TPTP Problem File: SEV667+1.p
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%------------------------------------------------------------------------------
% File : SEV667+1 : TPTP v9.3.0. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Quotients.projf well defined
% 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 : Quotients.projf.well.defined.p [Kal26]
% Status : Theorem
% Rating : 0.70 v9.3.0
% Syntax : Number of formulae : 2863 (1150 unt; 0 def)
% Number of atoms : 9536 (2459 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6775 ( 102 ~; 688 |;1487 &)
% (1096 <=>;3402 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 598 ( 597 usr; 0 prp; 1-23 aty)
% Number of functors : 1633 (1633 usr;1080 con; 0-22 aty)
% Number of variables : 9122 (8544 !; 578 ?)
% 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.nat$10134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2410134___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__10135] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10135)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10135)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2410134___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__10135)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$10156',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__10157] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__10157)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__10157)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__10157)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$21728',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__21741___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__21733] :
( t(Vvar__2___24Anonymous__21733,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__21734] :
( t(Vvar__3___24Anonymous__21734,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__21733,Vvar__3___24Anonymous__21734)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2421728___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__21733)),Vvar__3___24Anonymous__21734)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.N$824',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__type__827___24t(Vv__CANONICAL__0,Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_24824___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
| ? [Vvar__0___24Anonymous__825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__825)
& Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__825)
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_24824___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(c_24__let__4__P_27__810___24a1(Vv__CANONICAL__0),happ(happ(Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0),Vv__CANONICAL__1),c_24__let__5__f_27__811___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vvar__0___24Anonymous__825) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$10151',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2410151___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__10152] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10152)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10152)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2410151___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10152) )
| ? [Vvar__0___24Anonymous__10153] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10153)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10153)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2410151___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10153) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$23516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__23517] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23517)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23517)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2423516___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__23532__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__23517)) )
| ? [Vvar__0___24Anonymous__23524] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23524)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23524)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2423516___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23524) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2423516___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_4_P\'_810',axiom,
! [V0__P,V4__p] : c_24__let__4__P_27__810___24a2(V0__P,V4__p) = happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V4__p)) ).
fof('$_def_$_let_5_f\'_811',axiom,
! [V0__P,V2__f,V5__p] : c_24__let__5__f_27__811___24a3(V0__P,V2__f,V5__p) = happ(V2__f,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V5__p)) ).
fof('$_def_$_let_var_6_p_15966_15969',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15965] : c_24__let__var__6__p__15966__15969___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15965) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15965) ).
fof('$_def_$_let_var_6_p_15968_15970',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15967] : c_24__let__var__6__p__15968__15970___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15967) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15967) ).
fof('$_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__6415] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6415)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6415)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__6416] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6416)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6416)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__6419] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6419)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__6419)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__6416,Vvar__0___24Anonymous__6419) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_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('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_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('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__925___24a1(V0__A)) ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__159782] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__159782)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__159782)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__159782,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
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('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_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__84250] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__84250)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__84250)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( 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('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__5575] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__5575)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5575) ) ).
fof('$_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.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__5578] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__5578)
& ? [Vvar__1___24Anonymous__5579] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5579)
& ? [Vvar__2___24Anonymous__5580] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__5580)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__5578,Vvar__1___24Anonymous__5579,Vvar__2___24Anonymous__5580)
& ( ? [Vvar__0___24Anonymous__5593] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5593)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5593)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__5593,Vvar__2___24Anonymous__5580) )
| ? [Vvar__0___24Anonymous__5594] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5594)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5594)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__5594,Vvar__0___24Anonymous__5578) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__5579 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__5576] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__5576)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__5576) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__39048] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__39048)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__39048,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
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__6078] :
( t(Vvar__1___24Anonymous__6078,V0__A)
& ? [Vvar__2___24Anonymous__6079] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__6079)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6078,Vvar__2___24Anonymous__6079)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__6078,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__6079,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__6054] :
( t(Vvar__2___24Anonymous__6054,V0__A)
& ? [Vvar__3___24Anonymous__6055] :
( t(Vvar__3___24Anonymous__6055,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__6054,Vvar__3___24Anonymous__6055)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__6054 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.implb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__3886] :
( t(Vvar__1___24Anonymous__3886,V0__A)
& ? [Vvar__2___24Anonymous__3887] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3887)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3886,Vvar__2___24Anonymous__3887)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__3887)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__32790___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__32788] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32788)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32788)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__32788),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__32788)) ) ) ) ) ).
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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__6066] :
( t(Vvar__2___24Anonymous__6066,V0__A)
& ? [Vvar__3___24Anonymous__6067] :
( t(Vvar__3___24Anonymous__6067,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__6066,Vvar__3___24Anonymous__6067)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__6067 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.xorb',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_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Logic_Type.notT',axiom,
! [V0__A] :
( cCoq_2eInit_2eLogic__Type_2enotT___24a1(V0__A)
<=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> p(c_24False) ) ) ).
fof('$_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__4184] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4184)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4184)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__4184,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__24157] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24157)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24157)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__24158] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24158)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24158)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__24161] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24161)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24161)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__24158,Vvar__0___24Anonymous__24161) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8625] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8625)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8625)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8625)
& ( ( Vvar__0___24Anonymous__8625 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8628] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8628)
& Vvar__0___24Anonymous__8625 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8628)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__8628)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.double',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2edouble___24a1(V0__n) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V0__n) ).
fof('$_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__8595] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8595)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8595)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__8596] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8596)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8596)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__8599] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8599)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8599)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__8596,Vvar__0___24Anonymous__8599) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__8620] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8620)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8620)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8620)
& ( ( Vvar__0___24Anonymous__8620 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__8623] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8623)
& Vvar__0___24Anonymous__8620 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8623)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__8623) ) ) ) ) ) ) ) ).
fof('$_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__8602] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8602)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8602)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__8605] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8605)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8605)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__8602,Vvar__0___24Anonymous__8605) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.max',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__8608] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8608)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8608)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8611] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8611)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8611)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__8608,Vvar__0___24Anonymous__8611)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8614] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8614)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8614)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__8617] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8617)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8617)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__8614,Vvar__0___24Anonymous__8617)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.mul',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__4189] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4189)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4189)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__4189,V2__m)) ) ) ) ).
fof('$_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__4192] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4192)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4192)
& 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__4192)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__4182] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4182)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4182)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__4182 ) ) ) ).
fof('$_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__8589] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8589)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8589)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__8592] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8592)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8592)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__8589,Vvar__0___24Anonymous__8592) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__39505] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__39505)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__39505) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__159779] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__159779)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__159779)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__159779,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__4200] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4200)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4200)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__4200) ) ) ) ).
fof('$_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('$_def_Coq.Init.Specif.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__27856___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__27850] :
( t(Vvar__2__x__27850,V0__A)
& p(happ(V1__P,Vvar__2__x__27850))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__27850)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__27850 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__27879___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__27873] :
( t(Vvar__2__x__27873,V0__A)
& ? [Vvar__3___24Anonymous__27874] :
( t(Vvar__3___24Anonymous__27874,happ(V1__P,Vvar__2__x__27873))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__27873,Vvar__3___24Anonymous__27874)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__27873 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__8389] :
( t(Vvar__1___24Anonymous__8389,V0__A)
& ? [Vvar__2___24Anonymous__8390] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8390)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8389,Vvar__2___24Anonymous__8390)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__8389 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__8390) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__8401] :
( t(Vvar__1___24Anonymous__8401,V1__B)
& ? [Vvar__2___24Anonymous__8402] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8402)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8401,Vvar__2___24Anonymous__8402)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__8402,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__8401)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__8432] :
( t(Vvar__1___24Anonymous__8432,V1__B)
& ? [Vvar__2___24Anonymous__8433] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__8433)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__8432,Vvar__2___24Anonymous__8433)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__8432),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__8433)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,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_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__8377] :
( t(Vvar__1___24Anonymous__8377,V0__A)
& ? [Vvar__2___24Anonymous__8378] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__8378)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__8377,Vvar__2___24Anonymous__8378)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__8377 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__52633] :
( t(Vvar__1___24Anonymous__52633,V0__A)
& ? [Vvar__2___24Anonymous__52634] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__52634)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__52633,Vvar__2___24Anonymous__52634)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__52633 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__52636] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__52636)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__52636)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__52643] :
( t(Vvar__1___24Anonymous__52643,V0__A)
& ? [Vvar__2___24Anonymous__52644] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__52644)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__52643,Vvar__2___24Anonymous__52644)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__52636,Vvar__2___24Anonymous__52644,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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.ChoiceFacts.DependentFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__38958___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,happ(V1__B,V3__x))
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__38965___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle)
<=> ! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__5865___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__92___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
! [V0__A,V1__B,V2__R] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3(V0__A,V1__B,V2__R)
<=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__92___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__38975___24t(V0__A,V1__R)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__n),V3__y)) ) )
=> ? [V3__f] :
( c_24__type__975___24t(V0__A,V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(happ(V1__R,V4__n),happ(V3__f,V4__n))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalDependentChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__50___24t(V0__A,V1__R)
=> ( ! [V2__x] :
( t(V2__x,V0__A)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__x),V3__y)) ) )
=> ! [V3__x0] :
( t(V3__x0,V0__A)
=> ? [V4__f] :
( c_24__type__975___24t(V0__A,V4__f)
& happ(V4__f,cCoq_2eInit_2eDatatypes_2eO) = V3__x0
& ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> p(happ(happ(V1__R,happ(V4__f,V5__n)),happ(V4__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__n)))) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__50___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R)
=> ? [V3__f] :
( c_24__type__912___24t(V0__A,V3__f)
& ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(happ(happ(V1__R,V4__x),happ(V3__f,V4__x)))
& ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__x_27))
=> happ(V3__f,V4__x) = happ(V3__f,V5__x_27) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__50___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__5865___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__x_27] :
( t(V6__x_27,V0__A)
=> ! [V7__y] :
( t(V7__y,V1__B)
=> ( p(happ(happ(V2__R,V5__x),V6__x_27))
=> ( p(happ(happ(V3__T,V5__x),V7__y))
=> p(happ(happ(V3__T,V6__x_27),V7__y)) ) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ? [V7__y] :
( t(V7__y,V1__B)
& p(happ(happ(V3__T,V6__x),V7__y)) ) )
=> ? [V7__f] :
( c_24__type__92___24t(V0__A,V1__B,V7__f)
& ! [V8__x] :
( t(V8__x,V0__A)
=> ( p(happ(happ(V3__T,V8__x),happ(V7__f,V8__x)))
& ! [V9__x_27] :
( t(V9__x_27,V0__A)
=> ( p(happ(happ(V2__R,V8__x),V9__x_27))
=> happ(V7__f,V8__x) = happ(V7__f,V9__x_27) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__50___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__5865___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ? [V6__y] :
( t(V6__y,V1__B)
& ! [V7__x_27] :
( t(V7__x_27,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V7__x_27))
=> p(happ(happ(V3__T,V7__x_27),V6__y)) ) ) ) )
=> ? [V6__f] :
( c_24__type__92___24t(V0__A,V1__B,V6__f)
& ! [V7__x] :
( t(V7__x,V0__A)
=> ( p(happ(happ(V3__T,V7__x),happ(V6__f,V7__x)))
& ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> happ(V6__f,V7__x) = happ(V6__f,V8__x_27) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.BoolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eBoolP)
<=> ! [V0__C] :
( cProp___24t(V0__C)
=> ( p(V0__C)
=> ( p(V0__C)
=> p(V0__C) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2___24t(V0__A,V1__P)
=> ! [V2___24Anonymous] :
( t(V2___24Anonymous,V0__A)
=> ? [V3__x] :
( t(V3__x,V0__A)
& ( ? [V4__x] :
( t(V4__x,V0__A)
& p(happ(V1__P,V4__x)) )
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.GodelDummett',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eGodelDummett)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
=> p(V1__B) )
| ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.IndependenceOfGeneralPremises',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2___24t(V0__A,V1__P)
=> ! [V2__Q] :
( cProp___24t(V2__Q)
=> ! [V3___24Anonymous] :
( t(V3___24Anonymous,V0__A)
=> ( ( p(V2__Q)
=> ? [V5__x] :
( t(V5__x,V0__A)
& p(happ(V1__P,V5__x)) ) )
=> ? [V5__x] :
( t(V5__x,V0__A)
& ( p(V2__Q)
=> p(happ(V1__P,V5__x)) ) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__C] :
( cProp___24t(V2__C)
=> ( ( p(V2__C)
=> ( p(V0__A)
| p(V1__B) ) )
=> ( ( p(V2__C)
=> p(V0__A) )
| ( p(V2__C)
=> p(V1__B) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ClassicalFacts.generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V0__A)
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.provable_prop_extensionality',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprovable__prop__extensionality)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> V0__A = c_24True ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(V1__B) )
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
! [V0__U,V1__P,V2__p,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V0__U,V1__P,V2__p,V3__x)
<=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
! [V0__U,V1__x,V2__P] :
( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P)
<=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_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('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
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('$_def_Coq.NArith.BinNat.N.peano_rect',axiom,
! [V0__P,V1__f0,V2__f,V3__n] : cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__f0,V2__f,V3__n) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_24824___24a4(V0__P,V1__f0,V2__f,V3__n) ).
fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__859___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__4692] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4692)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4692)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__4695] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4695)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4695)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__4692,Vvar__0___24Anonymous__4695)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__31950] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31950)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31950)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31950)
& ( ? [Vvar__0___24Anonymous__31954] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31954)
& Vvar__0___24Anonymous__31950 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31954)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31954) )
| ? [Vvar__0___24Anonymous__31955] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31955)
& Vvar__0___24Anonymous__31950 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31955)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31955) )
| ( Vvar__0___24Anonymous__31950 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__38027] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38027)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38027)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38027)) ) ) ) ).
fof('$_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__30623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30623)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30623)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__30624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30624)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30624)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30627)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30627)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__30624,Vvar__0___24Anonymous__30627) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30629] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30629)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30629)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30629)
& ( ? [Vvar__0___24Anonymous__30633] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30633)
& Vvar__0___24Anonymous__30629 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30633)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30634] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30634)
& Vvar__0___24Anonymous__30629 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30634)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__30629 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__38044] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38044)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38044)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__38047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38047)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__38047)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__38044,Vvar__0___24Anonymous__38047) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.max',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V1__n_27 )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__n_27) = V0__n ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.min',axiom,
! [V0__n,V1__n_27] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n_27)
=> ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V0__n )
| ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__n_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__n_27) = V1__n_27 ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__4699] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4699)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4699)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__4702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4702)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4702)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__4699,Vvar__0___24Anonymous__4702)) ) ) ) ) ) ) ) ).
fof('$_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__4691] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4691)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__4691)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__4691) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__787] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__787)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__787)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__787)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__40256] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__40256)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__40256) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23421)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23421)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__23421,V1__n) ) ) ) ).
fof('$_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__23425] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23425)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23425)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__23425) ) ) ) ).
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.eq',axiom,
cCoq_2ePArith_2eBinPos_2ePos_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
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] :
( 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('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_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.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__31957] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31957)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31957)
& ( ? [Vvar__0___24Anonymous__31961] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31961)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31961)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31957,Vvar__0___24Anonymous__31961) )
| ? [Vvar__0___24Anonymous__31962] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31962)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31962)
& 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__31963] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31963)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31963)
& ( ? [Vvar__0___24Anonymous__31967] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31967)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31967)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31968] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31968)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31968)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31963,Vvar__0___24Anonymous__31968) )
| ( 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__31969] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31969)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31969)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31970] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31970)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31970)
& 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.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__23445] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23445)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23445)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__23445),Vvar__0___24Anonymous__23445)) )
| ? [Vvar__0___24Anonymous__23446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23446)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23446)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__23446),Vvar__0___24Anonymous__23446) )
| ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__23461] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23461)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23461)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__23461,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__23462] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23462)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23462)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__23462,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__5016] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5016)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5016)
& 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__5016,V2__y))) )
| ? [Vvar__0___24Anonymous__5017] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5017)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5017)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5017,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__86183] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__86183)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__86183)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__86183)
& ( ( Vvar__0___24Anonymous__86183 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__86186] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__86186)
& Vvar__0___24Anonymous__86183 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__86186)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__86183)) ) ) ) ) ) ) ) ).
fof('$_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__87241] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__87241)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__87241)
& 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__87241)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__38070] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38070)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__38070)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__38070)) )
| ? [Vvar__0___24Anonymous__38071] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38071)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__38071)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__38071)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_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__38067] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38067)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__38067)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__38067 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__4911] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4911)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4911)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__4911)) )
| ? [Vvar__0___24Anonymous__4912] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4912)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__4912)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__4912) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__40259] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__40259)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__40259) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__159844] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__159844)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__159844)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__159857___24a1(Vvar__0___24Anonymous__159844) )
| ? [Vvar__0___24Anonymous__159848] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__159848)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__159848)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__159864___24a1(Vvar__0___24Anonymous__159848) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__159868 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__9911] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9911)
& ? [Vvar__1__Qden__9912] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9912)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9911,Vvar__1__Qden__9912)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__9912 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__9906] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9906)
& ? [Vvar__1__Qden__9907] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9907)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9906,Vvar__1__Qden__9907)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__9906 ) ) ) ).
fof('$_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('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__24322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24322)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__24322)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__24322) )
| ? [Vvar__0___24Anonymous__24323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24323)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__24323)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__24323)) ) ) ) ).
fof('$_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] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.commut',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V4__y),V3__x))
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V2__R2,V6__z),V4__y))
=> cCoq_2eInit_2eLogic_2eex2___24a3(V0__A,c_24__lam__4325___24a3(V0__A,V2__R2,V3__x),c_24__lam__4329___24a3(V0__A,V1__R1,V6__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.equiv',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V0__A,V1__R)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.inclusion',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V3__x),V4__y))
=> p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__50___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.same_relation',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__R1,V2__R2)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
& cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__R2,V1__R1) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Operators.transp',axiom,
! [V0__A,V1__R,V2__x,V3__y] :
( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,V1__R,V2__x,V3__y)
<=> p(happ(happ(V1__R,V3__y),V2__x)) ) ).
fof('$_def_Coq.Relations.Relation_Operators.union',axiom,
! [V0__A,V1__R1,V2__R2,V3__x,V4__y] :
( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V0__A,V1__R1,V2__R2,V3__x,V4__y)
<=> ( p(happ(happ(V1__R1,V3__x),V4__y))
| p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Ensembles.Ensemble',axiom,
! [V0__U] : cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U) = c_24__type__2___24a1(V0__U) ).
fof('$_def_Coq.Sets.Ensembles.In',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x)
<=> p(happ(V1__A,V2__x)) ) ).
fof('$_def_Coq.Sets.Ensembles.Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ) ).
fof('$_def_Coq.Sets.Image.injective',axiom,
! [V0__U,V1__V,V2__f] :
( cCoq_2eSets_2eImage_2einjective___24a3(V0__U,V1__V,V2__f)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__y] :
( t(V4__y,V0__U)
=> ( happ(V2__f,V3__x) = happ(V2__f,V4__y)
=> V3__x = V4__y ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Rel',axiom,
! [V0__U] : cCoq_2eSets_2ePartial__Order_2eRel___24a1(V0__U) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) ).
fof('$_def_Coq.Sets.Relations_1.Antisymmetric',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__50___24a1(V0__U) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt = cCoq_2eNArith_2eBinNat_2eN_2elt ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__23436] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__23436)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__23436) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__23441] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__23441)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__23441) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__23386] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__23386)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__23386) ) ).
fof('$_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__23560] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__23560)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__23560) ) ).
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.t',axiom,
! [Vvar__23563] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__23563)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__23563) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__23631] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__23631)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__23631) ) ).
fof('$_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('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
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] :
( 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('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__23581] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23581)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23581)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23581) )
| ? [Vvar__0___24Anonymous__23582] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23582)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23582)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23582) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__5756] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5756)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5756)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5756) )
| ? [Vvar__0___24Anonymous__5757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5757)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5757)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5757) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__86950] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__86950)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__86950)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__86950) )
| ? [Vvar__0___24Anonymous__86951] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__86951)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__86951)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__86951) ) ) ) ).
fof('$_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__5707] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5707)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5707)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__5711] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5711)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5711)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__5707,Vvar__0___24Anonymous__5711)) )
| ? [Vvar__0___24Anonymous__5712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5712)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5712)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__5707,Vvar__0___24Anonymous__5712) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5713] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5713)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5713)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__5717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5717)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5717)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__5717,Vvar__0___24Anonymous__5713) )
| ? [Vvar__0___24Anonymous__5718] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5718)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5718)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__5713,Vvar__0___24Anonymous__5718)) ) ) ) ) ) ) ) ).
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__5739] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5739)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5739)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__5740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5740)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5740)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__5741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5741)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5741)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__5745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5745)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5745)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__5741,Vvar__0___24Anonymous__5745) )
| ? [Vvar__0___24Anonymous__5746] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5746)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5746)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__5747] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5747)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5747)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__5751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5751)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5751)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__5752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5752)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5752)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__5747,Vvar__0___24Anonymous__5752)) ) ) ) ) ) ) ) ).
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__5769] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__5769)
& ? [Vvar__3___24Anonymous__5770] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__5770)
& 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__5769,Vvar__3___24Anonymous__5770)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__5769 ) ) ) ) ).
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__23598] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23598)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23598)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23598)
& ( ? [Vvar__0___24Anonymous__23602] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23602)
& Vvar__0___24Anonymous__23598 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23602)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23603)
& Vvar__0___24Anonymous__23598 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23603)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__23598 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__23604] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23604)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23604)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23604)
& ( ? [Vvar__0___24Anonymous__23608] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23608)
& Vvar__0___24Anonymous__23604 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23608)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23609)
& Vvar__0___24Anonymous__23604 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23609)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__23604 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__23594] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__23594)
& ? [Vvar__3___24Anonymous__23595] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__23595)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__23594,Vvar__3___24Anonymous__23595)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__23595 ) ) ) ) ).
fof('$_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__5726] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5726)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5726)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5730)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5730)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5726,Vvar__0___24Anonymous__5730)) )
| ? [Vvar__0___24Anonymous__5731] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5731)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5731)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5726,Vvar__0___24Anonymous__5731)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__5732] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5732)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5732)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5736)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5736)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5732,Vvar__0___24Anonymous__5736)) )
| ? [Vvar__0___24Anonymous__5737] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5737)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5737)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__5732,Vvar__0___24Anonymous__5737)) ) ) ) ) ) ) ) ).
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__23612] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23612)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23612)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23612)
& ( ? [Vvar__0___24Anonymous__23616] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23616)
& Vvar__0___24Anonymous__23612 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23616)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__23617] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23617)
& Vvar__0___24Anonymous__23612 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23617)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__23612 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__23618] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23618)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23618)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23618)
& ( ? [Vvar__0___24Anonymous__23622] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23622)
& Vvar__0___24Anonymous__23618 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23622)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__23623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23623)
& Vvar__0___24Anonymous__23618 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23623)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__23618 = 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__23583] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23583)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23583)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23583) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__5762] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5762)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5762)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__5762)) ) ) ) ).
fof('$_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__5722] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5722)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5722)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5722) )
| ? [Vvar__0___24Anonymous__5723] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5723)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5723)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5723) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__31974] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31974)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31974)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__31974) )
| ? [Vvar__0___24Anonymous__31975] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31975)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31975)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__40262] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__40262)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__40262) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__5760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5760)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5760)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5760) )
| ? [Vvar__0___24Anonymous__5761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5761)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5761)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__38749] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38749)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__38749)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__38749) )
| ? [Vvar__0___24Anonymous__38750] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__38750)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__38750)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__23586] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23586)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23586)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__23586 )
| ? [Vvar__0___24Anonymous__23587] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23587)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23587)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
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.eqm',axiom,
! [V0__N,V1__a,V2__b] :
( cCoq_2eZArith_2eZdiv_2eeqm___24a3(V0__N,V1__a,V2__b)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V1__a,V0__N) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V2__b,V0__N) ) ).
