ).
fof('$tdef_$_type_17408',axiom,
! [V_24Y] :
( c_24__type__17408___24t(V_24Y)
<=> t(V_24Y,c_24__type__17408) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_521',axiom,
! [V_24Y] :
( c_24__type__521___24t(V_24Y)
<=> t(V_24Y,c_24__type__521) ) ).
fof('$tdef_$_type_49309',axiom,
! [V_24Y] :
( c_24__type__49309___24t(V_24Y)
<=> t(V_24Y,c_24__type__49309) ) ).
fof('$tdef_$_type_21449',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__21449___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__21449___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_22037',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22037___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22037___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__14400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__14400___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_38490',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38490___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38490___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9767',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9767___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9767___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31199',axiom,
! [V_24Y] :
( c_24__type__31199___24t(V_24Y)
<=> t(V_24Y,c_24__type__31199) ) ).
fof('$tdef_$_type_18883',axiom,
! [V_24Y] :
( c_24__type__18883___24t(V_24Y)
<=> t(V_24Y,c_24__type__18883) ) ).
fof('$tdef_$_type_5712',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5712___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5712___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.prod',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4738',axiom,
! [V_24Y] :
( c_24__type__4738___24t(V_24Y)
<=> t(V_24Y,c_24__type__4738) ) ).
fof('$tdef_$_type_3430',axiom,
! [V_24Y] :
( c_24__type__3430___24t(V_24Y)
<=> t(V_24Y,c_24__type__3430) ) ).
fof('$tdef_$_type_35134',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__35134___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__35134___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3287',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3287___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3287___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35',axiom,
! [V_24Y] :
( c_24__type__35___24t(V_24Y)
<=> t(V_24Y,c_24__type__35) ) ).
fof('$tdef_$_type_10008',axiom,
! [V_24Y] :
( c_24__type__10008___24t(V_24Y)
<=> t(V_24Y,c_24__type__10008) ) ).
fof('$tdef_$_type_20633',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20633___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20633___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_21911',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21911___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21911___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26549',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26549___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26549___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21041',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__21041___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__21041___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_2465',axiom,
! [V_24Y] :
( c_24__type__2465___24t(V_24Y)
<=> t(V_24Y,c_24__type__2465) ) ).
fof('$tdef_$_type_1081',axiom,
! [V_24Y] :
( c_24__type__1081___24t(V_24Y)
<=> t(V_24Y,c_24__type__1081) ) ).
fof('$tdef_$_type_27639',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27639___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27639___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_5794',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5794___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5794___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22547',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22547___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22547___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33364',axiom,
! [V_24Y] :
( c_24__type__33364___24t(V_24Y)
<=> t(V_24Y,c_24__type__33364) ) ).
fof('$tdef_$_type_45373',axiom,
! [V_24Y] :
( c_24__type__45373___24t(V_24Y)
<=> t(V_24Y,c_24__type__45373) ) ).
fof('$tdef_$_type_29077',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29077___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29077___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4663',axiom,
! [V_24Y] :
( c_24__type__4663___24t(V_24Y)
<=> t(V_24Y,c_24__type__4663) ) ).
fof('$tdef_$_type_9205',axiom,
! [V_24Y] :
( c_24__type__9205___24t(V_24Y)
<=> t(V_24Y,c_24__type__9205) ) ).
fof('$tdef_$_type_22575',axiom,
! [V_24Y] :
( c_24__type__22575___24t(V_24Y)
<=> t(V_24Y,c_24__type__22575) ) ).
fof('$tdef_$_type_22190',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__22190___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__22190___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_9804',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9804___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9804___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_43783',axiom,
! [V_24Y] :
( c_24__type__43783___24t(V_24Y)
<=> t(V_24Y,c_24__type__43783) ) ).
fof('$tdef_$_type_19799',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19799___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19799___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_5212',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5212___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5212___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.Tauto.clause',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2eclause___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_411',axiom,
! [V_24Y] :
( c_24__type__411___24t(V_24Y)
<=> t(V_24Y,c_24__type__411) ) ).
fof('$tdef_$_type_31196',axiom,
! [V_24Y] :
( c_24__type__31196___24t(V_24Y)
<=> t(V_24Y,c_24__type__31196) ) ).
fof('$tdef_$_type_30672',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30672___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30672___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2463',axiom,
! [V_24Y] :
( c_24__type__2463___24t(V_24Y)
<=> t(V_24Y,c_24__type__2463) ) ).
fof('$tdef_$_type_35117',axiom,
! [V_24Y] :
( c_24__type__35117___24t(V_24Y)
<=> t(V_24Y,c_24__type__35117) ) ).
fof('$tdef_$_type_17416',axiom,
! [V_24Y] :
( c_24__type__17416___24t(V_24Y)
<=> t(V_24Y,c_24__type__17416) ) ).
fof('$tdef_Coq.Vectors.VectorDef.t',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30662',axiom,
! [V_24Y] :
( c_24__type__30662___24t(V_24Y)
<=> t(V_24Y,c_24__type__30662) ) ).
fof('$tdef_$_type_36402',axiom,
! [V_24Y] :
( c_24__type__36402___24t(V_24Y)
<=> t(V_24Y,c_24__type__36402) ) ).
fof('$tdef_$_type_31207',axiom,
! [V_24Y] :
( c_24__type__31207___24t(V_24Y)
<=> t(V_24Y,c_24__type__31207) ) ).
fof('$tdef_$_type_17061',axiom,
! [V_24Y] :
( c_24__type__17061___24t(V_24Y)
<=> t(V_24Y,c_24__type__17061) ) ).