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__23245] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23245)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23245)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23245)
& ( ? [Vvar__0___24Anonymous__23249] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23249)
& Vvar__0___24Anonymous__23245 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23249)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23250] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23250)
& Vvar__0___24Anonymous__23245 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23250)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__23245 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23251] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23251)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23251)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23251)
& ( ? [Vvar__0___24Anonymous__23255] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23255)
& Vvar__0___24Anonymous__23251 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23255)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23256] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23256)
& Vvar__0___24Anonymous__23251 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23256)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__23251 = 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__23257] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23257)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23257)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23257)
& ( ? [Vvar__0___24Anonymous__23261] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23261)
& Vvar__0___24Anonymous__23257 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23261)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23262)
& Vvar__0___24Anonymous__23257 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23262)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__23257 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23263)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23263)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23263)
& ( ? [Vvar__0___24Anonymous__23267] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23267)
& Vvar__0___24Anonymous__23263 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23267)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__23268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23268)
& Vvar__0___24Anonymous__23263 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23268)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__23263 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.Is_power',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__23270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23270)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23270)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__23271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23271)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23271)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__23271) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Znat.neq',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__6177___24a1(V0__D) ).
fof('$_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__10086] :
( t(Vvar__1___24Anonymous__10086,V1__A)
& ? [Vvar__2___24Anonymous__10087] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10087)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10087)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__10086,Vvar__2___24Anonymous__10087)
& ( ( Vvar__2___24Anonymous__10087 = 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__10086)) ) )
| ? [Vvar__1___24Anonymous__10098] :
( t(Vvar__1___24Anonymous__10098,V1__A)
& ? [Vvar__2___24Anonymous__10099] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__10099)
& Vvar__2___24Anonymous__10087 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__10098,Vvar__2___24Anonymous__10099)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__10086))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__10087) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__31879] :
( t(Vvar__1___24Anonymous__31879,V1__A)
& ? [Vvar__2___24Anonymous__31880] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__31880)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__31879,Vvar__2___24Anonymous__31880)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__31879))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__31880,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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.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('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.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__8340] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8340)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8340)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8340)
& ( ? [Vvar__0___24Anonymous__8344] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8344)
& Vvar__0___24Anonymous__8340 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8344)
& 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__8340))) )
| ? [Vvar__0___24Anonymous__8345] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8345)
& Vvar__0___24Anonymous__8340 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__8345)
& 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__8340))) )
| ( Vvar__0___24Anonymous__8340 = 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__8346] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8346)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8346)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__8346)
& ( ? [Vvar__0___24Anonymous__8350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8350)
& Vvar__0___24Anonymous__8346 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8350)
& 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__8346)) )
| ? [Vvar__0___24Anonymous__8351] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8351)
& Vvar__0___24Anonymous__8346 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__8351)
& 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__8346)) )
| ( Vvar__0___24Anonymous__8346 = 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('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__8305] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8305)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__8305)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__8305))) )
| ? [Vvar__0___24Anonymous__8306] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__8306)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__8306)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__8306)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.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__24993] :
( t(Vvar__1___24Anonymous__24993,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__24993)
& ( ? [Vvar__1___24Anonymous__25003] :
( t(Vvar__1___24Anonymous__25003,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__25003)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__24993),Vvar__1___24Anonymous__25003) )
| ? [Vvar__1___24Anonymous__25005] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25005)
& ? [Vvar__2___24Anonymous__25006] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__25006)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__25005,Vvar__2___24Anonymous__25006)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__25009] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__25009)
& ? [Vvar__2___24Anonymous__25010] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__25010)
& ? [Vvar__3___24Anonymous__25011] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__25011)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__25009,Vvar__2___24Anonymous__25010,Vvar__3___24Anonymous__25011)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__25016] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25016)
& ? [Vvar__2___24Anonymous__25017] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__25017)
& ( 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__25016,Vvar__2___24Anonymous__25017)
& ( ? [Vvar__1___24Anonymous__25037] :
( t(Vvar__1___24Anonymous__25037,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__25037)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__25039] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25039)
& ? [Vvar__2___24Anonymous__25040] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__25040)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25016)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25039)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__25039,Vvar__2___24Anonymous__25040)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__25016,Vvar__1___24Anonymous__25039) = 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__25017,Vvar__2___24Anonymous__25040) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__25016,Vvar__1___24Anonymous__25039) = 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__25016,Vvar__1___24Anonymous__25039) = 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__25045] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__25045)
& ? [Vvar__2___24Anonymous__25046] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__25046)
& ? [Vvar__3___24Anonymous__25047] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__25047)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__25045,Vvar__2___24Anonymous__25046,Vvar__3___24Anonymous__25047)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__25052] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__25052)
& ? [Vvar__2___24Anonymous__25053] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__25053)
& ? [Vvar__3___24Anonymous__25054] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__25054)
& ( 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__25052,Vvar__2___24Anonymous__25053,Vvar__3___24Anonymous__25054)
& ( ? [Vvar__1___24Anonymous__25087] :
( t(Vvar__1___24Anonymous__25087,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__25087)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__25089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__25089)
& ? [Vvar__2___24Anonymous__25090] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__25090)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__25089,Vvar__2___24Anonymous__25090)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__25093] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__25093)
& ? [Vvar__2___24Anonymous__25094] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__25094)
& ? [Vvar__3___24Anonymous__25095] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__25095)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__25053)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__25094)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__25093,Vvar__2___24Anonymous__25094,Vvar__3___24Anonymous__25095)
& ( ( cType___24t(V0__C)
=> ( c_24__type__22063___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__25052)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__25093)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__25053,Vvar__2___24Anonymous__25094) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__25052,Vvar__1___24Anonymous__25093) = 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__25054,Vvar__3___24Anonymous__25095) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__25052,Vvar__1___24Anonymous__25093) = 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__25053,Vvar__2___24Anonymous__25094) = 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__25053,Vvar__2___24Anonymous__25094) = 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('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__40108] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__40108)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__40108)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__40108),V4__x,Vvar__0___24Anonymous__40108) )
| ? [Vvar__0___24Anonymous__40109] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__40109)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__40109)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__40109),V4__x,Vvar__0___24Anonymous__40109) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__15985] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15985)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__15985)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__15985) ) ) ) ) ).
fof('$_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__15965] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15965)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15965)
& 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__15966__15969___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15965)),c_24__let__var__6__p__15966__15969___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15965))) )
| ? [Vvar__0___24Anonymous__15967] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15967)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15967)
& 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__15968__15970___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15967)),c_24__let__var__6__p__15968__15970___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__15967)) )
| ( 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('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Quotients.InducedFunction2.projf',axiom,
! [V0__a] : cQuotients_2eInducedFunction2_2eprojf___24a1(V0__a) = cQuotients_2equotient__projection___24a3(cB,cS,cf___24a1(V0__a)) ).
fof('$_def_Quotients.equiv_class',axiom,
! [V0__A,V1__R,V2__x] : cQuotients_2eequiv__class___24a3(V0__A,V1__R,V2__x) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__A,c_24__lam__4329___24a3(V0__A,V1__R,V2__x)) ).
fof('$_def_Quotients.equiv_classes',axiom,
! [V0__A,V1__R] : cQuotients_2eequiv__classes___24a2(V0__A,V1__R) = cCoq_2eSets_2eImage_2eIm___24a4(V0__A,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__A),cQuotients_2eequiv__class___24a2(V0__A,V1__R)) ).
fof('$_def_Quotients.induced_function',axiom,
! [V0__A,V1__B,V2__R,V3__f,V6__xbar] : cQuotients_2einduced__function___24a5(V0__A,V1__B,V2__R,V3__f,V6__xbar) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V1__B,c_24__lam__178372___24a5(V0__A,V1__B,V2__R,V3__f,V6__xbar),cCoq_2eLogic_2eDescription_2econstructive__definite__description___24a3(V1__B,c_24__lam__178387___24a5(V0__A,V1__B,V2__R,V3__f,V6__xbar),cQuotients_2edescription__of__fbar___24a5(V0__A,V1__B,V2__R,V3__f,V6__xbar))) ).
fof('$_def_Quotients.quotient',axiom,
! [V0__A,V1__R] : cQuotients_2equotient___24a2(V0__A,V1__R) = cCoq_2eInit_2eSpecif_2esig___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),c_24__lam__163830___24a2(V0__A,V1__R)) ).
fof('$_def_Quotients.quotient_projection',axiom,
! [V0__A,V1__R,V2__x] : cQuotients_2equotient__projection___24a3(V0__A,V1__R,V2__x) = cCoq_2eInit_2eSpecif_2eexist___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),cCoq_2eSets_2eEnsembles_2eIn___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),cQuotients_2eequiv__classes___24a2(V0__A,V1__R)),cQuotients_2eequiv__class___24a3(V0__A,V1__R,V2__x),cQuotients_2eequiv__class__in__quotient___24a3(V0__A,V1__R,V2__x)) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5848,Vvar__1___24Anonymous__5849,Vvar__0__P__5850,Vvar__1___24Anonymous__5851] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5848) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5850) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__23545,Vvar__1___24Anonymous__23546,Vvar__2___24Anonymous__23547] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23545,Vvar__1___24Anonymous__23546,Vvar__2___24Anonymous__23547) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__6144,Vvar__1__Plt__6145,Vvar__2__Pgt__6146,Vvar__3___24Anonymous__6147,Vvar__0__Peq__6148,Vvar__1__Plt__6149,Vvar__2__Pgt__6150,Vvar__3___24Anonymous__6151] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6144,Vvar__1__Plt__6145,Vvar__2__Pgt__6146) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6148,Vvar__1__Plt__6149,Vvar__2__Pgt__6150) ).
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__230] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__230) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__5982,Vvar__1___24Anonymous__5983,Vvar__0__A__5984] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5982,Vvar__1___24Anonymous__5983) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5984) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__6008,Vvar__1__B__6009,Vvar__2___24Anonymous__6010,Vvar__0__A__6011,Vvar__1__B__6012,Vvar__2___24Anonymous__6013] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__6008,Vvar__1__B__6009,Vvar__2___24Anonymous__6010) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__6011,Vvar__1__B__6012,Vvar__2___24Anonymous__6013) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3857,Vvar__0__A__3858,Vvar__1___24Anonymous__3859,Vvar__2___24Anonymous__3860] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3857) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3858,Vvar__1___24Anonymous__3859,Vvar__2___24Anonymous__3860) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__39055,Vvar__1__f__39056,Vvar__0__i__39057,Vvar__1__f__39058,Vvar__2__e__39059] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__39055,Vvar__1__f__39056) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__39057,Vvar__1__f__39058,Vvar__2__e__39059) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__32972] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__32972) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__32996,Vvar__0__d__32997] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__32996) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__32997) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__22627,Vvar__1__B__22628,Vvar__2___24Anonymous__22629,Vvar__0__A__22630,Vvar__1__B__22631,Vvar__2___24Anonymous__22632] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22627,Vvar__1__B__22628,Vvar__2___24Anonymous__22629) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22630,Vvar__1__B__22631) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__4497,Vvar__1__B__4498,Vvar__2___24Anonymous__4499,Vvar__0__A__4500,Vvar__1__B__4501,Vvar__2___24Anonymous__4502] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4497,Vvar__1__B__4498) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4500,Vvar__1__B__4501) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__375] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__375) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1254] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1254) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1200,Vvar__0___24Anonymous__1201] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1200) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1201) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__23535,Vvar__1___24Anonymous__23536] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__23535,Vvar__1___24Anonymous__23536) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__4980] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__4980) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__10176,Vvar__1___24Anonymous__10177,Vvar__0__x__10178,Vvar__1__n__10179,Vvar__2___24Anonymous__10180] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__10176) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__10178,Vvar__1__n__10179) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__22648,Vvar__1___24Anonymous__22649] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22648,Vvar__1___24Anonymous__22649) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__9853,Vvar__1__lt__9854,Vvar__2__eq__9855,Vvar__3__x__9856,Vvar__4__y__9857,Vvar__5___24Anonymous__9858,Vvar__0__X__9859,Vvar__1__lt__9860,Vvar__2__eq__9861,Vvar__3__x__9862,Vvar__4__y__9863,Vvar__5___24Anonymous__9864] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9853,Vvar__1__lt__9854,Vvar__2__eq__9855,Vvar__3__x__9856,Vvar__4__y__9857) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9859,Vvar__1__lt__9860,Vvar__2__eq__9861,Vvar__3__x__9862,Vvar__4__y__9863) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__8295,Vvar__0__n__8296,Vvar__1___24Anonymous__8297] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8295) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8296,Vvar__1___24Anonymous__8297) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__23108,Vvar__0__A__23109,Vvar__1__h__23110,Vvar__2__n__23111,Vvar__3___24Anonymous__23112] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__23108) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__23109,Vvar__1__h__23110,Vvar__2__n__23111,Vvar__3___24Anonymous__23112) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__6303,Vvar__1___24Anonymous__6304,Vvar__0__C__6305,Vvar__1___24Anonymous__6306] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6303,Vvar__1___24Anonymous__6304) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6305,Vvar__1___24Anonymous__6306) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__6367,Vvar__1___24Anonymous__6368,Vvar__0__C__6369,Vvar__1___24Anonymous__6370,Vvar__2___24Anonymous__6371] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6367,Vvar__1___24Anonymous__6368) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6369,Vvar__1___24Anonymous__6370,Vvar__2___24Anonymous__6371) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__6404,Vvar__1___24Anonymous__6405] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__6404,Vvar__1___24Anonymous__6405) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
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('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__15601,Vvar__1___24Anonymous__15602,Vvar__0__C__15603,Vvar__1___24Anonymous__15604] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15601,Vvar__1___24Anonymous__15602) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15603,Vvar__1___24Anonymous__15604) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__23003,Vvar__1__TX__23004,Vvar__2__AA__23005,Vvar__3__AF__23006,Vvar__0__TA__23007,Vvar__1__TX__23008,Vvar__2__AA__23009,Vvar__3__AF__23010] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__23003,Vvar__1__TX__23004,Vvar__2__AA__23005,Vvar__3__AF__23006) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__23007,Vvar__1__TX__23008,Vvar__2__AA__23009,Vvar__3__AF__23010) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__37300,Vvar__0__A__37301,Vvar__1___24Anonymous__37302] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37300) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37301,Vvar__1___24Anonymous__37302) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__23189,Vvar__1___24Anonymous__23190] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__23189,Vvar__1___24Anonymous__23190) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__7472,Vvar__0__C__7473] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7472) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7473) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__15900,Vvar__0__C__15901] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15900) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15901) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__15676,Vvar__1___24Anonymous__15677,Vvar__0__C__15678,Vvar__1___24Anonymous__15679,Vvar__2___24Anonymous__15680] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15676,Vvar__1___24Anonymous__15677) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15678,Vvar__1___24Anonymous__15679,Vvar__2___24Anonymous__15680) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__15710,Vvar__1___24Anonymous__15711] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15710,Vvar__1___24Anonymous__15711) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__22151,Vvar__1__req__22152,Vvar__2__reqb__22153,Vvar__3___24Anonymous__22154] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__22151,Vvar__1__req__22152,Vvar__2__reqb__22153) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_fix_23532_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__23533] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23533)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23533)
& c_24__fix__23532__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__23532__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__23533)) )
| ? [Vvar__0___24Anonymous__23534] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23534)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23534)
& c_24__fix__23532__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23534) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__23532__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__5856,Vvar__0__P__5857,Vvar__1___24Anonymous__5858,Vvar__1___24Anonymous__5859] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5856) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5857)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5856 = Vvar__0__P__5857 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__5852,Vvar__0__P__5853,Vvar__1___24Anonymous__5854,Vvar__1___24Anonymous__5855] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5852) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5853)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__5852 = Vvar__0__P__5853 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__23548,Vvar__0___24Anonymous__23549,Vvar__1___24Anonymous__23550,Vvar__1___24Anonymous__23551,Vvar__2___24Anonymous__23552,Vvar__2___24Anonymous__23553] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23548,Vvar__1___24Anonymous__23550,Vvar__2___24Anonymous__23552) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23549,Vvar__1___24Anonymous__23551,Vvar__2___24Anonymous__23553)
=> ( Vvar__2___24Anonymous__23552 = Vvar__2___24Anonymous__23553
& Vvar__1___24Anonymous__23550 = Vvar__1___24Anonymous__23551
& Vvar__0___24Anonymous__23548 = Vvar__0___24Anonymous__23549 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__6152,Vvar__0__Peq__6153,Vvar__1__Plt__6154,Vvar__1__Plt__6155,Vvar__2__Pgt__6156,Vvar__2__Pgt__6157,Vvar__3___24Anonymous__6158,Vvar__3___24Anonymous__6159] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6152,Vvar__1__Plt__6154,Vvar__2__Pgt__6156) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6153,Vvar__1__Plt__6155,Vvar__2__Pgt__6157)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__6156 = Vvar__2__Pgt__6157
& Vvar__1__Plt__6154 = Vvar__1__Plt__6155
& Vvar__0__Peq__6152 = Vvar__0__Peq__6153 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__6168,Vvar__0__Peq__6169,Vvar__1__Plt__6170,Vvar__1__Plt__6171,Vvar__2__Pgt__6172,Vvar__2__Pgt__6173,Vvar__3___24Anonymous__6174,Vvar__3___24Anonymous__6175] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__6168,Vvar__1__Plt__6170,Vvar__2__Pgt__6172) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__6169,Vvar__1__Plt__6171,Vvar__2__Pgt__6173)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__6172 = Vvar__2__Pgt__6173
& Vvar__1__Plt__6170 = Vvar__1__Plt__6171
& Vvar__0__Peq__6168 = Vvar__0__Peq__6169 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__6160,Vvar__0__Peq__6161,Vvar__1__Plt__6162,Vvar__1__Plt__6163,Vvar__2__Pgt__6164,Vvar__2__Pgt__6165,Vvar__3___24Anonymous__6166,Vvar__3___24Anonymous__6167] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6160,Vvar__1__Plt__6162,Vvar__2__Pgt__6164) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6161,Vvar__1__Plt__6163,Vvar__2__Pgt__6165)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__6164 = Vvar__2__Pgt__6165
& Vvar__1__Plt__6162 = Vvar__1__Plt__6163
& Vvar__0__Peq__6160 = Vvar__0__Peq__6161 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__5989,Vvar__0__A__5990] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5989) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5990)
=> Vvar__0__A__5989 = Vvar__0__A__5990 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__231,Vvar__0___24Anonymous__232] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__231) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__232)
=> Vvar__0___24Anonymous__231 = Vvar__0___24Anonymous__232 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__5985,Vvar__0__A__5986,Vvar__1___24Anonymous__5987,Vvar__1___24Anonymous__5988] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5985,Vvar__1___24Anonymous__5987) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5986,Vvar__1___24Anonymous__5988)
=> ( Vvar__1___24Anonymous__5987 = Vvar__1___24Anonymous__5988
& Vvar__0__A__5985 = Vvar__0__A__5986 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3863,Vvar__0__A__3864,Vvar__1___24Anonymous__3865,Vvar__1___24Anonymous__3866,Vvar__2___24Anonymous__3867,Vvar__2___24Anonymous__3868] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3863,Vvar__1___24Anonymous__3865,Vvar__2___24Anonymous__3867) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3864,Vvar__1___24Anonymous__3866,Vvar__2___24Anonymous__3868)
=> ( Vvar__2___24Anonymous__3867 = Vvar__2___24Anonymous__3868
& Vvar__1___24Anonymous__3865 = Vvar__1___24Anonymous__3866
& Vvar__0__A__3863 = Vvar__0__A__3864 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__6014,Vvar__0__A__6015,Vvar__1__B__6016,Vvar__1__B__6017,Vvar__2___24Anonymous__6018,Vvar__2___24Anonymous__6019] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__6014,Vvar__1__B__6016,Vvar__2___24Anonymous__6018) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__6015,Vvar__1__B__6017,Vvar__2___24Anonymous__6019)
=> ( Vvar__2___24Anonymous__6018 = Vvar__2___24Anonymous__6019
& Vvar__1__B__6016 = Vvar__1__B__6017
& Vvar__0__A__6014 = Vvar__0__A__6015 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__6020,Vvar__0__A__6021,Vvar__1__B__6022,Vvar__1__B__6023,Vvar__2___24Anonymous__6024,Vvar__2___24Anonymous__6025] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__6020,Vvar__1__B__6022,Vvar__2___24Anonymous__6024) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__6021,Vvar__1__B__6023,Vvar__2___24Anonymous__6025)
=> ( Vvar__2___24Anonymous__6024 = Vvar__2___24Anonymous__6025
& Vvar__1__B__6022 = Vvar__1__B__6023
& Vvar__0__A__6020 = Vvar__0__A__6021 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__3861,Vvar__0__A__3862] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3861) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3862)
=> Vvar__0__A__3861 = Vvar__0__A__3862 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__6034,Vvar__0__A__6035,Vvar__1__B__6036,Vvar__1__B__6037,Vvar__2___24Anonymous__6038,Vvar__2___24Anonymous__6039,Vvar__3___24Anonymous__6040,Vvar__3___24Anonymous__6041] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__6034,Vvar__1__B__6036,Vvar__2___24Anonymous__6038,Vvar__3___24Anonymous__6040) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__6035,Vvar__1__B__6037,Vvar__2___24Anonymous__6039,Vvar__3___24Anonymous__6041)
=> ( Vvar__3___24Anonymous__6040 = Vvar__3___24Anonymous__6041
& Vvar__2___24Anonymous__6038 = Vvar__2___24Anonymous__6039
& Vvar__1__B__6036 = Vvar__1__B__6037
& Vvar__0__A__6034 = Vvar__0__A__6035 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__32973,Vvar__0___24Anonymous__32974] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__32973) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__32974)
=> Vvar__0___24Anonymous__32973 = Vvar__0___24Anonymous__32974 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__32975,Vvar__0___24Anonymous__32976] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__32975) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__32976)
=> Vvar__0___24Anonymous__32975 = Vvar__0___24Anonymous__32976 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__32977,Vvar__0___24Anonymous__32978] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__32977) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__32978)
=> Vvar__0___24Anonymous__32977 = Vvar__0___24Anonymous__32978 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__32979,Vvar__0___24Anonymous__32980] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__32979) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__32980)
=> Vvar__0___24Anonymous__32979 = Vvar__0___24Anonymous__32980 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__32981,Vvar__0___24Anonymous__32982] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__32981) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__32982)
=> Vvar__0___24Anonymous__32981 = Vvar__0___24Anonymous__32982 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__32983,Vvar__0___24Anonymous__32984] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__32983) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__32984)
=> Vvar__0___24Anonymous__32983 = Vvar__0___24Anonymous__32984 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__32985,Vvar__0___24Anonymous__32986] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__32985) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__32986)
=> Vvar__0___24Anonymous__32985 = Vvar__0___24Anonymous__32986 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__32987,Vvar__0___24Anonymous__32988] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__32987) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__32988)
=> Vvar__0___24Anonymous__32987 = Vvar__0___24Anonymous__32988 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__32989,Vvar__0___24Anonymous__32990] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__32989) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__32990)
=> Vvar__0___24Anonymous__32989 = Vvar__0___24Anonymous__32990 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__32991,Vvar__0___24Anonymous__32992] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__32991) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__32992)
=> Vvar__0___24Anonymous__32991 = Vvar__0___24Anonymous__32992 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__39060,Vvar__0__i__39061,Vvar__1__f__39062,Vvar__1__f__39063] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__39060,Vvar__1__f__39062) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__39061,Vvar__1__f__39063)
=> ( Vvar__1__f__39062 = Vvar__1__f__39063
& Vvar__0__i__39060 = Vvar__0__i__39061 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__39064,Vvar__0__i__39065,Vvar__1__f__39066,Vvar__1__f__39067,Vvar__2__e__39068,Vvar__2__e__39069] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__39064,Vvar__1__f__39066,Vvar__2__e__39068) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__39065,Vvar__1__f__39067,Vvar__2__e__39069)
=> ( Vvar__2__e__39068 = Vvar__2__e__39069
& Vvar__1__f__39066 = Vvar__1__f__39067
& Vvar__0__i__39064 = Vvar__0__i__39065 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__33000,Vvar__0__d__33001] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__33000) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__33001)
=> Vvar__0__d__33000 = Vvar__0__d__33001 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__32998,Vvar__0__d__32999] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__32998) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__32999)
=> Vvar__0__d__32998 = Vvar__0__d__32999 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__22446,Vvar__0__A__22447,Vvar__1__P__22448,Vvar__1__P__22449,Vvar__2__x__22450,Vvar__2__x__22451,Vvar__3___24Anonymous__22452,Vvar__3___24Anonymous__22453] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__22446,Vvar__1__P__22448,Vvar__2__x__22450) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__22447,Vvar__1__P__22449,Vvar__2__x__22451)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__22450 = Vvar__2__x__22451
& Vvar__1__P__22448 = Vvar__1__P__22449
& Vvar__0__A__22446 = Vvar__0__A__22447 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__22508,Vvar__0__A__22509,Vvar__1__P__22510,Vvar__1__P__22511,Vvar__2__Q__22512,Vvar__2__Q__22513,Vvar__3__x__22514,Vvar__3__x__22515,Vvar__4___24Anonymous__22516,Vvar__4___24Anonymous__22517,Vvar__5___24Anonymous__22518,Vvar__5___24Anonymous__22519] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__22508,Vvar__1__P__22510,Vvar__2__Q__22512,Vvar__3__x__22514) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__22509,Vvar__1__P__22511,Vvar__2__Q__22513,Vvar__3__x__22515)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__22514 = Vvar__3__x__22515
& Vvar__2__Q__22512 = Vvar__2__Q__22513
& Vvar__1__P__22510 = Vvar__1__P__22511
& Vvar__0__A__22508 = Vvar__0__A__22509 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__22541,Vvar__0__A__22542,Vvar__1__P__22543,Vvar__1__P__22544,Vvar__2__x__22545,Vvar__2__x__22546,Vvar__3___24Anonymous__22547,Vvar__3___24Anonymous__22548] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__22541,Vvar__1__P__22543,Vvar__2__x__22545,Vvar__3___24Anonymous__22547) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__22542,Vvar__1__P__22544,Vvar__2__x__22546,Vvar__3___24Anonymous__22548)
=> ( Vvar__3___24Anonymous__22547 = Vvar__3___24Anonymous__22548
& Vvar__2__x__22545 = Vvar__2__x__22546
& Vvar__1__P__22543 = Vvar__1__P__22544
& Vvar__0__A__22541 = Vvar__0__A__22542 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__22603,Vvar__0__A__22604,Vvar__1__P__22605,Vvar__1__P__22606,Vvar__2__Q__22607,Vvar__2__Q__22608,Vvar__3__x__22609,Vvar__3__x__22610,Vvar__4___24Anonymous__22611,Vvar__4___24Anonymous__22612,Vvar__5___24Anonymous__22613,Vvar__5___24Anonymous__22614] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__22603,Vvar__1__P__22605,Vvar__2__Q__22607,Vvar__3__x__22609,Vvar__4___24Anonymous__22611,Vvar__5___24Anonymous__22613) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__22604,Vvar__1__P__22606,Vvar__2__Q__22608,Vvar__3__x__22610,Vvar__4___24Anonymous__22612,Vvar__5___24Anonymous__22614)
=> ( Vvar__5___24Anonymous__22613 = Vvar__5___24Anonymous__22614
& Vvar__4___24Anonymous__22611 = Vvar__4___24Anonymous__22612
& Vvar__3__x__22609 = Vvar__3__x__22610
& Vvar__2__Q__22607 = Vvar__2__Q__22608
& Vvar__1__P__22605 = Vvar__1__P__22606
& Vvar__0__A__22603 = Vvar__0__A__22604 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__22633,Vvar__0__A__22634,Vvar__1__B__22635,Vvar__1__B__22636,Vvar__2___24Anonymous__22637,Vvar__2___24Anonymous__22638] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22633,Vvar__1__B__22635,Vvar__2___24Anonymous__22637) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22634,Vvar__1__B__22636,Vvar__2___24Anonymous__22638)
=> ( Vvar__2___24Anonymous__22637 = Vvar__2___24Anonymous__22638
& Vvar__1__B__22635 = Vvar__1__B__22636
& Vvar__0__A__22633 = Vvar__0__A__22634 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__22639,Vvar__0__A__22640,Vvar__1__B__22641,Vvar__1__B__22642,Vvar__2___24Anonymous__22643,Vvar__2___24Anonymous__22644] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22639,Vvar__1__B__22641) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22640,Vvar__1__B__22642)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__22641 = Vvar__1__B__22642
& Vvar__0__A__22639 = Vvar__0__A__22640 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__4503,Vvar__0__A__4504,Vvar__1__B__4505,Vvar__1__B__4506,Vvar__2___24Anonymous__4507,Vvar__2___24Anonymous__4508] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4503,Vvar__1__B__4505) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4504,Vvar__1__B__4506)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__4505 = Vvar__1__B__4506
& Vvar__0__A__4503 = Vvar__0__A__4504 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__4509,Vvar__0__A__4510,Vvar__1__B__4511,Vvar__1__B__4512,Vvar__2___24Anonymous__4513,Vvar__2___24Anonymous__4514] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4509,Vvar__1__B__4511) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4510,Vvar__1__B__4512)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__4511 = Vvar__1__B__4512
& Vvar__0__A__4509 = Vvar__0__A__4510 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__376,Vvar__0___24Anonymous__377] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__376) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__377)
=> Vvar__0___24Anonymous__376 = Vvar__0___24Anonymous__377 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__1257,Vvar__0___24Anonymous__1258] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1257) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1258)
=> Vvar__0___24Anonymous__1257 = Vvar__0___24Anonymous__1258 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__1255,Vvar__0___24Anonymous__1256] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1255) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1256)
=> Vvar__0___24Anonymous__1255 = Vvar__0___24Anonymous__1256 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1202,Vvar__0___24Anonymous__1203] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1202) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1203)
=> Vvar__0___24Anonymous__1202 = Vvar__0___24Anonymous__1203 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1204,Vvar__0___24Anonymous__1205] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1204) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1205)
=> Vvar__0___24Anonymous__1204 = Vvar__0___24Anonymous__1205 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__23537,Vvar__0__p__23538,Vvar__1___24Anonymous__23539,Vvar__1___24Anonymous__23540] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__23537,Vvar__1___24Anonymous__23539) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__23538,Vvar__1___24Anonymous__23540)
=> ( Vvar__1___24Anonymous__23539 = Vvar__1___24Anonymous__23540
& Vvar__0__p__23537 = Vvar__0__p__23538 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__4981,Vvar__0___24Anonymous__4982] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__4981) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__4982)
=> Vvar__0___24Anonymous__4981 = Vvar__0___24Anonymous__4982 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__4312,Vvar__0__Qnum__4313,Vvar__1__Qden__4314,Vvar__1__Qden__4315] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4312,Vvar__1__Qden__4314) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4313,Vvar__1__Qden__4315)
=> ( Vvar__1__Qden__4314 = Vvar__1__Qden__4315
& Vvar__0__Qnum__4312 = Vvar__0__Qnum__4313 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__39531,Vvar__0__neg__39532,Vvar__1__cond__neg__39533,Vvar__1__cond__neg__39534] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__39531) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__39532)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__39531 = Vvar__0__neg__39532 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__39510,Vvar__0__nonneg__39511,Vvar__1__cond__nonneg__39512,Vvar__1__cond__nonneg__39513] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__39510) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__39511)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__39510 = Vvar__0__nonneg__39511 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__39524,Vvar__0__nonpos__39525,Vvar__1__cond__nonpos__39526,Vvar__1__cond__nonpos__39527] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__39524) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__39525)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__39524 = Vvar__0__nonpos__39525 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__9921,Vvar__0__nonzero__9922,Vvar__1__cond__nonzero__9923,Vvar__1__cond__nonzero__9924] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__9921) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__9922)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__9921 = Vvar__0__nonzero__9922 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__39517,Vvar__0__pos__39518,Vvar__1__cond__pos__39519,Vvar__1__cond__pos__39520] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__39517) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__39518)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__39517 = Vvar__0__pos__39518 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__10191,Vvar__0__x__10192,Vvar__1__n__10193,Vvar__1__n__10194,Vvar__2___24Anonymous__10195,Vvar__2___24Anonymous__10196] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__10191,Vvar__1__n__10193) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__10192,Vvar__1__n__10194)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__10193 = Vvar__1__n__10194
& Vvar__0__x__10191 = Vvar__0__x__10192 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__10181,Vvar__0__x__10182,Vvar__1___24Anonymous__10183,Vvar__1___24Anonymous__10184] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__10181) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__10182)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__10181 = Vvar__0__x__10182 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__10185,Vvar__0__x__10186,Vvar__1__n__10187,Vvar__1__n__10188,Vvar__2___24Anonymous__10189,Vvar__2___24Anonymous__10190] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__10185,Vvar__1__n__10187) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__10186,Vvar__1__n__10188)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__10187 = Vvar__1__n__10188
& Vvar__0__x__10185 = Vvar__0__x__10186 ) ) ).
fof('$_inj_Coq.Sets.Cpo.Definition_of_chain',axiom,
! [Vvar__0__U__39033,Vvar__0__U__39034,Vvar__1__PO__of__chain__39035,Vvar__1__PO__of__chain__39036,Vvar__2__Chain__cond__39037,Vvar__2__Chain__cond__39038] :
( cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(Vvar__0__U__39033,Vvar__1__PO__of__chain__39035) = cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(Vvar__0__U__39034,Vvar__1__PO__of__chain__39036)
=> ( c_24Proof = c_24Proof
& Vvar__1__PO__of__chain__39035 = Vvar__1__PO__of__chain__39036
& Vvar__0__U__39033 = Vvar__0__U__39034 ) ) ).
fof('$_inj_Coq.Sets.Cpo.Definition_of_cpo',axiom,
! [Vvar__0__U__39022,Vvar__0__U__39023,Vvar__1__PO__of__cpo__39024,Vvar__1__PO__of__cpo__39025,Vvar__2__Cpo__cond__39026,Vvar__2__Cpo__cond__39027] :
( cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(Vvar__0__U__39022,Vvar__1__PO__of__cpo__39024) = cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(Vvar__0__U__39023,Vvar__1__PO__of__cpo__39025)
=> ( c_24Proof = c_24Proof
& Vvar__1__PO__of__cpo__39024 = Vvar__1__PO__of__cpo__39025
& Vvar__0__U__39022 = Vvar__0__U__39023 ) ) ).
fof('$_inj_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
! [Vvar__0__U__4224,Vvar__0__U__4225,Vvar__1__Carrier__of__4226,Vvar__1__Carrier__of__4227,Vvar__2__Rel__of__4228,Vvar__2__Rel__of__4229,Vvar__3__PO__cond1__4230,Vvar__3__PO__cond1__4231,Vvar__4__PO__cond2__4232,Vvar__4__PO__cond2__4233] :
( cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__4224,Vvar__1__Carrier__of__4226,Vvar__2__Rel__of__4228) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__4225,Vvar__1__Carrier__of__4227,Vvar__2__Rel__of__4229)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__Rel__of__4228 = Vvar__2__Rel__of__4229
& Vvar__1__Carrier__of__4226 = Vvar__1__Carrier__of__4227
& Vvar__0__U__4224 = Vvar__0__U__4225 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__997,Vvar__0___24Anonymous__998,Vvar__1___24Anonymous__999,Vvar__1___24Anonymous__1000,Vvar__2___24Anonymous__1001,Vvar__2___24Anonymous__1002,Vvar__3___24Anonymous__1003,Vvar__3___24Anonymous__1004,Vvar__4___24Anonymous__1005,Vvar__4___24Anonymous__1006,Vvar__5___24Anonymous__1007,Vvar__5___24Anonymous__1008,Vvar__6___24Anonymous__1009,Vvar__6___24Anonymous__1010,Vvar__7___24Anonymous__1011,Vvar__7___24Anonymous__1012] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__997,Vvar__1___24Anonymous__999,Vvar__2___24Anonymous__1001,Vvar__3___24Anonymous__1003,Vvar__4___24Anonymous__1005,Vvar__5___24Anonymous__1007,Vvar__6___24Anonymous__1009,Vvar__7___24Anonymous__1011) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__998,Vvar__1___24Anonymous__1000,Vvar__2___24Anonymous__1002,Vvar__3___24Anonymous__1004,Vvar__4___24Anonymous__1006,Vvar__5___24Anonymous__1008,Vvar__6___24Anonymous__1010,Vvar__7___24Anonymous__1012)
=> ( Vvar__7___24Anonymous__1011 = Vvar__7___24Anonymous__1012
& Vvar__6___24Anonymous__1009 = Vvar__6___24Anonymous__1010
& Vvar__5___24Anonymous__1007 = Vvar__5___24Anonymous__1008
& Vvar__4___24Anonymous__1005 = Vvar__4___24Anonymous__1006
& Vvar__3___24Anonymous__1003 = Vvar__3___24Anonymous__1004
& Vvar__2___24Anonymous__1001 = Vvar__2___24Anonymous__1002
& Vvar__1___24Anonymous__999 = Vvar__1___24Anonymous__1000
& Vvar__0___24Anonymous__997 = Vvar__0___24Anonymous__998 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__22650,Vvar__0___24Anonymous__22651,Vvar__1___24Anonymous__22652,Vvar__1___24Anonymous__22653] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22650,Vvar__1___24Anonymous__22652) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22651,Vvar__1___24Anonymous__22653)
=> ( Vvar__1___24Anonymous__22652 = Vvar__1___24Anonymous__22653
& Vvar__0___24Anonymous__22650 = Vvar__0___24Anonymous__22651 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__9877,Vvar__0__X__9878,Vvar__1__lt__9879,Vvar__1__lt__9880,Vvar__2__eq__9881,Vvar__2__eq__9882,Vvar__3__x__9883,Vvar__3__x__9884,Vvar__4__y__9885,Vvar__4__y__9886,Vvar__5___24Anonymous__9887,Vvar__5___24Anonymous__9888] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9877,Vvar__1__lt__9879,Vvar__2__eq__9881,Vvar__3__x__9883,Vvar__4__y__9885) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9878,Vvar__1__lt__9880,Vvar__2__eq__9882,Vvar__3__x__9884,Vvar__4__y__9886)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9885 = Vvar__4__y__9886