fof('$tdef_$_type_2890',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__2890___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__2890___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4769',axiom,
! [V_24Y] :
( c_24__type__4769___24t(V_24Y)
<=> t(V_24Y,c_24__type__4769) ) ).
fof('$tdef_$_type_31380',axiom,
! [V_24Y] :
( c_24__type__31380___24t(V_24Y)
<=> t(V_24Y,c_24__type__31380) ) ).
fof('$tdef_$_type_34387',axiom,
! [V_24Y] :
( c_24__type__34387___24t(V_24Y)
<=> t(V_24Y,c_24__type__34387) ) ).
fof('$tdef_$_type_29570',axiom,
! [V_24Y] :
( c_24__type__29570___24t(V_24Y)
<=> t(V_24Y,c_24__type__29570) ) ).
fof('$tdef_$_type_24',axiom,
! [V_24Y] :
( c_24__type__24___24t(V_24Y)
<=> t(V_24Y,c_24__type__24) ) ).
fof('$tdef_$_type_2069',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2069___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2069___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_44501',axiom,
! [V_24Y] :
( c_24__type__44501___24t(V_24Y)
<=> t(V_24Y,c_24__type__44501) ) ).
fof('$tdef_$_type_31085',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31085___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31085___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33826',axiom,
! [V_24Y] :
( c_24__type__33826___24t(V_24Y)
<=> t(V_24Y,c_24__type__33826) ) ).
fof('$tdef_$_type_26587',axiom,
! [V_24Y] :
( c_24__type__26587___24t(V_24Y)
<=> t(V_24Y,c_24__type__26587) ) ).
fof('$tdef_$_type_35098',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35098___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35098___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8619',axiom,
! [V_24Y] :
( c_24__type__8619___24t(V_24Y)
<=> t(V_24Y,c_24__type__8619) ) ).
fof('$tdef_$_type_2468',axiom,
! [V_24Y] :
( c_24__type__2468___24t(V_24Y)
<=> t(V_24Y,c_24__type__2468) ) ).
fof('$tdef_$_type_3371',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3371___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3371___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_40129',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__40129___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__40129___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30990',axiom,
! [V_24Y] :
( c_24__type__30990___24t(V_24Y)
<=> t(V_24Y,c_24__type__30990) ) ).
fof('$tdef_$_type_17848',axiom,
! [V_24Y] :
( c_24__type__17848___24t(V_24Y)
<=> t(V_24Y,c_24__type__17848) ) ).
fof('$tdef_$_type_9960',axiom,
! [V_24Y] :
( c_24__type__9960___24t(V_24Y)
<=> t(V_24Y,c_24__type__9960) ) ).
fof('$tdef_$_type_24980',axiom,
! [V_24Y] :
( c_24__type__24980___24t(V_24Y)
<=> t(V_24Y,c_24__type__24980) ) ).
fof('$tdef_$_type_24728',axiom,
! [V_24Y] :
( c_24__type__24728___24t(V_24Y)
<=> t(V_24Y,c_24__type__24728) ) ).
fof('$tdef_$_type_24699',axiom,
! [V_24Y] :
( c_24__type__24699___24t(V_24Y)
<=> t(V_24Y,c_24__type__24699) ) ).
fof('$tdef_$_type_10042',axiom,
! [V_24Y] :
( c_24__type__10042___24t(V_24Y)
<=> t(V_24Y,c_24__type__10042) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_19373',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19373___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19373___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_33834',axiom,
! [V_24Y] :
( c_24__type__33834___24t(V_24Y)
<=> t(V_24Y,c_24__type__33834) ) ).
fof('$tdef_$_type_44643',axiom,
! [V_24Y] :
( c_24__type__44643___24t(V_24Y)
<=> t(V_24Y,c_24__type__44643) ) ).
fof('$tdef_$_type_3233',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__3233___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__3233___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3776',axiom,
! [V_24Y] :
( c_24__type__3776___24t(V_24Y)
<=> t(V_24Y,c_24__type__3776) ) ).
fof('$tdef_$_type_31202',axiom,
! [V_24Y] :
( c_24__type__31202___24t(V_24Y)
<=> t(V_24Y,c_24__type__31202) ) ).
fof('$tdef_$_type_36203',axiom,
! [V_24Y] :
( c_24__type__36203___24t(V_24Y)
<=> t(V_24Y,c_24__type__36203) ) ).
fof('$tdef_$_type_38371',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38371___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38371___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26369',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26369___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26369___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_38481',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38481___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38481___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_38412',axiom,
! [V_24Y] :
( c_24__type__38412___24t(V_24Y)
<=> t(V_24Y,c_24__type__38412) ) ).
fof('$tdef_$_type_34392',axiom,
! [V_24Y] :
( c_24__type__34392___24t(V_24Y)
<=> t(V_24Y,c_24__type__34392) ) ).
fof('$tdef_$_type_26753',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__26753___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__26753___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_33264',axiom,
! [V_24Y] :
( c_24__type__33264___24t(V_24Y)
<=> t(V_24Y,c_24__type__33264) ) ).
fof('$tdef_$_type_32115',axiom,
! [V_24Y] :
( c_24__type__32115___24t(V_24Y)
<=> t(V_24Y,c_24__type__32115) ) ).
fof('$tdef_$_type_27819',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27819___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27819___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_37328',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__37328___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__37328___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2372',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__2372___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__2372___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__P] :
( c_24__type__1___24t(V0__P)
=> ( ~ cDirectedSets_2efor__large_2eexists__arbitrarily__large___24a1(V0__P)
=> cDirectedSets_2efor__large_2eeventually___24a1(c_24__lam__34547___24a1(V0__P)) ) ) ).
%------------------------------------------------------------------------------