& Vvar__3__x__9883 = Vvar__3__x__9884
& Vvar__2__eq__9881 = Vvar__2__eq__9882
& Vvar__1__lt__9879 = Vvar__1__lt__9880
& Vvar__0__X__9877 = Vvar__0__X__9878 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__9889,Vvar__0__X__9890,Vvar__1__lt__9891,Vvar__1__lt__9892,Vvar__2__eq__9893,Vvar__2__eq__9894,Vvar__3__x__9895,Vvar__3__x__9896,Vvar__4__y__9897,Vvar__4__y__9898,Vvar__5___24Anonymous__9899,Vvar__5___24Anonymous__9900] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9889,Vvar__1__lt__9891,Vvar__2__eq__9893,Vvar__3__x__9895,Vvar__4__y__9897) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9890,Vvar__1__lt__9892,Vvar__2__eq__9894,Vvar__3__x__9896,Vvar__4__y__9898)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9897 = Vvar__4__y__9898
& Vvar__3__x__9895 = Vvar__3__x__9896
& Vvar__2__eq__9893 = Vvar__2__eq__9894
& Vvar__1__lt__9891 = Vvar__1__lt__9892
& Vvar__0__X__9889 = Vvar__0__X__9890 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__9865,Vvar__0__X__9866,Vvar__1__lt__9867,Vvar__1__lt__9868,Vvar__2__eq__9869,Vvar__2__eq__9870,Vvar__3__x__9871,Vvar__3__x__9872,Vvar__4__y__9873,Vvar__4__y__9874,Vvar__5___24Anonymous__9875,Vvar__5___24Anonymous__9876] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9865,Vvar__1__lt__9867,Vvar__2__eq__9869,Vvar__3__x__9871,Vvar__4__y__9873) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9866,Vvar__1__lt__9868,Vvar__2__eq__9870,Vvar__3__x__9872,Vvar__4__y__9874)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__9873 = Vvar__4__y__9874
& Vvar__3__x__9871 = Vvar__3__x__9872
& Vvar__2__eq__9869 = Vvar__2__eq__9870
& Vvar__1__lt__9867 = Vvar__1__lt__9868
& Vvar__0__X__9865 = Vvar__0__X__9866 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__8298,Vvar__0__n__8299] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8298) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8299)
=> Vvar__0__n__8298 = Vvar__0__n__8299 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__8300,Vvar__0__n__8301,Vvar__1___24Anonymous__8302,Vvar__1___24Anonymous__8303] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8300,Vvar__1___24Anonymous__8302) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8301,Vvar__1___24Anonymous__8303)
=> ( Vvar__1___24Anonymous__8302 = Vvar__1___24Anonymous__8303
& Vvar__0__n__8300 = Vvar__0__n__8301 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__23115,Vvar__0__A__23116,Vvar__1__h__23117,Vvar__1__h__23118,Vvar__2__n__23119,Vvar__2__n__23120,Vvar__3___24Anonymous__23121,Vvar__3___24Anonymous__23122] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__23115,Vvar__1__h__23117,Vvar__2__n__23119,Vvar__3___24Anonymous__23121) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__23116,Vvar__1__h__23118,Vvar__2__n__23120,Vvar__3___24Anonymous__23122)
=> ( Vvar__3___24Anonymous__23121 = Vvar__3___24Anonymous__23122
& Vvar__2__n__23119 = Vvar__2__n__23120
& Vvar__1__h__23117 = Vvar__1__h__23118
& Vvar__0__A__23115 = Vvar__0__A__23116 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__23113,Vvar__0__A__23114] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__23113) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__23114)
=> Vvar__0__A__23113 = Vvar__0__A__23114 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__23311,Vvar__0__a__23312,Vvar__1__b__23313,Vvar__1__b__23314,Vvar__2__u__23315,Vvar__2__u__23316,Vvar__3__v__23317,Vvar__3__v__23318,Vvar__4__d__23319,Vvar__4__d__23320,Vvar__5___24Anonymous__23321,Vvar__5___24Anonymous__23322,Vvar__6___24Anonymous__23323,Vvar__6___24Anonymous__23324] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__23311,Vvar__1__b__23313,Vvar__2__u__23315,Vvar__3__v__23317,Vvar__4__d__23319) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__23312,Vvar__1__b__23314,Vvar__2__u__23316,Vvar__3__v__23318,Vvar__4__d__23320)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__23319 = Vvar__4__d__23320
& Vvar__3__v__23317 = Vvar__3__v__23318
& Vvar__2__u__23315 = Vvar__2__u__23316
& Vvar__1__b__23313 = Vvar__1__b__23314
& Vvar__0__a__23311 = Vvar__0__a__23312 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__23372,Vvar__0__x__23373,Vvar__1__p__23374,Vvar__1__p__23375,Vvar__2__q__23376,Vvar__2__q__23377,Vvar__3__r__23378,Vvar__3__r__23379,Vvar__4___24Anonymous__23380,Vvar__4___24Anonymous__23381,Vvar__5___24Anonymous__23382,Vvar__5___24Anonymous__23383,Vvar__6___24Anonymous__23384,Vvar__6___24Anonymous__23385] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__23372,Vvar__1__p__23374,Vvar__2__q__23376,Vvar__3__r__23378) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__23373,Vvar__1__p__23375,Vvar__2__q__23377,Vvar__3__r__23379)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__23378 = Vvar__3__r__23379
& Vvar__2__q__23376 = Vvar__2__q__23377
& Vvar__1__p__23374 = Vvar__1__p__23375
& Vvar__0__x__23372 = Vvar__0__x__23373 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__6311,Vvar__0__C__6312,Vvar__1___24Anonymous__6313,Vvar__1___24Anonymous__6314] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6311,Vvar__1___24Anonymous__6313) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6312,Vvar__1___24Anonymous__6314)
=> ( Vvar__1___24Anonymous__6313 = Vvar__1___24Anonymous__6314
& Vvar__0__C__6311 = Vvar__0__C__6312 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__6315,Vvar__0__C__6316,Vvar__1___24Anonymous__6317,Vvar__1___24Anonymous__6318,Vvar__2___24Anonymous__6319,Vvar__2___24Anonymous__6320] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__6315,Vvar__1___24Anonymous__6317,Vvar__2___24Anonymous__6319) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__6316,Vvar__1___24Anonymous__6318,Vvar__2___24Anonymous__6320)
=> ( Vvar__2___24Anonymous__6319 = Vvar__2___24Anonymous__6320
& Vvar__1___24Anonymous__6317 = Vvar__1___24Anonymous__6318
& Vvar__0__C__6315 = Vvar__0__C__6316 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__6307,Vvar__0__C__6308,Vvar__1___24Anonymous__6309,Vvar__1___24Anonymous__6310] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6307,Vvar__1___24Anonymous__6309) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6308,Vvar__1___24Anonymous__6310)
=> ( Vvar__1___24Anonymous__6309 = Vvar__1___24Anonymous__6310
& Vvar__0__C__6307 = Vvar__0__C__6308 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__6327,Vvar__0__C__6328,Vvar__1___24Anonymous__6329,Vvar__1___24Anonymous__6330,Vvar__2___24Anonymous__6331,Vvar__2___24Anonymous__6332] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__6327,Vvar__1___24Anonymous__6329,Vvar__2___24Anonymous__6331) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__6328,Vvar__1___24Anonymous__6330,Vvar__2___24Anonymous__6332)
=> ( Vvar__2___24Anonymous__6331 = Vvar__2___24Anonymous__6332
& Vvar__1___24Anonymous__6329 = Vvar__1___24Anonymous__6330
& Vvar__0__C__6327 = Vvar__0__C__6328 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__6333,Vvar__0__C__6334,Vvar__1___24Anonymous__6335,Vvar__1___24Anonymous__6336] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__6333,Vvar__1___24Anonymous__6335) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__6334,Vvar__1___24Anonymous__6336)
=> ( Vvar__1___24Anonymous__6335 = Vvar__1___24Anonymous__6336
& Vvar__0__C__6333 = Vvar__0__C__6334 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__6337,Vvar__0__C__6338,Vvar__1___24Anonymous__6339,Vvar__1___24Anonymous__6340,Vvar__2___24Anonymous__6341,Vvar__2___24Anonymous__6342] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__6337,Vvar__1___24Anonymous__6339,Vvar__2___24Anonymous__6341) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__6338,Vvar__1___24Anonymous__6340,Vvar__2___24Anonymous__6342)
=> ( Vvar__2___24Anonymous__6341 = Vvar__2___24Anonymous__6342
& Vvar__1___24Anonymous__6339 = Vvar__1___24Anonymous__6340
& Vvar__0__C__6337 = Vvar__0__C__6338 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__6321,Vvar__0__C__6322,Vvar__1___24Anonymous__6323,Vvar__1___24Anonymous__6324,Vvar__2___24Anonymous__6325,Vvar__2___24Anonymous__6326] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__6321,Vvar__1___24Anonymous__6323,Vvar__2___24Anonymous__6325) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__6322,Vvar__1___24Anonymous__6324,Vvar__2___24Anonymous__6326)
=> ( Vvar__2___24Anonymous__6325 = Vvar__2___24Anonymous__6326
& Vvar__1___24Anonymous__6323 = Vvar__1___24Anonymous__6324
& Vvar__0__C__6321 = Vvar__0__C__6322 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__6382,Vvar__0__C__6383,Vvar__1___24Anonymous__6384,Vvar__1___24Anonymous__6385,Vvar__2___24Anonymous__6386,Vvar__2___24Anonymous__6387,Vvar__3___24Anonymous__6388,Vvar__3___24Anonymous__6389] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__6382,Vvar__1___24Anonymous__6384,Vvar__2___24Anonymous__6386,Vvar__3___24Anonymous__6388) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__6383,Vvar__1___24Anonymous__6385,Vvar__2___24Anonymous__6387,Vvar__3___24Anonymous__6389)
=> ( Vvar__3___24Anonymous__6388 = Vvar__3___24Anonymous__6389
& Vvar__2___24Anonymous__6386 = Vvar__2___24Anonymous__6387
& Vvar__1___24Anonymous__6384 = Vvar__1___24Anonymous__6385
& Vvar__0__C__6382 = Vvar__0__C__6383 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__6372,Vvar__0__C__6373,Vvar__1___24Anonymous__6374,Vvar__1___24Anonymous__6375] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6372,Vvar__1___24Anonymous__6374) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6373,Vvar__1___24Anonymous__6375)
=> ( Vvar__1___24Anonymous__6374 = Vvar__1___24Anonymous__6375
& Vvar__0__C__6372 = Vvar__0__C__6373 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__6376,Vvar__0__C__6377,Vvar__1___24Anonymous__6378,Vvar__1___24Anonymous__6379,Vvar__2___24Anonymous__6380,Vvar__2___24Anonymous__6381] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6376,Vvar__1___24Anonymous__6378,Vvar__2___24Anonymous__6380) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6377,Vvar__1___24Anonymous__6379,Vvar__2___24Anonymous__6381)
=> ( Vvar__2___24Anonymous__6380 = Vvar__2___24Anonymous__6381
& Vvar__1___24Anonymous__6378 = Vvar__1___24Anonymous__6379
& Vvar__0__C__6376 = Vvar__0__C__6377 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__6410,Vvar__0___24Anonymous__6411,Vvar__1___24Anonymous__6412,Vvar__1___24Anonymous__6413] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__6410,Vvar__1___24Anonymous__6412) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__6411,Vvar__1___24Anonymous__6413)
=> ( Vvar__1___24Anonymous__6412 = Vvar__1___24Anonymous__6413
& Vvar__0___24Anonymous__6410 = Vvar__0___24Anonymous__6411 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__6406,Vvar__0___24Anonymous__6407,Vvar__1___24Anonymous__6408,Vvar__1___24Anonymous__6409] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__6406,Vvar__1___24Anonymous__6408) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__6407,Vvar__1___24Anonymous__6409)
=> ( Vvar__1___24Anonymous__6408 = Vvar__1___24Anonymous__6409
& Vvar__0___24Anonymous__6406 = Vvar__0___24Anonymous__6407 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__10066,Vvar__0__r__10067] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__10066) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__10067)
=> Vvar__0__r__10066 = Vvar__0__r__10067 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__10054,Vvar__0__r1__10055,Vvar__1__r2__10056,Vvar__1__r2__10057] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__10054,Vvar__1__r2__10056) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__10055,Vvar__1__r2__10057)
=> ( Vvar__1__r2__10056 = Vvar__1__r2__10057
& Vvar__0__r1__10054 = Vvar__0__r1__10055 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__10058,Vvar__0__r1__10059,Vvar__1__r2__10060,Vvar__1__r2__10061] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__10058,Vvar__1__r2__10060) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__10059,Vvar__1__r2__10061)
=> ( Vvar__1__r2__10060 = Vvar__1__r2__10061
& Vvar__0__r1__10058 = Vvar__0__r1__10059 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__10068,Vvar__0__r__10069] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__10068) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__10069)
=> Vvar__0__r__10068 = Vvar__0__r__10069 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__10050,Vvar__0__r1__10051,Vvar__1__r2__10052,Vvar__1__r2__10053] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__10050,Vvar__1__r2__10052) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__10051,Vvar__1__r2__10053)
=> ( Vvar__1__r2__10052 = Vvar__1__r2__10053
& Vvar__0__r1__10050 = Vvar__0__r1__10051 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__10062,Vvar__0__r1__10063,Vvar__1__z__10064,Vvar__1__z__10065] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__10062,Vvar__1__z__10064) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__10063,Vvar__1__z__10065)
=> ( Vvar__1__z__10064 = Vvar__1__z__10065
& Vvar__0__r1__10062 = Vvar__0__r1__10063 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__10046,Vvar__0__r__10047] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__10046) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__10047)
=> Vvar__0__r__10046 = Vvar__0__r__10047 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__10048,Vvar__0__r__10049] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__10048) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__10049)
=> Vvar__0__r__10048 = Vvar__0__r__10049 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__15644,Vvar__0__T__15645,Vvar__1__Flhs__15646,Vvar__1__Flhs__15647,Vvar__2__Fop__15648,Vvar__2__Fop__15649,Vvar__3__Frhs__15650,Vvar__3__Frhs__15651] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__15644,Vvar__1__Flhs__15646,Vvar__2__Fop__15648,Vvar__3__Frhs__15650) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__15645,Vvar__1__Flhs__15647,Vvar__2__Fop__15649,Vvar__3__Frhs__15651)
=> ( Vvar__3__Frhs__15650 = Vvar__3__Frhs__15651
& Vvar__2__Fop__15648 = Vvar__2__Fop__15649
& Vvar__1__Flhs__15646 = Vvar__1__Flhs__15647
& Vvar__0__T__15644 = Vvar__0__T__15645 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__15625,Vvar__0__C__15626,Vvar__1___24Anonymous__15627,Vvar__1___24Anonymous__15628,Vvar__2___24Anonymous__15629,Vvar__2___24Anonymous__15630] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__15625,Vvar__1___24Anonymous__15627,Vvar__2___24Anonymous__15629) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__15626,Vvar__1___24Anonymous__15628,Vvar__2___24Anonymous__15630)
=> ( Vvar__2___24Anonymous__15629 = Vvar__2___24Anonymous__15630
& Vvar__1___24Anonymous__15627 = Vvar__1___24Anonymous__15628
& Vvar__0__C__15625 = Vvar__0__C__15626 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__15631,Vvar__0__C__15632,Vvar__1___24Anonymous__15633,Vvar__1___24Anonymous__15634] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__15631,Vvar__1___24Anonymous__15633) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__15632,Vvar__1___24Anonymous__15634)
=> ( Vvar__1___24Anonymous__15633 = Vvar__1___24Anonymous__15634
& Vvar__0__C__15631 = Vvar__0__C__15632 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__15605,Vvar__0__C__15606,Vvar__1___24Anonymous__15607,Vvar__1___24Anonymous__15608] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15605,Vvar__1___24Anonymous__15607) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15606,Vvar__1___24Anonymous__15608)
=> ( Vvar__1___24Anonymous__15607 = Vvar__1___24Anonymous__15608
& Vvar__0__C__15605 = Vvar__0__C__15606 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__15613,Vvar__0__C__15614,Vvar__1___24Anonymous__15615,Vvar__1___24Anonymous__15616,Vvar__2___24Anonymous__15617,Vvar__2___24Anonymous__15618] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__15613,Vvar__1___24Anonymous__15615,Vvar__2___24Anonymous__15617) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__15614,Vvar__1___24Anonymous__15616,Vvar__2___24Anonymous__15618)
=> ( Vvar__2___24Anonymous__15617 = Vvar__2___24Anonymous__15618
& Vvar__1___24Anonymous__15615 = Vvar__1___24Anonymous__15616
& Vvar__0__C__15613 = Vvar__0__C__15614 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__15619,Vvar__0__C__15620,Vvar__1___24Anonymous__15621,Vvar__1___24Anonymous__15622,Vvar__2___24Anonymous__15623,Vvar__2___24Anonymous__15624] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__15619,Vvar__1___24Anonymous__15621,Vvar__2___24Anonymous__15623) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__15620,Vvar__1___24Anonymous__15622,Vvar__2___24Anonymous__15624)
=> ( Vvar__2___24Anonymous__15623 = Vvar__2___24Anonymous__15624
& Vvar__1___24Anonymous__15621 = Vvar__1___24Anonymous__15622
& Vvar__0__C__15619 = Vvar__0__C__15620 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__15609,Vvar__0__C__15610,Vvar__1___24Anonymous__15611,Vvar__1___24Anonymous__15612] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15609,Vvar__1___24Anonymous__15611) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15610,Vvar__1___24Anonymous__15612)
=> ( Vvar__1___24Anonymous__15611 = Vvar__1___24Anonymous__15612
& Vvar__0__C__15609 = Vvar__0__C__15610 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__15635,Vvar__0__C__15636] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__15635) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__15636)
=> Vvar__0__C__15635 = Vvar__0__C__15636 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__23037,Vvar__0__TA__23038,Vvar__1__TX__23039,Vvar__1__TX__23040,Vvar__2__AA__23041,Vvar__2__AA__23042,Vvar__3__AF__23043,Vvar__3__AF__23044,Vvar__4___24Anonymous__23045,Vvar__4___24Anonymous__23046,Vvar__5___24Anonymous__23047,Vvar__5___24Anonymous__23048] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__23037,Vvar__1__TX__23039,Vvar__2__AA__23041,Vvar__3__AF__23043,Vvar__4___24Anonymous__23045,Vvar__5___24Anonymous__23047) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__23038,Vvar__1__TX__23040,Vvar__2__AA__23042,Vvar__3__AF__23044,Vvar__4___24Anonymous__23046,Vvar__5___24Anonymous__23048)
=> ( Vvar__5___24Anonymous__23047 = Vvar__5___24Anonymous__23048
& Vvar__4___24Anonymous__23045 = Vvar__4___24Anonymous__23046
& Vvar__3__AF__23043 = Vvar__3__AF__23044
& Vvar__2__AA__23041 = Vvar__2__AA__23042
& Vvar__1__TX__23039 = Vvar__1__TX__23040
& Vvar__0__TA__23037 = Vvar__0__TA__23038 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__23049,Vvar__0__TA__23050,Vvar__1__TX__23051,Vvar__1__TX__23052,Vvar__2__AA__23053,Vvar__2__AA__23054,Vvar__3__AF__23055,Vvar__3__AF__23056,Vvar__4___24Anonymous__23057,Vvar__4___24Anonymous__23058,Vvar__5___24Anonymous__23059,Vvar__5___24Anonymous__23060] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__23049,Vvar__1__TX__23051,Vvar__2__AA__23053,Vvar__3__AF__23055,Vvar__4___24Anonymous__23057,Vvar__5___24Anonymous__23059) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__23050,Vvar__1__TX__23052,Vvar__2__AA__23054,Vvar__3__AF__23056,Vvar__4___24Anonymous__23058,Vvar__5___24Anonymous__23060)
=> ( Vvar__5___24Anonymous__23059 = Vvar__5___24Anonymous__23060
& Vvar__4___24Anonymous__23057 = Vvar__4___24Anonymous__23058
& Vvar__3__AF__23055 = Vvar__3__AF__23056
& Vvar__2__AA__23053 = Vvar__2__AA__23054
& Vvar__1__TX__23051 = Vvar__1__TX__23052
& Vvar__0__TA__23049 = Vvar__0__TA__23050 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__23061,Vvar__0__TA__23062,Vvar__1__TX__23063,Vvar__1__TX__23064,Vvar__2__AA__23065,Vvar__2__AA__23066,Vvar__3__AF__23067,Vvar__3__AF__23068,Vvar__4___24Anonymous__23069,Vvar__4___24Anonymous__23070,Vvar__5___24Anonymous__23071,Vvar__5___24Anonymous__23072] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__23061,Vvar__1__TX__23063,Vvar__2__AA__23065,Vvar__3__AF__23067,Vvar__4___24Anonymous__23069,Vvar__5___24Anonymous__23071) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__23062,Vvar__1__TX__23064,Vvar__2__AA__23066,Vvar__3__AF__23068,Vvar__4___24Anonymous__23070,Vvar__5___24Anonymous__23072)
=> ( Vvar__5___24Anonymous__23071 = Vvar__5___24Anonymous__23072
& Vvar__4___24Anonymous__23069 = Vvar__4___24Anonymous__23070
& Vvar__3__AF__23067 = Vvar__3__AF__23068
& Vvar__2__AA__23065 = Vvar__2__AA__23066
& Vvar__1__TX__23063 = Vvar__1__TX__23064
& Vvar__0__TA__23061 = Vvar__0__TA__23062 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__23019,Vvar__0__TA__23020,Vvar__1__TX__23021,Vvar__1__TX__23022,Vvar__2__AA__23023,Vvar__2__AA__23024,Vvar__3__AF__23025,Vvar__3__AF__23026] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__23019,Vvar__1__TX__23021,Vvar__2__AA__23023,Vvar__3__AF__23025) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__23020,Vvar__1__TX__23022,Vvar__2__AA__23024,Vvar__3__AF__23026)
=> ( Vvar__3__AF__23025 = Vvar__3__AF__23026
& Vvar__2__AA__23023 = Vvar__2__AA__23024
& Vvar__1__TX__23021 = Vvar__1__TX__23022
& Vvar__0__TA__23019 = Vvar__0__TA__23020 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__23083,Vvar__0__TA__23084,Vvar__1__TX__23085,Vvar__1__TX__23086,Vvar__2__AA__23087,Vvar__2__AA__23088,Vvar__3__AF__23089,Vvar__3__AF__23090,Vvar__4___24Anonymous__23091,Vvar__4___24Anonymous__23092,Vvar__5___24Anonymous__23093,Vvar__5___24Anonymous__23094,Vvar__6___24Anonymous__23095,Vvar__6___24Anonymous__23096] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__23083,Vvar__1__TX__23085,Vvar__2__AA__23087,Vvar__3__AF__23089,Vvar__4___24Anonymous__23091,Vvar__5___24Anonymous__23093,Vvar__6___24Anonymous__23095) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__23084,Vvar__1__TX__23086,Vvar__2__AA__23088,Vvar__3__AF__23090,Vvar__4___24Anonymous__23092,Vvar__5___24Anonymous__23094,Vvar__6___24Anonymous__23096)
=> ( Vvar__6___24Anonymous__23095 = Vvar__6___24Anonymous__23096
& Vvar__5___24Anonymous__23093 = Vvar__5___24Anonymous__23094
& Vvar__4___24Anonymous__23091 = Vvar__4___24Anonymous__23092
& Vvar__3__AF__23089 = Vvar__3__AF__23090
& Vvar__2__AA__23087 = Vvar__2__AA__23088
& Vvar__1__TX__23085 = Vvar__1__TX__23086
& Vvar__0__TA__23083 = Vvar__0__TA__23084 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__23073,Vvar__0__TA__23074,Vvar__1__TX__23075,Vvar__1__TX__23076,Vvar__2__AA__23077,Vvar__2__AA__23078,Vvar__3__AF__23079,Vvar__3__AF__23080,Vvar__4___24Anonymous__23081,Vvar__4___24Anonymous__23082] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__23073,Vvar__1__TX__23075,Vvar__2__AA__23077,Vvar__3__AF__23079,Vvar__4___24Anonymous__23081) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__23074,Vvar__1__TX__23076,Vvar__2__AA__23078,Vvar__3__AF__23080,Vvar__4___24Anonymous__23082)
=> ( Vvar__4___24Anonymous__23081 = Vvar__4___24Anonymous__23082
& Vvar__3__AF__23079 = Vvar__3__AF__23080
& Vvar__2__AA__23077 = Vvar__2__AA__23078
& Vvar__1__TX__23075 = Vvar__1__TX__23076
& Vvar__0__TA__23073 = Vvar__0__TA__23074 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__23011,Vvar__0__TA__23012,Vvar__1__TX__23013,Vvar__1__TX__23014,Vvar__2__AA__23015,Vvar__2__AA__23016,Vvar__3__AF__23017,Vvar__3__AF__23018] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__23011,Vvar__1__TX__23013,Vvar__2__AA__23015,Vvar__3__AF__23017) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__23012,Vvar__1__TX__23014,Vvar__2__AA__23016,Vvar__3__AF__23018)
=> ( Vvar__3__AF__23017 = Vvar__3__AF__23018
& Vvar__2__AA__23015 = Vvar__2__AA__23016
& Vvar__1__TX__23013 = Vvar__1__TX__23014
& Vvar__0__TA__23011 = Vvar__0__TA__23012 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__23027,Vvar__0__TA__23028,Vvar__1__TX__23029,Vvar__1__TX__23030,Vvar__2__AA__23031,Vvar__2__AA__23032,Vvar__3__AF__23033,Vvar__3__AF__23034,Vvar__4___24Anonymous__23035,Vvar__4___24Anonymous__23036] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__23027,Vvar__1__TX__23029,Vvar__2__AA__23031,Vvar__3__AF__23033,Vvar__4___24Anonymous__23035) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__23028,Vvar__1__TX__23030,Vvar__2__AA__23032,Vvar__3__AF__23034,Vvar__4___24Anonymous__23036)
=> ( Vvar__4___24Anonymous__23035 = Vvar__4___24Anonymous__23036
& Vvar__3__AF__23033 = Vvar__3__AF__23034
& Vvar__2__AA__23031 = Vvar__2__AA__23032
& Vvar__1__TX__23029 = Vvar__1__TX__23030
& Vvar__0__TA__23027 = Vvar__0__TA__23028 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__37309,Vvar__0__A__37310,Vvar__1___24Anonymous__37311,Vvar__1___24Anonymous__37312,Vvar__2___24Anonymous__37313,Vvar__2___24Anonymous__37314,Vvar__3___24Anonymous__37315,Vvar__3___24Anonymous__37316] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__37309,Vvar__1___24Anonymous__37311,Vvar__2___24Anonymous__37313,Vvar__3___24Anonymous__37315) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__37310,Vvar__1___24Anonymous__37312,Vvar__2___24Anonymous__37314,Vvar__3___24Anonymous__37316)
=> ( Vvar__3___24Anonymous__37315 = Vvar__3___24Anonymous__37316
& Vvar__2___24Anonymous__37313 = Vvar__2___24Anonymous__37314
& Vvar__1___24Anonymous__37311 = Vvar__1___24Anonymous__37312
& Vvar__0__A__37309 = Vvar__0__A__37310 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__37305,Vvar__0__A__37306,Vvar__1___24Anonymous__37307,Vvar__1___24Anonymous__37308] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37305,Vvar__1___24Anonymous__37307) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37306,Vvar__1___24Anonymous__37308)
=> ( Vvar__1___24Anonymous__37307 = Vvar__1___24Anonymous__37308
& Vvar__0__A__37305 = Vvar__0__A__37306 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__37303,Vvar__0__A__37304] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37303) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37304)
=> Vvar__0__A__37303 = Vvar__0__A__37304 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__23195,Vvar__0___24Anonymous__23196,Vvar__1___24Anonymous__23197,Vvar__1___24Anonymous__23198] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__23195,Vvar__1___24Anonymous__23197) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__23196,Vvar__1___24Anonymous__23198)
=> ( Vvar__1___24Anonymous__23197 = Vvar__1___24Anonymous__23198
& Vvar__0___24Anonymous__23195 = Vvar__0___24Anonymous__23196 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__23199,Vvar__0___24Anonymous__23200,Vvar__1___24Anonymous__23201,Vvar__1___24Anonymous__23202,Vvar__2___24Anonymous__23203,Vvar__2___24Anonymous__23204] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__23199,Vvar__1___24Anonymous__23201,Vvar__2___24Anonymous__23203) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__23200,Vvar__1___24Anonymous__23202,Vvar__2___24Anonymous__23204)
=> ( Vvar__2___24Anonymous__23203 = Vvar__2___24Anonymous__23204
& Vvar__1___24Anonymous__23201 = Vvar__1___24Anonymous__23202
& Vvar__0___24Anonymous__23199 = Vvar__0___24Anonymous__23200 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__23191,Vvar__0___24Anonymous__23192,Vvar__1___24Anonymous__23193,Vvar__1___24Anonymous__23194] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__23191,Vvar__1___24Anonymous__23193) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__23192,Vvar__1___24Anonymous__23194)
=> ( Vvar__1___24Anonymous__23193 = Vvar__1___24Anonymous__23194
& Vvar__0___24Anonymous__23191 = Vvar__0___24Anonymous__23192 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__7476,Vvar__0__C__7477] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7476) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7477)
=> Vvar__0__C__7476 = Vvar__0__C__7477 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__7474,Vvar__0__C__7475] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7474) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7475)
=> Vvar__0__C__7474 = Vvar__0__C__7475 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__7482,Vvar__0__C__7483,Vvar__1___24Anonymous__7484,Vvar__1___24Anonymous__7485] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7482,Vvar__1___24Anonymous__7484) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7483,Vvar__1___24Anonymous__7485)
=> ( Vvar__1___24Anonymous__7484 = Vvar__1___24Anonymous__7485
& Vvar__0__C__7482 = Vvar__0__C__7483 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__7486,Vvar__0__C__7487,Vvar__1___24Anonymous__7488,Vvar__1___24Anonymous__7489,Vvar__2___24Anonymous__7490,Vvar__2___24Anonymous__7491] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7486,Vvar__1___24Anonymous__7488,Vvar__2___24Anonymous__7490) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7487,Vvar__1___24Anonymous__7489,Vvar__2___24Anonymous__7491)
=> ( Vvar__2___24Anonymous__7490 = Vvar__2___24Anonymous__7491
& Vvar__1___24Anonymous__7488 = Vvar__1___24Anonymous__7489
& Vvar__0__C__7486 = Vvar__0__C__7487 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__7478,Vvar__0__C__7479,Vvar__1___24Anonymous__7480,Vvar__1___24Anonymous__7481] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7478,Vvar__1___24Anonymous__7480) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7479,Vvar__1___24Anonymous__7481)
=> ( Vvar__1___24Anonymous__7480 = Vvar__1___24Anonymous__7481
& Vvar__0__C__7478 = Vvar__0__C__7479 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__7512,Vvar__0__C__7513,Vvar__1___24Anonymous__7514,Vvar__1___24Anonymous__7515,Vvar__2___24Anonymous__7516,Vvar__2___24Anonymous__7517] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7512,Vvar__1___24Anonymous__7514,Vvar__2___24Anonymous__7516) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7513,Vvar__1___24Anonymous__7515,Vvar__2___24Anonymous__7517)
=> ( Vvar__2___24Anonymous__7516 = Vvar__2___24Anonymous__7517
& Vvar__1___24Anonymous__7514 = Vvar__1___24Anonymous__7515
& Vvar__0__C__7512 = Vvar__0__C__7513 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__7508,Vvar__0__C__7509,Vvar__1___24Anonymous__7510,Vvar__1___24Anonymous__7511] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7508,Vvar__1___24Anonymous__7510) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7509,Vvar__1___24Anonymous__7511)
=> ( Vvar__1___24Anonymous__7510 = Vvar__1___24Anonymous__7511
& Vvar__0__C__7508 = Vvar__0__C__7509 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__7498,Vvar__0__C__7499,Vvar__1___24Anonymous__7500,Vvar__1___24Anonymous__7501,Vvar__2___24Anonymous__7502,Vvar__2___24Anonymous__7503] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7498,Vvar__1___24Anonymous__7500,Vvar__2___24Anonymous__7502) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7499,Vvar__1___24Anonymous__7501,Vvar__2___24Anonymous__7503)
=> ( Vvar__2___24Anonymous__7502 = Vvar__2___24Anonymous__7503
& Vvar__1___24Anonymous__7500 = Vvar__1___24Anonymous__7501
& Vvar__0__C__7498 = Vvar__0__C__7499 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__7504,Vvar__0__C__7505,Vvar__1___24Anonymous__7506,Vvar__1___24Anonymous__7507] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7504,Vvar__1___24Anonymous__7506) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7505,Vvar__1___24Anonymous__7507)
=> ( Vvar__1___24Anonymous__7506 = Vvar__1___24Anonymous__7507
& Vvar__0__C__7504 = Vvar__0__C__7505 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__7518,Vvar__0__C__7519,Vvar__1___24Anonymous__7520,Vvar__1___24Anonymous__7521,Vvar__2___24Anonymous__7522,Vvar__2___24Anonymous__7523] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7518,Vvar__1___24Anonymous__7520,Vvar__2___24Anonymous__7522) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7519,Vvar__1___24Anonymous__7521,Vvar__2___24Anonymous__7523)
=> ( Vvar__2___24Anonymous__7522 = Vvar__2___24Anonymous__7523
& Vvar__1___24Anonymous__7520 = Vvar__1___24Anonymous__7521
& Vvar__0__C__7518 = Vvar__0__C__7519 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__7492,Vvar__0__C__7493,Vvar__1___24Anonymous__7494,Vvar__1___24Anonymous__7495,Vvar__2___24Anonymous__7496,Vvar__2___24Anonymous__7497] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7492,Vvar__1___24Anonymous__7494,Vvar__2___24Anonymous__7496) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7493,Vvar__1___24Anonymous__7495,Vvar__2___24Anonymous__7497)
=> ( Vvar__2___24Anonymous__7496 = Vvar__2___24Anonymous__7497
& Vvar__1___24Anonymous__7494 = Vvar__1___24Anonymous__7495
& Vvar__0__C__7492 = Vvar__0__C__7493 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__7530,Vvar__0__C__7531,Vvar__1__num__7532,Vvar__1__num__7533,Vvar__2__denum__7534,Vvar__2__denum__7535,Vvar__3__condition__7536,Vvar__3__condition__7537] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7530,Vvar__1__num__7532,Vvar__2__denum__7534,Vvar__3__condition__7536) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7531,Vvar__1__num__7533,Vvar__2__denum__7535,Vvar__3__condition__7537)
=> ( Vvar__3__condition__7536 = Vvar__3__condition__7537
& Vvar__2__denum__7534 = Vvar__2__denum__7535
& Vvar__1__num__7532 = Vvar__1__num__7533
& Vvar__0__C__7530 = Vvar__0__C__7531 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__7544,Vvar__0__C__7545,Vvar__1__rsplit__left__7546,Vvar__1__rsplit__left__7547,Vvar__2__rsplit__common__7548,Vvar__2__rsplit__common__7549,Vvar__3__rsplit__right__7550,Vvar__3__rsplit__right__7551] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7544,Vvar__1__rsplit__left__7546,Vvar__2__rsplit__common__7548,Vvar__3__rsplit__right__7550) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7545,Vvar__1__rsplit__left__7547,Vvar__2__rsplit__common__7549,Vvar__3__rsplit__right__7551)
=> ( Vvar__3__rsplit__right__7550 = Vvar__3__rsplit__right__7551
& Vvar__2__rsplit__common__7548 = Vvar__2__rsplit__common__7549
& Vvar__1__rsplit__left__7546 = Vvar__1__rsplit__left__7547
& Vvar__0__C__7544 = Vvar__0__C__7545 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__39475,Vvar__0__hypo__type__39476,Vvar__1__hypo__proof__39477,Vvar__1__hypo__proof__39478] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__39475,Vvar__1__hypo__proof__39477) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__39476,Vvar__1__hypo__proof__39478)
=> ( Vvar__1__hypo__proof__39477 = Vvar__1__hypo__proof__39478
& Vvar__0__hypo__type__39475 = Vvar__0__hypo__type__39476 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__15904,Vvar__0__C__15905] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15904) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15905)
=> Vvar__0__C__15904 = Vvar__0__C__15905 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__15902,Vvar__0__C__15903] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15902) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15903)
=> Vvar__0__C__15902 = Vvar__0__C__15903 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__15910,Vvar__0__C__15911,Vvar__1___24Anonymous__15912,Vvar__1___24Anonymous__15913] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__15910,Vvar__1___24Anonymous__15912) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__15911,Vvar__1___24Anonymous__15913)
=> ( Vvar__1___24Anonymous__15912 = Vvar__1___24Anonymous__15913
& Vvar__0__C__15910 = Vvar__0__C__15911 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__15914,Vvar__0__C__15915,Vvar__1___24Anonymous__15916,Vvar__1___24Anonymous__15917,Vvar__2___24Anonymous__15918,Vvar__2___24Anonymous__15919] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__15914,Vvar__1___24Anonymous__15916,Vvar__2___24Anonymous__15918) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__15915,Vvar__1___24Anonymous__15917,Vvar__2___24Anonymous__15919)
=> ( Vvar__2___24Anonymous__15918 = Vvar__2___24Anonymous__15919
& Vvar__1___24Anonymous__15916 = Vvar__1___24Anonymous__15917
& Vvar__0__C__15914 = Vvar__0__C__15915 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__15906,Vvar__0__C__15907,Vvar__1___24Anonymous__15908,Vvar__1___24Anonymous__15909] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__15906,Vvar__1___24Anonymous__15908) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__15907,Vvar__1___24Anonymous__15909)
=> ( Vvar__1___24Anonymous__15908 = Vvar__1___24Anonymous__15909
& Vvar__0__C__15906 = Vvar__0__C__15907 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__15926,Vvar__0__C__15927,Vvar__1___24Anonymous__15928,Vvar__1___24Anonymous__15929,Vvar__2___24Anonymous__15930,Vvar__2___24Anonymous__15931] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__15926,Vvar__1___24Anonymous__15928,Vvar__2___24Anonymous__15930) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__15927,Vvar__1___24Anonymous__15929,Vvar__2___24Anonymous__15931)
=> ( Vvar__2___24Anonymous__15930 = Vvar__2___24Anonymous__15931
& Vvar__1___24Anonymous__15928 = Vvar__1___24Anonymous__15929
& Vvar__0__C__15926 = Vvar__0__C__15927 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__15932,Vvar__0__C__15933,Vvar__1___24Anonymous__15934,Vvar__1___24Anonymous__15935] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__15932,Vvar__1___24Anonymous__15934) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__15933,Vvar__1___24Anonymous__15935)
=> ( Vvar__1___24Anonymous__15934 = Vvar__1___24Anonymous__15935
& Vvar__0__C__15932 = Vvar__0__C__15933 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__15936,Vvar__0__C__15937,Vvar__1___24Anonymous__15938,Vvar__1___24Anonymous__15939,Vvar__2___24Anonymous__15940,Vvar__2___24Anonymous__15941] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__15936,Vvar__1___24Anonymous__15938,Vvar__2___24Anonymous__15940) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__15937,Vvar__1___24Anonymous__15939,Vvar__2___24Anonymous__15941)
=> ( Vvar__2___24Anonymous__15940 = Vvar__2___24Anonymous__15941
& Vvar__1___24Anonymous__15938 = Vvar__1___24Anonymous__15939
& Vvar__0__C__15936 = Vvar__0__C__15937 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__15920,Vvar__0__C__15921,Vvar__1___24Anonymous__15922,Vvar__1___24Anonymous__15923,Vvar__2___24Anonymous__15924,Vvar__2___24Anonymous__15925] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__15920,Vvar__1___24Anonymous__15922,Vvar__2___24Anonymous__15924) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__15921,Vvar__1___24Anonymous__15923,Vvar__2___24Anonymous__15925)
=> ( Vvar__2___24Anonymous__15924 = Vvar__2___24Anonymous__15925
& Vvar__1___24Anonymous__15922 = Vvar__1___24Anonymous__15923
& Vvar__0__C__15920 = Vvar__0__C__15921 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__15691,Vvar__0__C__15692,Vvar__1___24Anonymous__15693,Vvar__1___24Anonymous__15694,Vvar__2___24Anonymous__15695,Vvar__2___24Anonymous__15696,Vvar__3___24Anonymous__15697,Vvar__3___24Anonymous__15698] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__15691,Vvar__1___24Anonymous__15693,Vvar__2___24Anonymous__15695,Vvar__3___24Anonymous__15697) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__15692,Vvar__1___24Anonymous__15694,Vvar__2___24Anonymous__15696,Vvar__3___24Anonymous__15698)
=> ( Vvar__3___24Anonymous__15697 = Vvar__3___24Anonymous__15698
& Vvar__2___24Anonymous__15695 = Vvar__2___24Anonymous__15696
& Vvar__1___24Anonymous__15693 = Vvar__1___24Anonymous__15694
& Vvar__0__C__15691 = Vvar__0__C__15692 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__15681,Vvar__0__C__15682,Vvar__1___24Anonymous__15683,Vvar__1___24Anonymous__15684] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15681,Vvar__1___24Anonymous__15683) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15682,Vvar__1___24Anonymous__15684)
=> ( Vvar__1___24Anonymous__15683 = Vvar__1___24Anonymous__15684
& Vvar__0__C__15681 = Vvar__0__C__15682 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__15685,Vvar__0__C__15686,Vvar__1___24Anonymous__15687,Vvar__1___24Anonymous__15688,Vvar__2___24Anonymous__15689,Vvar__2___24Anonymous__15690] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15685,Vvar__1___24Anonymous__15687,Vvar__2___24Anonymous__15689) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15686,Vvar__1___24Anonymous__15688,Vvar__2___24Anonymous__15690)
=> ( Vvar__2___24Anonymous__15689 = Vvar__2___24Anonymous__15690
& Vvar__1___24Anonymous__15687 = Vvar__1___24Anonymous__15688
& Vvar__0__C__15685 = Vvar__0__C__15686 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__15716,Vvar__0___24Anonymous__15717,Vvar__1___24Anonymous__15718,Vvar__1___24Anonymous__15719] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__15716,Vvar__1___24Anonymous__15718) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__15717,Vvar__1___24Anonymous__15719)
=> ( Vvar__1___24Anonymous__15718 = Vvar__1___24Anonymous__15719
& Vvar__0___24Anonymous__15716 = Vvar__0___24Anonymous__15717 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__15712,Vvar__0___24Anonymous__15713,Vvar__1___24Anonymous__15714,Vvar__1___24Anonymous__15715] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15712,Vvar__1___24Anonymous__15714) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15713,Vvar__1___24Anonymous__15715)
=> ( Vvar__1___24Anonymous__15714 = Vvar__1___24Anonymous__15715
& Vvar__0___24Anonymous__15712 = Vvar__0___24Anonymous__15713 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__22155,Vvar__0__R__22156,Vvar__1__req__22157,Vvar__1__req__22158,Vvar__2__reqb__22159,Vvar__2__reqb__22160,Vvar__3___24Anonymous__22161,Vvar__3___24Anonymous__22162] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__22155,Vvar__1__req__22157,Vvar__2__reqb__22159) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__22156,Vvar__1__req__22158,Vvar__2__reqb__22160)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__22159 = Vvar__2__reqb__22160
& Vvar__1__req__22157 = Vvar__1__req__22158
& Vvar__0__R__22155 = Vvar__0__R__22156 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__22163,Vvar__0__R__22164,Vvar__1__rO__22165,Vvar__1__rO__22166,Vvar__2__rI__22167,Vvar__2__rI__22168,Vvar__3__radd__22169,Vvar__3__radd__22170,Vvar__4__rmul__22171,Vvar__4__rmul__22172,Vvar__5__rsub__22173,Vvar__5__rsub__22174,Vvar__6__ropp__22175,Vvar__6__ropp__22176,Vvar__7__req__22177,Vvar__7__req__22178,Vvar__8__C__22179,Vvar__8__C__22180,Vvar__9__cO__22181,Vvar__9__cO__22182,Vvar__10__cI__22183,Vvar__10__cI__22184,Vvar__11__cadd__22185,Vvar__11__cadd__22186,Vvar__12__cmul__22187,Vvar__12__cmul__22188,Vvar__13__csub__22189,Vvar__13__csub__22190,Vvar__14__copp__22191,Vvar__14__copp__22192,Vvar__15__ceqb__22193,Vvar__15__ceqb__22194,Vvar__16__phi__22195,Vvar__16__phi__22196,Vvar__17___24Anonymous__22197,Vvar__17___24Anonymous__22198] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__22163,Vvar__1__rO__22165,Vvar__2__rI__22167,Vvar__3__radd__22169,Vvar__4__rmul__22171,Vvar__5__rsub__22173,Vvar__6__ropp__22175,Vvar__7__req__22177,Vvar__8__C__22179,Vvar__9__cO__22181,Vvar__10__cI__22183,Vvar__11__cadd__22185,Vvar__12__cmul__22187,Vvar__13__csub__22189,Vvar__14__copp__22191,Vvar__15__ceqb__22193,Vvar__16__phi__22195) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__22164,Vvar__1__rO__22166,Vvar__2__rI__22168,Vvar__3__radd__22170,Vvar__4__rmul__22172,Vvar__5__rsub__22174,Vvar__6__ropp__22176,Vvar__7__req__22178,Vvar__8__C__22180,Vvar__9__cO__22182,Vvar__10__cI__22184,Vvar__11__cadd__22186,Vvar__12__cmul__22188,Vvar__13__csub__22190,Vvar__14__copp__22192,Vvar__15__ceqb__22194,Vvar__16__phi__22196)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__22195 = Vvar__16__phi__22196
& Vvar__15__ceqb__22193 = Vvar__15__ceqb__22194
& Vvar__14__copp__22191 = Vvar__14__copp__22192
& Vvar__13__csub__22189 = Vvar__13__csub__22190
& Vvar__12__cmul__22187 = Vvar__12__cmul__22188
& Vvar__11__cadd__22185 = Vvar__11__cadd__22186
& Vvar__10__cI__22183 = Vvar__10__cI__22184
& Vvar__9__cO__22181 = Vvar__9__cO__22182
& Vvar__8__C__22179 = Vvar__8__C__22180
& Vvar__7__req__22177 = Vvar__7__req__22178
& Vvar__6__ropp__22175 = Vvar__6__ropp__22176
& Vvar__5__rsub__22173 = Vvar__5__rsub__22174
& Vvar__4__rmul__22171 = Vvar__4__rmul__22172
& Vvar__3__radd__22169 = Vvar__3__radd__22170
& Vvar__2__rI__22167 = Vvar__2__rI__22168
& Vvar__1__rO__22165 = Vvar__1__rO__22166
& Vvar__0__R__22163 = Vvar__0__R__22164 ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__31631,Vvar__1__k__31633,Vvar__2___24Anonymous__31634] :
( c_24__type__31648___24t(Vvar__0__P__31631,Vvar__1__k__31633,Vvar__2___24Anonymous__31634,Vvar__0__P__31631)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__31633)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__31634)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__31631,Vvar__1__k__31633,Vvar__2___24Anonymous__31634)
=> ( Vvar__2___24Anonymous__31634 = Vvar__1__k__31633
| ? [Vvar__2__l__31642] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__31642)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__31631,Vvar__1__k__31633,Vvar__2__l__31642)
& p(happ(Vvar__0__P__31631,Vvar__2__l__31642))
& Vvar__2___24Anonymous__31634 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__31642) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__6453] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6453)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__6453)
=> ( Vvar__0___24Anonymous__6453 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__6455] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6455)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__6455)
& Vvar__0___24Anonymous__6453 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6455) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__6457] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__6457)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__6457)
=> ? [Vvar__0__n__6459] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6459)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__6459)
& Vvar__0___24Anonymous__6457 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__6459) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__5838,Vvar__1___24Anonymous__5839,VX5840] :
( cProp___24t(Vvar__0__P__5838)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__5839)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__5838,Vvar__1___24Anonymous__5839,VX5840)
=> ( ( p(Vvar__0__P__5838)
& Vvar__1___24Anonymous__5839 = cCoq_2eInit_2eDatatypes_2etrue
& VX5840 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__5838) )
| ( ~ p(Vvar__0__P__5838)
& Vvar__1___24Anonymous__5839 = cCoq_2eInit_2eDatatypes_2efalse
& VX5840 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__5838) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX23541] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX23541)
=> ( VX23541 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__23542] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__23542)
& ? [Vvar__1___24Anonymous__23543] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__23543)
& ? [Vvar__2___24Anonymous__23544] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__23544)
& VX23541 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__23542,Vvar__1___24Anonymous__23543,Vvar__2___24Anonymous__23544) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX1261] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX1261)
=> ( VX1261 = cCoq_2eInit_2eByte_2ex00
| VX1261 = cCoq_2eInit_2eByte_2ex01
| VX1261 = cCoq_2eInit_2eByte_2ex02
| VX1261 = cCoq_2eInit_2eByte_2ex03
| VX1261 = cCoq_2eInit_2eByte_2ex04
| VX1261 = cCoq_2eInit_2eByte_2ex05
| VX1261 = cCoq_2eInit_2eByte_2ex06
| VX1261 = cCoq_2eInit_2eByte_2ex07
| VX1261 = cCoq_2eInit_2eByte_2ex08
| VX1261 = cCoq_2eInit_2eByte_2ex09
| VX1261 = cCoq_2eInit_2eByte_2ex0a
| VX1261 = cCoq_2eInit_2eByte_2ex0b
| VX1261 = cCoq_2eInit_2eByte_2ex0c
| VX1261 = cCoq_2eInit_2eByte_2ex0d
| VX1261 = cCoq_2eInit_2eByte_2ex0e
| VX1261 = cCoq_2eInit_2eByte_2ex0f
| VX1261 = cCoq_2eInit_2eByte_2ex10
| VX1261 = cCoq_2eInit_2eByte_2ex11
| VX1261 = cCoq_2eInit_2eByte_2ex12
| VX1261 = cCoq_2eInit_2eByte_2ex13
| VX1261 = cCoq_2eInit_2eByte_2ex14
| VX1261 = cCoq_2eInit_2eByte_2ex15
| VX1261 = cCoq_2eInit_2eByte_2ex16
| VX1261 = cCoq_2eInit_2eByte_2ex17
| VX1261 = cCoq_2eInit_2eByte_2ex18
| VX1261 = cCoq_2eInit_2eByte_2ex19
| VX1261 = cCoq_2eInit_2eByte_2ex1a
| VX1261 = cCoq_2eInit_2eByte_2ex1b
| VX1261 = cCoq_2eInit_2eByte_2ex1c
| VX1261 = cCoq_2eInit_2eByte_2ex1d
| VX1261 = cCoq_2eInit_2eByte_2ex1e
| VX1261 = cCoq_2eInit_2eByte_2ex1f
| VX1261 = cCoq_2eInit_2eByte_2ex20
| VX1261 = cCoq_2eInit_2eByte_2ex21
| VX1261 = cCoq_2eInit_2eByte_2ex22
| VX1261 = cCoq_2eInit_2eByte_2ex23
| VX1261 = cCoq_2eInit_2eByte_2ex24
| VX1261 = cCoq_2eInit_2eByte_2ex25
| VX1261 = cCoq_2eInit_2eByte_2ex26
| VX1261 = cCoq_2eInit_2eByte_2ex27
| VX1261 = cCoq_2eInit_2eByte_2ex28
| VX1261 = cCoq_2eInit_2eByte_2ex29
| VX1261 = cCoq_2eInit_2eByte_2ex2a
| VX1261 = cCoq_2eInit_2eByte_2ex2b
| VX1261 = cCoq_2eInit_2eByte_2ex2c
| VX1261 = cCoq_2eInit_2eByte_2ex2d
| VX1261 = cCoq_2eInit_2eByte_2ex2e
| VX1261 = cCoq_2eInit_2eByte_2ex2f
| VX1261 = cCoq_2eInit_2eByte_2ex30
| VX1261 = cCoq_2eInit_2eByte_2ex31
| VX1261 = cCoq_2eInit_2eByte_2ex32
| VX1261 = cCoq_2eInit_2eByte_2ex33
| VX1261 = cCoq_2eInit_2eByte_2ex34
| VX1261 = cCoq_2eInit_2eByte_2ex35
| VX1261 = cCoq_2eInit_2eByte_2ex36
| VX1261 = cCoq_2eInit_2eByte_2ex37
| VX1261 = cCoq_2eInit_2eByte_2ex38
| VX1261 = cCoq_2eInit_2eByte_2ex39
| VX1261 = cCoq_2eInit_2eByte_2ex3a
| VX1261 = cCoq_2eInit_2eByte_2ex3b
| VX1261 = cCoq_2eInit_2eByte_2ex3c
| VX1261 = cCoq_2eInit_2eByte_2ex3d
| VX1261 = cCoq_2eInit_2eByte_2ex3e
| VX1261 = cCoq_2eInit_2eByte_2ex3f
| VX1261 = cCoq_2eInit_2eByte_2ex40
| VX1261 = cCoq_2eInit_2eByte_2ex41
| VX1261 = cCoq_2eInit_2eByte_2ex42
| VX1261 = cCoq_2eInit_2eByte_2ex43
| VX1261 = cCoq_2eInit_2eByte_2ex44
| VX1261 = cCoq_2eInit_2eByte_2ex45
| VX1261 = cCoq_2eInit_2eByte_2ex46
| VX1261 = cCoq_2eInit_2eByte_2ex47
| VX1261 = cCoq_2eInit_2eByte_2ex48
| VX1261 = cCoq_2eInit_2eByte_2ex49
| VX1261 = cCoq_2eInit_2eByte_2ex4a
| VX1261 = cCoq_2eInit_2eByte_2ex4b
| VX1261 = cCoq_2eInit_2eByte_2ex4c
| VX1261 = cCoq_2eInit_2eByte_2ex4d
| VX1261 = cCoq_2eInit_2eByte_2ex4e
| VX1261 = cCoq_2eInit_2eByte_2ex4f
| VX1261 = cCoq_2eInit_2eByte_2ex50
| VX1261 = cCoq_2eInit_2eByte_2ex51
| VX1261 = cCoq_2eInit_2eByte_2ex52
| VX1261 = cCoq_2eInit_2eByte_2ex53
| VX1261 = cCoq_2eInit_2eByte_2ex54
| VX1261 = cCoq_2eInit_2eByte_2ex55
| VX1261 = cCoq_2eInit_2eByte_2ex56
| VX1261 = cCoq_2eInit_2eByte_2ex57
| VX1261 = cCoq_2eInit_2eByte_2ex58
| VX1261 = cCoq_2eInit_2eByte_2ex59
| VX1261 = cCoq_2eInit_2eByte_2ex5a
| VX1261 = cCoq_2eInit_2eByte_2ex5b
| VX1261 = cCoq_2eInit_2eByte_2ex5c
| VX1261 = cCoq_2eInit_2eByte_2ex5d
| VX1261 = cCoq_2eInit_2eByte_2ex5e
| VX1261 = cCoq_2eInit_2eByte_2ex5f
| VX1261 = cCoq_2eInit_2eByte_2ex60
| VX1261 = cCoq_2eInit_2eByte_2ex61
| VX1261 = cCoq_2eInit_2eByte_2ex62
| VX1261 = cCoq_2eInit_2eByte_2ex63
| VX1261 = cCoq_2eInit_2eByte_2ex64
| VX1261 = cCoq_2eInit_2eByte_2ex65
| VX1261 = cCoq_2eInit_2eByte_2ex66
| VX1261 = cCoq_2eInit_2eByte_2ex67
| VX1261 = cCoq_2eInit_2eByte_2ex68
| VX1261 = cCoq_2eInit_2eByte_2ex69
| VX1261 = cCoq_2eInit_2eByte_2ex6a
| VX1261 = cCoq_2eInit_2eByte_2ex6b
| VX1261 = cCoq_2eInit_2eByte_2ex6c
| VX1261 = cCoq_2eInit_2eByte_2ex6d
| VX1261 = cCoq_2eInit_2eByte_2ex6e
| VX1261 = cCoq_2eInit_2eByte_2ex6f
| VX1261 = cCoq_2eInit_2eByte_2ex70
| VX1261 = cCoq_2eInit_2eByte_2ex71
| VX1261 = cCoq_2eInit_2eByte_2ex72
| VX1261 = cCoq_2eInit_2eByte_2ex73
| VX1261 = cCoq_2eInit_2eByte_2ex74
| VX1261 = cCoq_2eInit_2eByte_2ex75
| VX1261 = cCoq_2eInit_2eByte_2ex76
| VX1261 = cCoq_2eInit_2eByte_2ex77
| VX1261 = cCoq_2eInit_2eByte_2ex78
| VX1261 = cCoq_2eInit_2eByte_2ex79
| VX1261 = cCoq_2eInit_2eByte_2ex7a
| VX1261 = cCoq_2eInit_2eByte_2ex7b
| VX1261 = cCoq_2eInit_2eByte_2ex7c
| VX1261 = cCoq_2eInit_2eByte_2ex7d
| VX1261 = cCoq_2eInit_2eByte_2ex7e
| VX1261 = cCoq_2eInit_2eByte_2ex7f
| VX1261 = cCoq_2eInit_2eByte_2ex80
| VX1261 = cCoq_2eInit_2eByte_2ex81
| VX1261 = cCoq_2eInit_2eByte_2ex82
| VX1261 = cCoq_2eInit_2eByte_2ex83
| VX1261 = cCoq_2eInit_2eByte_2ex84
| VX1261 = cCoq_2eInit_2eByte_2ex85
| VX1261 = cCoq_2eInit_2eByte_2ex86
| VX1261 = cCoq_2eInit_2eByte_2ex87
| VX1261 = cCoq_2eInit_2eByte_2ex88
| VX1261 = cCoq_2eInit_2eByte_2ex89
| VX1261 = cCoq_2eInit_2eByte_2ex8a
| VX1261 = cCoq_2eInit_2eByte_2ex8b
| VX1261 = cCoq_2eInit_2eByte_2ex8c
| VX1261 = cCoq_2eInit_2eByte_2ex8d
| VX1261 = cCoq_2eInit_2eByte_2ex8e
| VX1261 = cCoq_2eInit_2eByte_2ex8f
| VX1261 = cCoq_2eInit_2eByte_2ex90
| VX1261 = cCoq_2eInit_2eByte_2ex91
| VX1261 = cCoq_2eInit_2eByte_2ex92
| VX1261 = cCoq_2eInit_2eByte_2ex93
| VX1261 = cCoq_2eInit_2eByte_2ex94
| VX1261 = cCoq_2eInit_2eByte_2ex95
| VX1261 = cCoq_2eInit_2eByte_2ex96
| VX1261 = cCoq_2eInit_2eByte_2ex97
| VX1261 = cCoq_2eInit_2eByte_2ex98
| VX1261 = cCoq_2eInit_2eByte_2ex99
| VX1261 = cCoq_2eInit_2eByte_2ex9a
| VX1261 = cCoq_2eInit_2eByte_2ex9b
| VX1261 = cCoq_2eInit_2eByte_2ex9c
| VX1261 = cCoq_2eInit_2eByte_2ex9d
| VX1261 = cCoq_2eInit_2eByte_2ex9e
| VX1261 = cCoq_2eInit_2eByte_2ex9f
| VX1261 = cCoq_2eInit_2eByte_2exa0
| VX1261 = cCoq_2eInit_2eByte_2exa1
| VX1261 = cCoq_2eInit_2eByte_2exa2
| VX1261 = cCoq_2eInit_2eByte_2exa3
| VX1261 = cCoq_2eInit_2eByte_2exa4
| VX1261 = cCoq_2eInit_2eByte_2exa5
| VX1261 = cCoq_2eInit_2eByte_2exa6
| VX1261 = cCoq_2eInit_2eByte_2exa7
| VX1261 = cCoq_2eInit_2eByte_2exa8
| VX1261 = cCoq_2eInit_2eByte_2exa9
| VX1261 = cCoq_2eInit_2eByte_2exaa
| VX1261 = cCoq_2eInit_2eByte_2exab
| VX1261 = cCoq_2eInit_2eByte_2exac
| VX1261 = cCoq_2eInit_2eByte_2exad
| VX1261 = cCoq_2eInit_2eByte_2exae
| VX1261 = cCoq_2eInit_2eByte_2exaf
| VX1261 = cCoq_2eInit_2eByte_2exb0
| VX1261 = cCoq_2eInit_2eByte_2exb1
| VX1261 = cCoq_2eInit_2eByte_2exb2
| VX1261 = cCoq_2eInit_2eByte_2exb3
| VX1261 = cCoq_2eInit_2eByte_2exb4
| VX1261 = cCoq_2eInit_2eByte_2exb5
| VX1261 = cCoq_2eInit_2eByte_2exb6
| VX1261 = cCoq_2eInit_2eByte_2exb7
| VX1261 = cCoq_2eInit_2eByte_2exb8
| VX1261 = cCoq_2eInit_2eByte_2exb9
| VX1261 = cCoq_2eInit_2eByte_2exba
| VX1261 = cCoq_2eInit_2eByte_2exbb
| VX1261 = cCoq_2eInit_2eByte_2exbc
| VX1261 = cCoq_2eInit_2eByte_2exbd
| VX1261 = cCoq_2eInit_2eByte_2exbe
| VX1261 = cCoq_2eInit_2eByte_2exbf
| VX1261 = cCoq_2eInit_2eByte_2exc0
| VX1261 = cCoq_2eInit_2eByte_2exc1
| VX1261 = cCoq_2eInit_2eByte_2exc2
| VX1261 = cCoq_2eInit_2eByte_2exc3
| VX1261 = cCoq_2eInit_2eByte_2exc4
| VX1261 = cCoq_2eInit_2eByte_2exc5
| VX1261 = cCoq_2eInit_2eByte_2exc6
| VX1261 = cCoq_2eInit_2eByte_2exc7
| VX1261 = cCoq_2eInit_2eByte_2exc8
| VX1261 = cCoq_2eInit_2eByte_2exc9
| VX1261 = cCoq_2eInit_2eByte_2exca
| VX1261 = cCoq_2eInit_2eByte_2excb
| VX1261 = cCoq_2eInit_2eByte_2excc
| VX1261 = cCoq_2eInit_2eByte_2excd
| VX1261 = cCoq_2eInit_2eByte_2exce
| VX1261 = cCoq_2eInit_2eByte_2excf
| VX1261 = cCoq_2eInit_2eByte_2exd0
| VX1261 = cCoq_2eInit_2eByte_2exd1
| VX1261 = cCoq_2eInit_2eByte_2exd2
| VX1261 = cCoq_2eInit_2eByte_2exd3
| VX1261 = cCoq_2eInit_2eByte_2exd4
| VX1261 = cCoq_2eInit_2eByte_2exd5
| VX1261 = cCoq_2eInit_2eByte_2exd6
| VX1261 = cCoq_2eInit_2eByte_2exd7
| VX1261 = cCoq_2eInit_2eByte_2exd8
| VX1261 = cCoq_2eInit_2eByte_2exd9
| VX1261 = cCoq_2eInit_2eByte_2exda
| VX1261 = cCoq_2eInit_2eByte_2exdb
| VX1261 = cCoq_2eInit_2eByte_2exdc
| VX1261 = cCoq_2eInit_2eByte_2exdd
| VX1261 = cCoq_2eInit_2eByte_2exde
| VX1261 = cCoq_2eInit_2eByte_2exdf
| VX1261 = cCoq_2eInit_2eByte_2exe0
| VX1261 = cCoq_2eInit_2eByte_2exe1
| VX1261 = cCoq_2eInit_2eByte_2exe2
| VX1261 = cCoq_2eInit_2eByte_2exe3
| VX1261 = cCoq_2eInit_2eByte_2exe4
| VX1261 = cCoq_2eInit_2eByte_2exe5
| VX1261 = cCoq_2eInit_2eByte_2exe6
| VX1261 = cCoq_2eInit_2eByte_2exe7
| VX1261 = cCoq_2eInit_2eByte_2exe8
| VX1261 = cCoq_2eInit_2eByte_2exe9
| VX1261 = cCoq_2eInit_2eByte_2exea
| VX1261 = cCoq_2eInit_2eByte_2exeb
| VX1261 = cCoq_2eInit_2eByte_2exec
| VX1261 = cCoq_2eInit_2eByte_2exed
| VX1261 = cCoq_2eInit_2eByte_2exee
| VX1261 = cCoq_2eInit_2eByte_2exef
| VX1261 = cCoq_2eInit_2eByte_2exf0
| VX1261 = cCoq_2eInit_2eByte_2exf1
| VX1261 = cCoq_2eInit_2eByte_2exf2
| VX1261 = cCoq_2eInit_2eByte_2exf3
| VX1261 = cCoq_2eInit_2eByte_2exf4
| VX1261 = cCoq_2eInit_2eByte_2exf5
| VX1261 = cCoq_2eInit_2eByte_2exf6
| VX1261 = cCoq_2eInit_2eByte_2exf7
| VX1261 = cCoq_2eInit_2eByte_2exf8
| VX1261 = cCoq_2eInit_2eByte_2exf9
| VX1261 = cCoq_2eInit_2eByte_2exfa
| VX1261 = cCoq_2eInit_2eByte_2exfb
| VX1261 = cCoq_2eInit_2eByte_2exfc
| VX1261 = cCoq_2eInit_2eByte_2exfd
| VX1261 = cCoq_2eInit_2eByte_2exfe
| VX1261 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__5967,Vvar__1__Q__5968,Vvar__2___24Anonymous__5969] :
( cProp___24t(Vvar__0__P__5967)
=> ( cProp___24t(Vvar__1__Q__5968)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__5969)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__5967,Vvar__1__Q__5968,Vvar__2___24Anonymous__5969)
=> ( ( p(Vvar__0__P__5967)
& Vvar__2___24Anonymous__5969 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__5968)
& Vvar__2___24Anonymous__5969 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__6086,Vvar__1__Plt__6087,Vvar__2__Pgt__6088,Vvar__3___24Anonymous__6089] :
( cProp___24t(Vvar__0__Peq__6086)
=> ( cProp___24t(Vvar__1__Plt__6087)
=> ( cProp___24t(Vvar__2__Pgt__6088)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__6089)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__6086,Vvar__1__Plt__6087,Vvar__2__Pgt__6088,Vvar__3___24Anonymous__6089)
=> ( ( p(Vvar__0__Peq__6086)
& Vvar__3___24Anonymous__6089 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__6087)
& Vvar__3___24Anonymous__6089 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__6088)
& Vvar__3___24Anonymous__6089 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__6103,Vvar__1__Plt__6104,Vvar__2__Pgt__6105,Vvar__3___24Anonymous__6106,VX6107] :
( cProp___24t(Vvar__0__Peq__6103)
=> ( cProp___24t(Vvar__1__Plt__6104)
=> ( cProp___24t(Vvar__2__Pgt__6105)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__6106)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__6103,Vvar__1__Plt__6104,Vvar__2__Pgt__6105,Vvar__3___24Anonymous__6106,VX6107)
=> ( ( p(Vvar__0__Peq__6103)
& Vvar__3___24Anonymous__6106 = cCoq_2eInit_2eDatatypes_2eEq
& VX6107 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__6103,Vvar__1__Plt__6104,Vvar__2__Pgt__6105) )
| ( p(Vvar__1__Plt__6104)
& Vvar__3___24Anonymous__6106 = cCoq_2eInit_2eDatatypes_2eLt
& VX6107 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__6103,Vvar__1__Plt__6104,Vvar__2__Pgt__6105) )
| ( p(Vvar__2__Pgt__6105)
& Vvar__3___24Anonymous__6106 = cCoq_2eInit_2eDatatypes_2eGt
& VX6107 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__6103,Vvar__1__Plt__6104,Vvar__2__Pgt__6105) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX3845] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX3845)
=> ( VX3845 = cCoq_2eInit_2eDatatypes_2etrue
| VX3845 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX3892] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX3892)
=> ( VX3892 = cCoq_2eInit_2eDatatypes_2eEq
| VX3892 = cCoq_2eInit_2eDatatypes_2eLt
| VX3892 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__39040] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__39040)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__39040)
=> Vvar__0___24Anonymous__39040 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__39042,Vvar__1__a__39043,Vvar__2___24Anonymous__39044] :
( cType___24t(Vvar__0__A__39042)
=> ( t(Vvar__1__a__39043,Vvar__0__A__39042)
=> ( t(Vvar__2___24Anonymous__39044,Vvar__0__A__39042)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__39042,Vvar__1__a__39043,Vvar__2___24Anonymous__39044)
=> Vvar__2___24Anonymous__39044 = Vvar__1__a__39043 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__3851,VX3852] :
( cType___24t(Vvar__0__A__3851)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3851,VX3852)
=> ( VX3852 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3851)
| ? [Vvar__1___24Anonymous__3855] :
( t(Vvar__1___24Anonymous__3855,Vvar__0__A__3851)
& ? [Vvar__2___24Anonymous__3856] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3851,Vvar__2___24Anonymous__3856)
& VX3852 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3851,Vvar__1___24Anonymous__3855,Vvar__2___24Anonymous__3856) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX228] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX228)
=> ( VX228 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__229] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__229)
& VX228 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__229) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__5977,VX5978] :
( cType___24t(Vvar__0__A__5977)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__5977,VX5978)
=> ( ? [Vvar__1___24Anonymous__5980] :
( t(Vvar__1___24Anonymous__5980,Vvar__0__A__5977)
& VX5978 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__5977,Vvar__1___24Anonymous__5980) )
| VX5978 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__5977) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__6026,Vvar__1__B__6027,VX6028] :
( cType___24t(Vvar__0__A__6026)
=> ( cType___24t(Vvar__1__B__6027)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__6026,Vvar__1__B__6027,VX6028)
=> ? [Vvar__2___24Anonymous__6031] :
( t(Vvar__2___24Anonymous__6031,Vvar__0__A__6026)
& ? [Vvar__3___24Anonymous__6032] :
( t(Vvar__3___24Anonymous__6032,Vvar__1__B__6027)
& VX6028 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__6026,Vvar__1__B__6027,Vvar__2___24Anonymous__6031,Vvar__3___24Anonymous__6032) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__5996,Vvar__1__B__5997,VX5998] :
( cType___24t(Vvar__0__A__5996)
=> ( cType___24t(Vvar__1__B__5997)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__5996,Vvar__1__B__5997,VX5998)
=> ( ? [Vvar__2___24Anonymous__6001] :
( t(Vvar__2___24Anonymous__6001,Vvar__0__A__5996)
& VX5998 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__5996,Vvar__1__B__5997,Vvar__2___24Anonymous__6001) )
| ? [Vvar__2___24Anonymous__6004] :
( t(Vvar__2___24Anonymous__6004,Vvar__1__B__5997)
& VX5998 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__5996,Vvar__1__B__5997,Vvar__2___24Anonymous__6004) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX3844] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX3844)
=> VX3844 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX39049] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX39049)
=> ( ? [Vvar__0__i__39050] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__39050)
& ? [Vvar__1__f__39051] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__39051)
& VX39049 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__39050,Vvar__1__f__39051) ) )
| ? [Vvar__0__i__39052] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__39052)
& ? [Vvar__1__f__39053] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__39053)
& ? [Vvar__2__e__39054] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__39054)
& VX39049 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__39052,Vvar__1__f__39053,Vvar__2__e__39054) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX32993] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX32993)
=> ( ? [Vvar__0__d__32994] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__32994)
& VX32993 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__32994) )
| ? [Vvar__0__d__32995] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__32995)
& VX32993 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__32995) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX32862] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX32862)
=> ( VX32862 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__32863] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32863)
& VX32862 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__32863) )
| ? [Vvar__0___24Anonymous__32864] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32864)
& VX32862 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__32864) )
| ? [Vvar__0___24Anonymous__32865] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32865)
& VX32862 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__32865) )
| ? [Vvar__0___24Anonymous__32866] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32866)
& VX32862 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__32866) )
| ? [Vvar__0___24Anonymous__32867] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32867)
& VX32862 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__32867) )
| ? [Vvar__0___24Anonymous__32868] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32868)
& VX32862 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__32868) )
| ? [Vvar__0___24Anonymous__32869] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32869)
& VX32862 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__32869) )
| ? [Vvar__0___24Anonymous__32870] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32870)
& VX32862 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__32870) )
| ? [Vvar__0___24Anonymous__32871] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32871)
& VX32862 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__32871) )
| ? [Vvar__0___24Anonymous__32872] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32872)
& VX32862 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__32872) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__4263,Vvar__1___24Anonymous__4264] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4263)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__4264)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__4263,Vvar__1___24Anonymous__4264)
=> ( Vvar__1___24Anonymous__4264 = Vvar__0__n__4263
| ? [Vvar__1__m__4268] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__4268)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__4263,Vvar__1__m__4268)
& Vvar__1___24Anonymous__4264 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__4268) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__22425,Vvar__1__P__22426,VX22429] :
( cType___24t(Vvar__0__A__22425)
=> ( c_24__type__22439___24t(Vvar__0__A__22425,Vvar__1__P__22426,Vvar__1__P__22426)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__22425,Vvar__1__P__22426,VX22429)
=> ? [Vvar__2__x__22434] :
( t(Vvar__2__x__22434,Vvar__0__A__22425)
& p(happ(Vvar__1__P__22426,Vvar__2__x__22434))
& VX22429 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__22425,Vvar__1__P__22426,Vvar__2__x__22434) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__22464,Vvar__1__P__22465,Vvar__2__Q__22468,VX22471] :
( cType___24t(Vvar__0__A__22464)
=> ( c_24__type__22488___24t(Vvar__0__A__22464,Vvar__1__P__22465,Vvar__2__Q__22468,Vvar__1__P__22465)
=> ( c_24__type__22496___24t(Vvar__0__A__22464,Vvar__1__P__22465,Vvar__2__Q__22468,Vvar__2__Q__22468)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__22464,Vvar__1__P__22465,Vvar__2__Q__22468,VX22471)
=> ? [Vvar__3__x__22479] :
( t(Vvar__3__x__22479,Vvar__0__A__22464)
& p(happ(Vvar__1__P__22465,Vvar__3__x__22479))
& p(happ(Vvar__2__Q__22468,Vvar__3__x__22479))
& VX22471 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__22464,Vvar__1__P__22465,Vvar__2__Q__22468,Vvar__3__x__22479) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__22520,Vvar__1__P__22521,VX22524] :
( cType___24t(Vvar__0__A__22520)
=> ( c_24__type__22534___24t(Vvar__0__A__22520,Vvar__1__P__22521,Vvar__1__P__22521)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__22520,Vvar__1__P__22521,VX22524)
=> ? [Vvar__2__x__22529] :
( t(Vvar__2__x__22529,Vvar__0__A__22520)
& ? [Vvar__3___24Anonymous__22530] :
( t(Vvar__3___24Anonymous__22530,happ(Vvar__1__P__22521,Vvar__2__x__22529))
& VX22524 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__22520,Vvar__1__P__22521,Vvar__2__x__22529,Vvar__3___24Anonymous__22530) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__22559,Vvar__1__P__22560,Vvar__2__Q__22563,VX22566] :
( cType___24t(Vvar__0__A__22559)
=> ( c_24__type__22583___24t(Vvar__0__A__22559,Vvar__1__P__22560,Vvar__2__Q__22563,Vvar__1__P__22560)
=> ( c_24__type__22591___24t(Vvar__0__A__22559,Vvar__1__P__22560,Vvar__2__Q__22563,Vvar__2__Q__22563)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__22559,Vvar__1__P__22560,Vvar__2__Q__22563,VX22566)
=> ? [Vvar__3__x__22574] :
( t(Vvar__3__x__22574,Vvar__0__A__22559)
& ? [Vvar__4___24Anonymous__22575] :
( t(Vvar__4___24Anonymous__22575,happ(Vvar__1__P__22560,Vvar__3__x__22574))
& ? [Vvar__5___24Anonymous__22576] :
( t(Vvar__5___24Anonymous__22576,happ(Vvar__2__Q__22563,Vvar__3__x__22574))
& VX22566 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__22559,Vvar__1__P__22560,Vvar__2__Q__22563,Vvar__3__x__22574,Vvar__4___24Anonymous__22575,Vvar__5___24Anonymous__22576) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__4485,Vvar__1__B__4486,VX4487] :
( cProp___24t(Vvar__0__A__4485)
=> ( cProp___24t(Vvar__1__B__4486)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__4485,Vvar__1__B__4486,VX4487)
=> ( ( p(Vvar__0__A__4485)
& VX4487 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__4485,Vvar__1__B__4486) )
| ( p(Vvar__1__B__4486)
& VX4487 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__4485,Vvar__1__B__4486) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__22615,Vvar__1__B__22616,VX22617] :
( cType___24t(Vvar__0__A__22615)
=> ( cProp___24t(Vvar__1__B__22616)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__22615,Vvar__1__B__22616,VX22617)
=> ( ? [Vvar__2___24Anonymous__22620] :
( t(Vvar__2___24Anonymous__22620,Vvar__0__A__22615)
& VX22617 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__22615,Vvar__1__B__22616,Vvar__2___24Anonymous__22620) )
| ( p(Vvar__1__B__22616)
& VX22617 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__22615,Vvar__1__B__22616) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__23123,Vvar__1__R__23124,Vvar__2__x__23129] :
( cType___24t(Vvar__0__A__23123)
=> ( c_24__type__23158___24t(Vvar__0__A__23123,Vvar__1__R__23124,Vvar__2__x__23129,Vvar__1__R__23124)
=> ( t(Vvar__2__x__23129,Vvar__0__A__23123)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__23123,Vvar__1__R__23124,Vvar__2__x__23129)
=> ( ! [Vvar__var__var__var__var__3__y__23139__23141__23143__23145__23147] :
( t(Vvar__var__var__var__var__3__y__23139__23141__23143__23145__23147,Vvar__0__A__23123)
=> ( p(happ(happ(Vvar__1__R__23124,Vvar__var__var__var__var__3__y__23139__23141__23143__23145__23147),Vvar__2__x__23129))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__23123,Vvar__1__R__23124,Vvar__var__var__var__var__3__y__23139__23141__23143__23145__23147) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__8459,Vvar__1__a__8460,Vvar__2___24Anonymous__8461,Vvar__3___24Anonymous__8462] :
( cType___24t(Vvar__0__A__8459)
=> ( t(Vvar__1__a__8460,Vvar__0__A__8459)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8459,Vvar__2___24Anonymous__8461)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8459,Vvar__3___24Anonymous__8462)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__8459,Vvar__1__a__8460,Vvar__2___24Anonymous__8461,Vvar__3___24Anonymous__8462)
=> ( ? [Vvar__2__l__8466] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8459,Vvar__2__l__8466)
& Vvar__3___24Anonymous__8462 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8459,Vvar__1__a__8460,Vvar__2__l__8466)
& Vvar__2___24Anonymous__8461 = Vvar__2__l__8466 )
| ? [Vvar__2__x__8469] :
( t(Vvar__2__x__8469,Vvar__0__A__8459)
& ? [Vvar__3__l__8470] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8459,Vvar__3__l__8470)
& ? [Vvar__4__l_27__8471] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8459,Vvar__4__l_27__8471)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__8459,Vvar__1__a__8460,Vvar__3__l__8470,Vvar__4__l_27__8471)
& Vvar__3___24Anonymous__8462 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8459,Vvar__2__x__8469,Vvar__4__l_27__8471)
& Vvar__2___24Anonymous__8461 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8459,Vvar__2__x__8469,Vvar__3__l__8470) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__8482,Vvar__1__P__8483,Vvar__2___24Anonymous__8486] :
( cType___24t(Vvar__0__A__8482)
=> ( c_24__type__8504___24t(Vvar__0__A__8482,Vvar__1__P__8483,Vvar__2___24Anonymous__8486,Vvar__1__P__8483)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8482,Vvar__2___24Anonymous__8486)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__8482,Vvar__1__P__8483,Vvar__2___24Anonymous__8486)
=> ( Vvar__2___24Anonymous__8486 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8482)
| ? [Vvar__2__x__8496] :
( t(Vvar__2__x__8496,Vvar__0__A__8482)
& ? [Vvar__3__l__8497] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8482,Vvar__3__l__8497)
& p(happ(Vvar__1__P__8483,Vvar__2__x__8496))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__8482,Vvar__1__P__8483,Vvar__3__l__8497)
& Vvar__2___24Anonymous__8486 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8482,Vvar__2__x__8496,Vvar__3__l__8497) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__8506,Vvar__1__B__8507,Vvar__2__R__8508,Vvar__3___24Anonymous__8513,Vvar__4___24Anonymous__8514] :
( cType___24t(Vvar__0__A__8506)
=> ( cType___24t(Vvar__1__B__8507)
=> ( c_24__type__8551___24t(Vvar__0__A__8506,Vvar__1__B__8507,Vvar__2__R__8508,Vvar__3___24Anonymous__8513,Vvar__4___24Anonymous__8514,Vvar__2__R__8508)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8506,Vvar__3___24Anonymous__8513)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__8507,Vvar__4___24Anonymous__8514)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__8506,Vvar__1__B__8507,Vvar__2__R__8508,Vvar__3___24Anonymous__8513,Vvar__4___24Anonymous__8514)
=> ( ( Vvar__4___24Anonymous__8514 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__8507)
& Vvar__3___24Anonymous__8513 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8506) )
| ? [Vvar__3__x__8530] :
( t(Vvar__3__x__8530,Vvar__0__A__8506)
& ? [Vvar__4__y__8531] :
( t(Vvar__4__y__8531,Vvar__1__B__8507)
& ? [Vvar__5__l__8532] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8506,Vvar__5__l__8532)
& ? [Vvar__6__l_27__8533] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__8507,Vvar__6__l_27__8533)
& p(happ(happ(Vvar__2__R__8508,Vvar__3__x__8530),Vvar__4__y__8531))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__8506,Vvar__1__B__8507,Vvar__2__R__8508,Vvar__5__l__8532,Vvar__6__l_27__8533)
& Vvar__4___24Anonymous__8514 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__8507,Vvar__4__y__8531,Vvar__6__l_27__8533)
& Vvar__3___24Anonymous__8513 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8506,Vvar__3__x__8530,Vvar__5__l__8532) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__8553,Vvar__1__R__8554,Vvar__2___24Anonymous__8559] :
( cType___24t(Vvar__0__A__8553)
=> ( c_24__type__8586___24t(Vvar__0__A__8553,Vvar__1__R__8554,Vvar__2___24Anonymous__8559,Vvar__1__R__8554)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8553,Vvar__2___24Anonymous__8559)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__8553,Vvar__1__R__8554,Vvar__2___24Anonymous__8559)
=> ( Vvar__2___24Anonymous__8559 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8553)
| ? [Vvar__2__a__8573] :
( t(Vvar__2__a__8573,Vvar__0__A__8553)
& ? [Vvar__3__l__8574] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8553,Vvar__3__l__8574)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__8553,happ(Vvar__1__R__8554,Vvar__2__a__8573),Vvar__3__l__8574)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__8553,Vvar__1__R__8554,Vvar__3__l__8574)
& Vvar__2___24Anonymous__8559 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8553,Vvar__2__a__8573,Vvar__3__l__8574) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__8473,Vvar__1___24Anonymous__8474] :
( cType___24t(Vvar__0__A__8473)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8473,Vvar__1___24Anonymous__8474)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8473,Vvar__1___24Anonymous__8474)
=> ( Vvar__1___24Anonymous__8474 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8473)
| ? [Vvar__1__x__8478] :
( t(Vvar__1__x__8478,Vvar__0__A__8473)
& ? [Vvar__2__l__8479] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8473,Vvar__2__l__8479)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__8473,Vvar__1__x__8478,Vvar__2__l__8479)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8473,Vvar__2__l__8479)
& Vvar__1___24Anonymous__8474 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8473,Vvar__1__x__8478,Vvar__2__l__8479) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2__x__22205,Vvar__3___24Anonymous__22206] :
( cType___24t(Vvar__0__A__22199)
=> ( c_24__type__22239___24t(Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2__x__22205,Vvar__3___24Anonymous__22206,Vvar__1__eqA__22200)
=> ( t(Vvar__2__x__22205,Vvar__0__A__22199)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__3___24Anonymous__22206)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2__x__22205,Vvar__3___24Anonymous__22206)
=> ( ? [Vvar__3__y__22215] :
( t(Vvar__3__y__22215,Vvar__0__A__22199)
& ? [Vvar__4__l__22216] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__4__l__22216)
& p(happ(happ(Vvar__1__eqA__22200,Vvar__2__x__22205),Vvar__3__y__22215))
& Vvar__3___24Anonymous__22206 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22199,Vvar__3__y__22215,Vvar__4__l__22216) ) )
| ? [Vvar__3__y__22225] :
( t(Vvar__3__y__22225,Vvar__0__A__22199)
& ? [Vvar__4__l__22226] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22199,Vvar__4__l__22226)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22199,Vvar__1__eqA__22200,Vvar__2__x__22205,Vvar__4__l__22226)
& Vvar__3___24Anonymous__22206 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22199,Vvar__3__y__22225,Vvar__4__l__22226) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__22241,Vvar__1__eqA__22242,Vvar__2___24Anonymous__22247] :
( cType___24t(Vvar__0__A__22241)
=> ( c_24__type__22274___24t(Vvar__0__A__22241,Vvar__1__eqA__22242,Vvar__2___24Anonymous__22247,Vvar__1__eqA__22242)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22241,Vvar__2___24Anonymous__22247)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__22241,Vvar__1__eqA__22242,Vvar__2___24Anonymous__22247)
=> ( Vvar__2___24Anonymous__22247 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22241)
| ? [Vvar__2__x__22261] :
( t(Vvar__2__x__22261,Vvar__0__A__22241)
& ? [Vvar__3__l__22262] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22241,Vvar__3__l__22262)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__22241,Vvar__1__eqA__22242,Vvar__2__x__22261,Vvar__3__l__22262)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__22241,Vvar__1__eqA__22242,Vvar__3__l__22262)
& Vvar__2___24Anonymous__22247 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22241,Vvar__2__x__22261,Vvar__3__l__22262) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__22276,Vvar__1__eqA__22277,Vvar__2___24Anonymous__22282,Vvar__3___24Anonymous__22283] :
( cType___24t(Vvar__0__A__22276)
=> ( c_24__type__22314___24t(Vvar__0__A__22276,Vvar__1__eqA__22277,Vvar__2___24Anonymous__22282,Vvar__3___24Anonymous__22283,Vvar__1__eqA__22277)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22276,Vvar__2___24Anonymous__22282)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22276,Vvar__3___24Anonymous__22283)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__22276,Vvar__1__eqA__22277,Vvar__2___24Anonymous__22282,Vvar__3___24Anonymous__22283)
=> ( ( Vvar__3___24Anonymous__22283 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22276)
& Vvar__2___24Anonymous__22282 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22276) )
| ? [Vvar__2__x__22297] :
( t(Vvar__2__x__22297,Vvar__0__A__22276)
& ? [Vvar__3__x_27__22298] :
( t(Vvar__3__x_27__22298,Vvar__0__A__22276)
& ? [Vvar__4__l__22299] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22276,Vvar__4__l__22299)
& ? [Vvar__5__l_27__22300] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22276,Vvar__5__l_27__22300)
& p(happ(happ(Vvar__1__eqA__22277,Vvar__2__x__22297),Vvar__3__x_27__22298))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__22276,Vvar__1__eqA__22277,Vvar__4__l__22299,Vvar__5__l_27__22300)
& Vvar__3___24Anonymous__22283 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22276,Vvar__3__x_27__22298,Vvar__5__l_27__22300)
& Vvar__2___24Anonymous__22282 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22276,Vvar__2__x__22297,Vvar__4__l__22299) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.boolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(c_24True) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.has_fixpoint',axiom,
! [Vvar__0__A__5938] :
( cProp___24t(Vvar__0__A__5938)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__5938)
=> ( ( ( p(Vvar__0__A__5938)
=> p(Vvar__0__A__5938) )
=> p(Vvar__0__A__5938) )
& ( ( p(Vvar__0__A__5938)
=> p(Vvar__0__A__5938) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__5914,Vvar__1__B__5915] :
( cProp___24t(Vvar__0__A__5914)
=> ( cProp___24t(Vvar__1__B__5915)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__5914,Vvar__1__B__5915)
=> ( ( p(Vvar__0__A__5914)
=> p(Vvar__1__B__5915) )
& ( p(Vvar__1__B__5915)
=> p(Vvar__0__A__5914) )
& ( p(Vvar__1__B__5915)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__6421,Vvar__1__P__6422,Vvar__2__p__6425,Vvar__3__x__6426,Vvar__4__q__6427,Vvar__5___24Anonymous__6428] :
( cType___24t(Vvar__0__U__6421)
=> ( c_24__type__6443___24t(Vvar__0__U__6421,Vvar__1__P__6422,Vvar__2__p__6425,Vvar__3__x__6426,Vvar__4__q__6427,Vvar__5___24Anonymous__6428,Vvar__1__P__6422)
=> ( t(Vvar__2__p__6425,Vvar__0__U__6421)
=> ( t(Vvar__3__x__6426,happ(Vvar__1__P__6422,Vvar__2__p__6425))
=> ( t(Vvar__4__q__6427,Vvar__0__U__6421)
=> ( t(Vvar__5___24Anonymous__6428,happ(Vvar__1__P__6422,Vvar__4__q__6427))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__6421,Vvar__1__P__6422,Vvar__2__p__6425,Vvar__3__x__6426,Vvar__4__q__6427,Vvar__5___24Anonymous__6428)
=> ( Vvar__5___24Anonymous__6428 = Vvar__3__x__6426
& Vvar__4__q__6427 = Vvar__2__p__6425 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__3974,Vvar__1__P__3975,Vvar__2__p__3978,Vvar__3__x__3979,Vvar__4__q__3980,Vvar__5__y__3981] :
( cType___24t(Vvar__0__U__3974)
=> ( c_24__type__4000___24t(Vvar__0__U__3974,Vvar__1__P__3975,Vvar__2__p__3978,Vvar__3__x__3979,Vvar__4__q__3980,Vvar__5__y__3981,Vvar__1__P__3975)
=> ( t(Vvar__2__p__3978,Vvar__0__U__3974)
=> ( t(Vvar__3__x__3979,happ(Vvar__1__P__3975,Vvar__2__p__3978))
=> ( t(Vvar__4__q__3980,Vvar__0__U__3974)
=> ( t(Vvar__5__y__3981,happ(Vvar__1__P__3975,Vvar__4__q__3980))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__3974,Vvar__1__P__3975,Vvar__2__p__3978,Vvar__3__x__3979,Vvar__4__q__3980,Vvar__5__y__3981)
=> ( Vvar__4__q__3980 = Vvar__2__p__3978
& Vvar__3__x__3979 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__3974,Vvar__4__q__3980,Vvar__1__P__3975,Vvar__5__y__3981,Vvar__2__p__3978)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX373] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX373)
=> ( VX373 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__374] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__374)
& VX373 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__374) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1248] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1248)
=> ( VX1248 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__1249] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1249)
& VX1248 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1249) )
| ? [Vvar__0___24Anonymous__1250] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1250)
& VX1248 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1250) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1195] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1195)
=> ( ? [Vvar__0___24Anonymous__1196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1196)
& VX1195 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1196) )
| ? [Vvar__0___24Anonymous__1197] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1197)
& VX1195 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1197) )
| VX1195 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__23478,VX23479] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23478)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__23478,VX23479)
=> ( ( Vvar__0___24Anonymous__23478 = cCoq_2eNumbers_2eBinNums_2exH
& VX23479 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__23480] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__23480)
& ? [Vvar__1___24Anonymous__23481] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__23480,Vvar__1___24Anonymous__23481)
& Vvar__0___24Anonymous__23478 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2423516___24a2(Vvar__0___24Anonymous__23478,Vvar__0__p__23480)
& VX23479 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__23480,Vvar__1___24Anonymous__23481) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__5509,Vvar__1__q__5510,Vvar__2___24Anonymous__5511] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__5509)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__5510)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__5511)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__5509,Vvar__1__q__5510,Vvar__2___24Anonymous__5511)
=> ( ( Vvar__0__p__5509 = Vvar__1__q__5510
& Vvar__2___24Anonymous__5511 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__5518] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__5518)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__5510,Vvar__2__r__5518) = Vvar__0__p__5509
& Vvar__2___24Anonymous__5511 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__5518) )
| ? [Vvar__2__r__5522] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__5522)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__5509,Vvar__2__r__5522) = Vvar__1__q__5510
& Vvar__2___24Anonymous__5511 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX4977] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX4977)
=> ( VX4977 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__4978] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4978)
& VX4977 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__4978) )
| VX4977 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX4309] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX4309)
=> ? [Vvar__0__Qnum__4310] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__4310)
& ? [Vvar__1__Qden__4311] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__4311)
& VX4309 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__4310,Vvar__1__Qden__4311) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX39528] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX39528)
=> ? [Vvar__0__neg__39529] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__39529)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__39529,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX39528 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__39529) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX39507] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX39507)
=> ? [Vvar__0__nonneg__39508] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__39508)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__39508)
& VX39507 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__39508) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX39521] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX39521)
=> ? [Vvar__0__nonpos__39522] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__39522)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__39522,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX39521 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__39522) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX9918] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX9918)
=> ? [Vvar__0__nonzero__9919] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__9919)
& Vvar__0__nonzero__9919 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX9918 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__9919) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX39514] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX39514)
=> ? [Vvar__0__pos__39515] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__39515)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__39515)
& VX39514 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__39515) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__10108,Vvar__1___24Anonymous__10109,VX10110] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__10108)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__10109)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__10108,Vvar__1___24Anonymous__10109,VX10110)
=> ( ( Vvar__0__x__10108 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__10109 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX10110 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__10108) )
| ? [Vvar__1__n__10114] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__10114)
& Vvar__0__x__10108 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__10114)
& Vvar__1___24Anonymous__10109 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2410134___24a3(Vvar__0__x__10108,Vvar__1___24Anonymous__10109,Vvar__1__n__10114)
& VX10110 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__10108,Vvar__1__n__10114) )
| ? [Vvar__1__n__10119] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__10119)
& Vvar__0__x__10108 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__10119))
& Vvar__1___24Anonymous__10109 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2410151___24a3(Vvar__0__x__10108,Vvar__1___24Anonymous__10109,Vvar__1__n__10119)
& VX10110 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__10108,Vvar__1__n__10119) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__428,Vvar__1__R__429] :
( cType___24t(Vvar__0__A__428)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__428,Vvar__1__R__429)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__428,Vvar__1__R__429)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__428,Vvar__1__R__429)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__428,Vvar__1__R__429)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__57,Vvar__1__R__58] :
( cType___24t(Vvar__0__A__57)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__57,Vvar__1__R__58)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__57,Vvar__1__R__58)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__57,Vvar__1__R__58)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__57,Vvar__1__R__58)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__57,Vvar__1__R__58)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__420,Vvar__1__R__421] :
( cType___24t(Vvar__0__A__420)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__420,Vvar__1__R__421)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__420,Vvar__1__R__421)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__420,Vvar__1__R__421)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__420,Vvar__1__R__421)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__420,Vvar__1__R__421)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__413,Vvar__1__R__414] :
( cType___24t(Vvar__0__A__413)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__413,Vvar__1__R__414)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__413,Vvar__1__R__414)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__413,Vvar__1__R__414)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__413,Vvar__1__R__414)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__548,Vvar__1__R__549,Vvar__2__x__550,Vvar__3___24Anonymous__551] :
( cType___24t(Vvar__0__A__548)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__548,Vvar__1__R__549)
=> ( t(Vvar__2__x__550,Vvar__0__A__548)
=> ( t(Vvar__3___24Anonymous__551,Vvar__0__A__548)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__548,Vvar__1__R__549,Vvar__2__x__550,Vvar__3___24Anonymous__551)
=> ( ? [Vvar__3__y__556] :
( t(Vvar__3__y__556,Vvar__0__A__548)
& p(happ(happ(Vvar__1__R__549,Vvar__2__x__550),Vvar__3__y__556))
& Vvar__3___24Anonymous__551 = Vvar__3__y__556 )
| Vvar__3___24Anonymous__551 = Vvar__2__x__550 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__65,Vvar__1__R__66,Vvar__1___24Anonymous__67,Vvar__2___24Anonymous__68] :
( cType___24t(Vvar__0__A__65)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__65,Vvar__1__R__66)
=> ( t(Vvar__1___24Anonymous__67,Vvar__0__A__65)
=> ( t(Vvar__2___24Anonymous__68,Vvar__0__A__65)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__65,Vvar__1__R__66,Vvar__1___24Anonymous__67,Vvar__2___24Anonymous__68)
=> ( ? [Vvar__2__x__72] :
( t(Vvar__2__x__72,Vvar__0__A__65)
& ? [Vvar__3__y__73] :
( t(Vvar__3__y__73,Vvar__0__A__65)
& p(happ(happ(Vvar__1__R__66,Vvar__2__x__72),Vvar__3__y__73))
& Vvar__2___24Anonymous__68 = Vvar__3__y__73
& Vvar__1___24Anonymous__67 = Vvar__2__x__72 ) )
| ? [Vvar__2__x__77] :
( t(Vvar__2__x__77,Vvar__0__A__65)
& Vvar__2___24Anonymous__68 = Vvar__2__x__77
& Vvar__1___24Anonymous__67 = Vvar__2__x__77 )
| ? [Vvar__2__x__80] :
( t(Vvar__2__x__80,Vvar__0__A__65)
& ? [Vvar__3__y__81] :
( t(Vvar__3__y__81,Vvar__0__A__65)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__65,Vvar__1__R__66,Vvar__2__x__80,Vvar__3__y__81)
& Vvar__2___24Anonymous__68 = Vvar__2__x__80
& Vvar__1___24Anonymous__67 = Vvar__3__y__81 ) )
| ? [Vvar__2__x__85] :
( t(Vvar__2__x__85,Vvar__0__A__65)
& ? [Vvar__3__y__86] :
( t(Vvar__3__y__86,Vvar__0__A__65)
& ? [Vvar__4__z__87] :
( t(Vvar__4__z__87,Vvar__0__A__65)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__65,Vvar__1__R__66,Vvar__2__x__85,Vvar__3__y__86)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__65,Vvar__1__R__66,Vvar__3__y__86,Vvar__4__z__87)
& Vvar__2___24Anonymous__68 = Vvar__4__z__87
& Vvar__1___24Anonymous__67 = Vvar__2__x__85 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__710,Vvar__1__R__711,Vvar__2__x__712,Vvar__3___24Anonymous__713] :
( cType___24t(Vvar__0__A__710)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__710,Vvar__1__R__711)
=> ( t(Vvar__2__x__712,Vvar__0__A__710)
=> ( t(Vvar__3___24Anonymous__713,Vvar__0__A__710)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__710,Vvar__1__R__711,Vvar__2__x__712,Vvar__3___24Anonymous__713)
=> ( Vvar__3___24Anonymous__713 = Vvar__2__x__712
| ? [Vvar__3__y__721] :
( t(Vvar__3__y__721,Vvar__0__A__710)
& ? [Vvar__4__z__722] :
( t(Vvar__4__z__722,Vvar__0__A__710)
& ( p(happ(happ(Vvar__1__R__711,Vvar__2__x__712),Vvar__3__y__721))
| p(happ(happ(Vvar__1__R__711,Vvar__3__y__721),Vvar__2__x__712)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__710,Vvar__1__R__711,Vvar__3__y__721,Vvar__4__z__722)
& Vvar__3___24Anonymous__713 = Vvar__4__z__722 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__745,Vvar__1__R__746,Vvar__2__x__747,Vvar__3___24Anonymous__748] :
( cType___24t(Vvar__0__A__745)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__745,Vvar__1__R__746)
=> ( t(Vvar__2__x__747,Vvar__0__A__745)
=> ( t(Vvar__3___24Anonymous__748,Vvar__0__A__745)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__745,Vvar__1__R__746,Vvar__2__x__747,Vvar__3___24Anonymous__748)
=> ( Vvar__3___24Anonymous__748 = Vvar__2__x__747
| ? [Vvar__3__y__756] :
( t(Vvar__3__y__756,Vvar__0__A__745)
& ? [Vvar__4__z__757] :
( t(Vvar__4__z__757,Vvar__0__A__745)
& ( p(happ(happ(Vvar__1__R__746,Vvar__3__y__756),Vvar__4__z__757))
| p(happ(happ(Vvar__1__R__746,Vvar__4__z__757),Vvar__3__y__756)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__745,Vvar__1__R__746,Vvar__2__x__747,Vvar__3__y__756)
& Vvar__3___24Anonymous__748 = Vvar__4__z__757 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__564,Vvar__1__R__565,Vvar__2__x__566,Vvar__3___24Anonymous__567] :
( cType___24t(Vvar__0__A__564)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__564,Vvar__1__R__565)
=> ( t(Vvar__2__x__566,Vvar__0__A__564)
=> ( t(Vvar__3___24Anonymous__567,Vvar__0__A__564)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__564,Vvar__1__R__565,Vvar__2__x__566,Vvar__3___24Anonymous__567)
=> ( ? [Vvar__3__y__572] :
( t(Vvar__3__y__572,Vvar__0__A__564)
& p(happ(happ(Vvar__1__R__565,Vvar__2__x__566),Vvar__3__y__572))
& Vvar__3___24Anonymous__567 = Vvar__3__y__572 )
| Vvar__3___24Anonymous__567 = Vvar__2__x__566
| ? [Vvar__3__y__580] :
( t(Vvar__3__y__580,Vvar__0__A__564)
& ? [Vvar__4__z__581] :
( t(Vvar__4__z__581,Vvar__0__A__564)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__564,Vvar__1__R__565,Vvar__2__x__566,Vvar__3__y__580)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__564,Vvar__1__R__565,Vvar__3__y__580,Vvar__4__z__581)
& Vvar__3___24Anonymous__567 = Vvar__4__z__581 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__612,Vvar__1__R__613,Vvar__2__x__614,Vvar__3___24Anonymous__615] :
( cType___24t(Vvar__0__A__612)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__612,Vvar__1__R__613)
=> ( t(Vvar__2__x__614,Vvar__0__A__612)
=> ( t(Vvar__3___24Anonymous__615,Vvar__0__A__612)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__612,Vvar__1__R__613,Vvar__2__x__614,Vvar__3___24Anonymous__615)
=> ( Vvar__3___24Anonymous__615 = Vvar__2__x__614
| ? [Vvar__3__y__623] :
( t(Vvar__3__y__623,Vvar__0__A__612)
& ? [Vvar__4__z__624] :
( t(Vvar__4__z__624,Vvar__0__A__612)
& p(happ(happ(Vvar__1__R__613,Vvar__2__x__614),Vvar__3__y__623))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__612,Vvar__1__R__613,Vvar__3__y__623,Vvar__4__z__624)
& Vvar__3___24Anonymous__615 = Vvar__4__z__624 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__647,Vvar__1__R__648,Vvar__2__x__649,Vvar__3___24Anonymous__650] :
( cType___24t(Vvar__0__A__647)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__647,Vvar__1__R__648)
=> ( t(Vvar__2__x__649,Vvar__0__A__647)
=> ( t(Vvar__3___24Anonymous__650,Vvar__0__A__647)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__647,Vvar__1__R__648,Vvar__2__x__649,Vvar__3___24Anonymous__650)
=> ( Vvar__3___24Anonymous__650 = Vvar__2__x__649
| ? [Vvar__3__y__658] :
( t(Vvar__3__y__658,Vvar__0__A__647)
& ? [Vvar__4__z__659] :
( t(Vvar__4__z__659,Vvar__0__A__647)
& p(happ(happ(Vvar__1__R__648,Vvar__3__y__658),Vvar__4__z__659))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__647,Vvar__1__R__648,Vvar__2__x__649,Vvar__3__y__658)
& Vvar__3___24Anonymous__650 = Vvar__4__z__659 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__443,Vvar__1__R__444,Vvar__2__x__445,Vvar__3___24Anonymous__446] :
( cType___24t(Vvar__0__A__443)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__443,Vvar__1__R__444)
=> ( t(Vvar__2__x__445,Vvar__0__A__443)
=> ( t(Vvar__3___24Anonymous__446,Vvar__0__A__443)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__443,Vvar__1__R__444,Vvar__2__x__445,Vvar__3___24Anonymous__446)
=> ( ? [Vvar__3__y__451] :
( t(Vvar__3__y__451,Vvar__0__A__443)
& p(happ(happ(Vvar__1__R__444,Vvar__2__x__445),Vvar__3__y__451))
& Vvar__3___24Anonymous__446 = Vvar__3__y__451 )
| ? [Vvar__3__y__456] :
( t(Vvar__3__y__456,Vvar__0__A__443)
& ? [Vvar__4__z__457] :
( t(Vvar__4__z__457,Vvar__0__A__443)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__443,Vvar__1__R__444,Vvar__2__x__445,Vvar__3__y__456)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__443,Vvar__1__R__444,Vvar__3__y__456,Vvar__4__z__457)
& Vvar__3___24Anonymous__446 = Vvar__4__z__457 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__486,Vvar__1__R__487,Vvar__2__x__488,Vvar__3___24Anonymous__489] :
( cType___24t(Vvar__0__A__486)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__486,Vvar__1__R__487)
=> ( t(Vvar__2__x__488,Vvar__0__A__486)
=> ( t(Vvar__3___24Anonymous__489,Vvar__0__A__486)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__486,Vvar__1__R__487,Vvar__2__x__488,Vvar__3___24Anonymous__489)
=> ( ? [Vvar__3__y__494] :
( t(Vvar__3__y__494,Vvar__0__A__486)
& p(happ(happ(Vvar__1__R__487,Vvar__2__x__488),Vvar__3__y__494))
& Vvar__3___24Anonymous__489 = Vvar__3__y__494 )
| ? [Vvar__3__y__499] :
( t(Vvar__3__y__499,Vvar__0__A__486)
& ? [Vvar__4__z__500] :
( t(Vvar__4__z__500,Vvar__0__A__486)
& p(happ(happ(Vvar__1__R__487,Vvar__2__x__488),Vvar__3__y__499))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__486,Vvar__1__R__487,Vvar__3__y__499,Vvar__4__z__500)
& Vvar__3___24Anonymous__489 = Vvar__4__z__500 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__515,Vvar__1__R__516,Vvar__2__x__517,Vvar__3___24Anonymous__518] :
( cType___24t(Vvar__0__A__515)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__515,Vvar__1__R__516)
=> ( t(Vvar__2__x__517,Vvar__0__A__515)
=> ( t(Vvar__3___24Anonymous__518,Vvar__0__A__515)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__515,Vvar__1__R__516,Vvar__2__x__517,Vvar__3___24Anonymous__518)
=> ( ? [Vvar__3__y__523] :
( t(Vvar__3__y__523,Vvar__0__A__515)
& p(happ(happ(Vvar__1__R__516,Vvar__2__x__517),Vvar__3__y__523))
& Vvar__3___24Anonymous__518 = Vvar__3__y__523 )
| ? [Vvar__3__y__528] :
( t(Vvar__3__y__528,Vvar__0__A__515)
& ? [Vvar__4__z__529] :
( t(Vvar__4__z__529,Vvar__0__A__515)
& p(happ(happ(Vvar__1__R__516,Vvar__3__y__528),Vvar__4__z__529))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__515,Vvar__1__R__516,Vvar__2__x__517,Vvar__3__y__528)
& Vvar__3___24Anonymous__518 = Vvar__4__z__529 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Chain',axiom,
! [Vvar__0__U__39028,VX39029] :
( cType___24t(Vvar__0__U__39028)
=> ( cCoq_2eSets_2eCpo_2eChain___24t(Vvar__0__U__39028,VX39029)
=> ? [Vvar__1__PO__of__chain__39031] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__39028,Vvar__1__PO__of__chain__39031)
& cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vvar__0__U__39028,Vvar__1__PO__of__chain__39031,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__39028,Vvar__1__PO__of__chain__39031))
& VX39029 = cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(Vvar__0__U__39028,Vvar__1__PO__of__chain__39031) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Cpo',axiom,
! [Vvar__0__U__39017,VX39018] :
( cType___24t(Vvar__0__U__39017)
=> ( cCoq_2eSets_2eCpo_2eCpo___24t(Vvar__0__U__39017,VX39018)
=> ? [Vvar__1__PO__of__cpo__39020] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__39017,Vvar__1__PO__of__cpo__39020)
& cCoq_2eSets_2eCpo_2eComplete___24a2(Vvar__0__U__39017,Vvar__1__PO__of__cpo__39020)
& VX39018 = cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(Vvar__0__U__39017,Vvar__1__PO__of__cpo__39020) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Couple',axiom,
! [Vvar__0__U__239,Vvar__1__x__240,Vvar__2__y__241,Vvar__1___24Anonymous__242] :
( cType___24t(Vvar__0__U__239)
=> ( t(Vvar__1__x__240,Vvar__0__U__239)
=> ( t(Vvar__2__y__241,Vvar__0__U__239)
=> ( t(Vvar__1___24Anonymous__242,Vvar__0__U__239)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(Vvar__0__U__239,Vvar__1__x__240,Vvar__2__y__241,Vvar__1___24Anonymous__242)
=> ( Vvar__1___24Anonymous__242 = Vvar__1__x__240
| Vvar__1___24Anonymous__242 = Vvar__2__y__241 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Disjoint',axiom,
! [Vvar__0__U__385,Vvar__1__B__386,Vvar__2__C__387] :
( cType___24t(Vvar__0__U__385)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__385,Vvar__1__B__386)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__385,Vvar__2__C__387)
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(Vvar__0__U__385,Vvar__1__B__386,Vvar__2__C__387)
=> ( ! [Vvar__var__var__var__var__3__x__393__394__395__396__397] :
( t(Vvar__var__var__var__var__3__x__393__394__395__396__397,Vvar__0__U__385)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__385,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__U__385,Vvar__1__B__386,Vvar__2__C__387),Vvar__var__var__var__var__3__x__393__394__395__396__397) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Full_set',axiom,
! [Vvar__0__U__233,Vvar__1___24Anonymous__234] :
( cType___24t(Vvar__0__U__233)
=> ( t(Vvar__1___24Anonymous__234,Vvar__0__U__233)
=> ( cCoq_2eSets_2eEnsembles_2eFull__set___24a2(Vvar__0__U__233,Vvar__1___24Anonymous__234)
=> ? [Vvar__1__x__237] :
( t(Vvar__1__x__237,Vvar__0__U__233)
& Vvar__1___24Anonymous__234 = Vvar__1__x__237 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Inhabited',axiom,
! [Vvar__0__U__157,Vvar__1__B__158] :
( cType___24t(Vvar__0__U__157)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__157,Vvar__1__B__158)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__157,Vvar__1__B__158)
=> ? [Vvar__2__x__162] :
( t(Vvar__2__x__162,Vvar__0__U__157)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__157,Vvar__1__B__158,Vvar__2__x__162)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Singleton',axiom,
! [Vvar__0__U__123,Vvar__1__x__124,Vvar__1___24Anonymous__125] :
( cType___24t(Vvar__0__U__123)
=> ( t(Vvar__1__x__124,Vvar__0__U__123)
=> ( t(Vvar__1___24Anonymous__125,Vvar__0__U__123)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(Vvar__0__U__123,Vvar__1__x__124,Vvar__1___24Anonymous__125)
=> Vvar__1___24Anonymous__125 = Vvar__1__x__124 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Triple',axiom,
! [Vvar__0__U__250,Vvar__1__x__251,Vvar__2__y__252,Vvar__3__z__253,Vvar__1___24Anonymous__254] :
( cType___24t(Vvar__0__U__250)
=> ( t(Vvar__1__x__251,Vvar__0__U__250)
=> ( t(Vvar__2__y__252,Vvar__0__U__250)
=> ( t(Vvar__3__z__253,Vvar__0__U__250)
=> ( t(Vvar__1___24Anonymous__254,Vvar__0__U__250)
=> ( cCoq_2eSets_2eEnsembles_2eTriple___24a5(Vvar__0__U__250,Vvar__1__x__251,Vvar__2__y__252,Vvar__3__z__253,Vvar__1___24Anonymous__254)
=> ( Vvar__1___24Anonymous__254 = Vvar__1__x__251
| Vvar__1___24Anonymous__254 = Vvar__2__y__252
| Vvar__1___24Anonymous__254 = Vvar__3__z__253 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Union',axiom,
! [Vvar__0__U__19,Vvar__1__B__20,Vvar__2__C__21,Vvar__1___24Anonymous__22] :
( cType___24t(Vvar__0__U__19)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__19,Vvar__1__B__20)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__19,Vvar__2__C__21)
=> ( t(Vvar__1___24Anonymous__22,Vvar__0__U__19)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(Vvar__0__U__19,Vvar__1__B__20,Vvar__2__C__21,Vvar__1___24Anonymous__22)
=> ( ? [Vvar__3__x__27] :
( t(Vvar__3__x__27,Vvar__0__U__19)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__19,Vvar__1__B__20,Vvar__3__x__27)
& Vvar__1___24Anonymous__22 = Vvar__3__x__27 )
| ? [Vvar__3__x__32] :
( t(Vvar__3__x__32,Vvar__0__U__19)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__19,Vvar__2__C__21,Vvar__3__x__32)
& Vvar__1___24Anonymous__22 = Vvar__3__x__32 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.cardinal',axiom,
! [Vvar__0__U__277,Vvar__1___24Anonymous__278,Vvar__2___24Anonymous__279] :
( cType___24t(Vvar__0__U__277)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__277,Vvar__1___24Anonymous__278)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__279)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__277,Vvar__1___24Anonymous__278,Vvar__2___24Anonymous__279)
=> ( ( Vvar__2___24Anonymous__279 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__278 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__277) )
| ? [Vvar__1__A__283] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__277,Vvar__1__A__283)
& ? [Vvar__2__n__284] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__284)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__277,Vvar__1__A__283,Vvar__2__n__284)
& ? [Vvar__4__x__286] :
( t(Vvar__4__x__286,Vvar__0__U__277)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__277,Vvar__1__A__283,Vvar__4__x__286)
& Vvar__2___24Anonymous__279 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__284)
& Vvar__1___24Anonymous__278 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__277,Vvar__1__A__283,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__277,Vvar__4__x__286)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Image.Im',axiom,
! [Vvar__0__U__188,Vvar__1__V__189,Vvar__2__X__190,Vvar__3__f__191,Vvar__1___24Anonymous__194] :
( cType___24t(Vvar__0__U__188)
=> ( cType___24t(Vvar__1__V__189)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__188,Vvar__2__X__190)
=> ( c_24__type__214___24t(Vvar__0__U__188,Vvar__1__V__189,Vvar__2__X__190,Vvar__3__f__191,Vvar__1___24Anonymous__194,Vvar__3__f__191)
=> ( t(Vvar__1___24Anonymous__194,Vvar__1__V__189)
=> ( cCoq_2eSets_2eImage_2eIm___24a5(Vvar__0__U__188,Vvar__1__V__189,Vvar__2__X__190,Vvar__3__f__191,Vvar__1___24Anonymous__194)
=> ? [Vvar__4__x__202] :
( t(Vvar__4__x__202,Vvar__0__U__188)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__188,Vvar__2__X__190,Vvar__4__x__202)
& ? [Vvar__6__y__204] :
( t(Vvar__6__y__204,Vvar__1__V__189)
& Vvar__6__y__204 = happ(Vvar__3__f__191,Vvar__4__x__202)
& Vvar__1___24Anonymous__194 = Vvar__6__y__204 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.PO',axiom,
! [Vvar__0__U__4217,VX4218] :
( cType___24t(Vvar__0__U__4217)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__4217,VX4218)
=> ? [Vvar__1__Carrier__of__4220] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__4217,Vvar__1__Carrier__of__4220)
& ? [Vvar__2__Rel__of__4221] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__4217,Vvar__2__Rel__of__4221)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__4217,Vvar__1__Carrier__of__4220)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__4217,Vvar__2__Rel__of__4221)
& VX4218 = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__4217,Vvar__1__Carrier__of__4220,Vvar__2__Rel__of__4221) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.covers',axiom,
! [Vvar__0__U__348,Vvar__1__p__349,Vvar__2__y__350,Vvar__3__x__351] :
( cType___24t(Vvar__0__U__348)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__348,Vvar__1__p__349)
=> ( t(Vvar__2__y__350,Vvar__0__U__348)
=> ( t(Vvar__3__x__351,Vvar__0__U__348)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(Vvar__0__U__348,Vvar__1__p__349,Vvar__2__y__350,Vvar__3__x__351)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__348,Vvar__1__p__349,Vvar__3__x__351,Vvar__2__y__350)
& ~ ? [Vvar__var__var__var__var__var__5__z__359__360__361__362__363__364] :
( t(Vvar__var__var__var__var__var__5__z__359__360__361__362__363__364,Vvar__0__U__348)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__348,Vvar__1__p__349,Vvar__3__x__351,Vvar__var__var__var__var__var__5__z__359__360__361__362__363__364)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__348,Vvar__1__p__349,Vvar__var__var__var__var__var__5__z__359__360__361__362__363__364,Vvar__2__y__350) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__22316,Vvar__1__R__22317,Vvar__2__a__22322,Vvar__3___24Anonymous__22323] :
( cType___24t(Vvar__0__A__22316)
=> ( c_24__type__22353___24t(Vvar__0__A__22316,Vvar__1__R__22317,Vvar__2__a__22322,Vvar__3___24Anonymous__22323,Vvar__1__R__22317)
=> ( t(Vvar__2__a__22322,Vvar__0__A__22316)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22316,Vvar__3___24Anonymous__22323)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__22316,Vvar__1__R__22317,Vvar__2__a__22322,Vvar__3___24Anonymous__22323)
=> ( Vvar__3___24Anonymous__22323 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22316)
| ? [Vvar__3__b__22339] :
( t(Vvar__3__b__22339,Vvar__0__A__22316)
& ? [Vvar__4__l__22340] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22316,Vvar__4__l__22340)
& p(happ(happ(Vvar__1__R__22317,Vvar__2__a__22322),Vvar__3__b__22339))
& Vvar__3___24Anonymous__22323 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22316,Vvar__3__b__22339,Vvar__4__l__22340) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__22355,Vvar__1__R__22356,Vvar__2___24Anonymous__22361] :
( cType___24t(Vvar__0__A__22355)
=> ( c_24__type__22388___24t(Vvar__0__A__22355,Vvar__1__R__22356,Vvar__2___24Anonymous__22361,Vvar__1__R__22356)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22355,Vvar__2___24Anonymous__22361)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__22355,Vvar__1__R__22356,Vvar__2___24Anonymous__22361)
=> ( Vvar__2___24Anonymous__22361 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22355)
| ? [Vvar__2__a__22375] :
( t(Vvar__2__a__22375,Vvar__0__A__22355)
& ? [Vvar__3__l__22376] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22355,Vvar__3__l__22376)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__22355,Vvar__1__R__22356,Vvar__3__l__22376)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__22355,Vvar__1__R__22356,Vvar__2__a__22375,Vvar__3__l__22376)
& Vvar__2___24Anonymous__22361 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22355,Vvar__2__a__22375,Vvar__3__l__22376) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__22390,Vvar__1__R__22391,Vvar__2___24Anonymous__22396] :
( cType___24t(Vvar__0__A__22390)
=> ( c_24__type__22423___24t(Vvar__0__A__22390,Vvar__1__R__22391,Vvar__2___24Anonymous__22396,Vvar__1__R__22391)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22390,Vvar__2___24Anonymous__22396)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__22390,Vvar__1__R__22391,Vvar__2___24Anonymous__22396)
=> ( Vvar__2___24Anonymous__22396 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__22390)
| ? [Vvar__2__a__22410] :
( t(Vvar__2__a__22410,Vvar__0__A__22390)
& ? [Vvar__3__l__22411] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__22390,Vvar__3__l__22411)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__22390,Vvar__1__R__22391,Vvar__3__l__22411)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__22390,happ(Vvar__1__R__22391,Vvar__2__a__22410),Vvar__3__l__22411)
& Vvar__2___24Anonymous__22396 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__22390,Vvar__2__a__22410,Vvar__3__l__22411) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX988] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX988)
=> ? [Vvar__0___24Anonymous__989] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__989)
& ? [Vvar__1___24Anonymous__990] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__990)
& ? [Vvar__2___24Anonymous__991] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__991)
& ? [Vvar__3___24Anonymous__992] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__992)
& ? [Vvar__4___24Anonymous__993] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__993)
& ? [Vvar__5___24Anonymous__994] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__994)
& ? [Vvar__6___24Anonymous__995] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__995)
& ? [Vvar__7___24Anonymous__996] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__996)
& VX988 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__989,Vvar__1___24Anonymous__990,Vvar__2___24Anonymous__991,Vvar__3___24Anonymous__992,Vvar__4___24Anonymous__993,Vvar__5___24Anonymous__994,Vvar__6___24Anonymous__995,Vvar__7___24Anonymous__996) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX22645] :
( cCoq_2eStrings_2eString_2estring___24t(VX22645)
=> ( VX22645 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__22646] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__22646)
& ? [Vvar__1___24Anonymous__22647] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__22647)
& VX22645 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__22646,Vvar__1___24Anonymous__22647) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721,VX9722] :
( cType___24t(Vvar__0__X__9709)
=> ( c_24__type__9782___24t(Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721,Vvar__1__lt__9710)
=> ( c_24__type__9801___24t(Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721,Vvar__2__eq__9715)
=> ( t(Vvar__3__x__9720,Vvar__0__X__9709)
=> ( t(Vvar__4__y__9721,Vvar__0__X__9709)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721,VX9722)
=> ( ( p(happ(happ(Vvar__1__lt__9710,Vvar__3__x__9720),Vvar__4__y__9721))
& VX9722 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721) )
| ( p(happ(happ(Vvar__2__eq__9715,Vvar__3__x__9720),Vvar__4__y__9721))
& VX9722 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721) )
| ( p(happ(happ(Vvar__1__lt__9710,Vvar__4__y__9721),Vvar__3__x__9720))
& VX9722 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__9709,Vvar__1__lt__9710,Vvar__2__eq__9715,Vvar__3__x__9720,Vvar__4__y__9721) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__23564,Vvar__1___24Anonymous__23565] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__23564)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__23565)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__23564,Vvar__1___24Anonymous__23565)
=> ( ? [Vvar__0__a__23567] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__23567)
& ? [Vvar__1__s__23568] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__23568)
& Vvar__1___24Anonymous__23565 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__23567,Vvar__1__s__23568)
& Vvar__0___24Anonymous__23564 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__23569] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__23569)
& ? [Vvar__1__s1__23570] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__23570)
& ? [Vvar__2__s2__23571] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__23571)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__23570,Vvar__2__s2__23571)
& Vvar__1___24Anonymous__23565 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__23569,Vvar__2__s2__23571)
& Vvar__0___24Anonymous__23564 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__23569,Vvar__1__s1__23570) ) ) )
| ? [Vvar__0__a__23573] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__23573)
& ? [Vvar__1__b__23574] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__23574)
& ? [Vvar__2__s1__23575] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__23575)
& ? [Vvar__3__s2__23576] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__23576)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__23573),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__23574))
& Vvar__1___24Anonymous__23565 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__23574,Vvar__3__s2__23576)
& Vvar__0___24Anonymous__23564 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__23573,Vvar__2__s1__23575) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX9901] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX9901)
=> ( VX9901 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX9901 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX9901 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__8288,VX8289] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8288)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__8288,VX8289)
=> ( ? [Vvar__0__n__8290] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__8290)
& Vvar__0___24Anonymous__8288 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__8290)
& VX8289 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__8290) )
| ? [Vvar__0__n__8291] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__8291)
& ? [Vvar__1___24Anonymous__8292] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__8291,Vvar__1___24Anonymous__8292)
& Vvar__0___24Anonymous__8288 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__8291)
& VX8289 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__8291,Vvar__1___24Anonymous__8292) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__23097,Vvar__1___24Anonymous__23098,VX23099] :
( cType___24t(Vvar__0__A__23097)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__23098)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__23097,Vvar__1___24Anonymous__23098,VX23099)
=> ( ( Vvar__1___24Anonymous__23098 = cCoq_2eInit_2eDatatypes_2eO
& VX23099 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__23097) )
| ? [Vvar__1__h__23102] :
( t(Vvar__1__h__23102,Vvar__0__A__23097)
& ? [Vvar__2__n__23103] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__23103)
& ? [Vvar__3___24Anonymous__23104] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__23097,Vvar__2__n__23103,Vvar__3___24Anonymous__23104)
& Vvar__1___24Anonymous__23098 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__23103)
& VX23099 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__23097,Vvar__1__h__23102,Vvar__2__n__23103,Vvar__3___24Anonymous__23104) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__23325,Vvar__1__b__23326,Vvar__2__d__23327] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__23325)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__23326)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__23327)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__23325,Vvar__1__b__23326,Vvar__2__d__23327)
=> ? [Vvar__3__u__23332] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__23332)
& ? [Vvar__4__v__23333] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__23333)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__23332,Vvar__0__a__23325),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__23333,Vvar__1__b__23326)) = Vvar__2__d__23327
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__23300,Vvar__1__b__23301,VX23302] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__23300)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__23301)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__23300,Vvar__1__b__23301,VX23302)
=> ? [Vvar__2__u__23305] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__23305)
& ? [Vvar__3__v__23306] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__23306)
& ? [Vvar__4__d__23307] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__23307)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__23305,Vvar__0__a__23300),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__23306,Vvar__1__b__23301)) = Vvar__4__d__23307
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__23300,Vvar__1__b__23301,Vvar__4__d__23307)
& VX23302 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__23300,Vvar__1__b__23301,Vvar__2__u__23305,Vvar__3__v__23306,Vvar__4__d__23307) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__23272,Vvar__1__b__23273,Vvar__2__g__23274] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__23272)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__23273)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__23274)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__23272,Vvar__1__b__23273,Vvar__2__g__23274)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__23274,Vvar__0__a__23272)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__23274,Vvar__1__b__23273)
& ! [Vvar__var__var__var__var__5__x__23282__23285__23288__23291__23294] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__23282__23285__23288__23291__23294)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__23282__23285__23288__23291__23294,Vvar__0__a__23272)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__23282__23285__23288__23291__23294,Vvar__1__b__23273)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__23282__23285__23288__23291__23294,Vvar__2__g__23274) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__23335] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__23335)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__23335)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__23335))
& ! [Vvar__var__var__2__n__23340__23342__23344] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__23340__23342__23344)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__23340__23342__23344)
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__23340__23342__23344,Vvar__0__p__23335)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__23340__23342__23344,Vvar__0__p__23335) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__23348,Vvar__1__p__23349,VX23350] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__23348)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__23349)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__23348,Vvar__1__p__23349,VX23350)
=> ? [Vvar__2__q__23353] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__23353)
& ? [Vvar__3__r__23354] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__23354)
& Vvar__0__x__23348 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__23353,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__23349)),Vvar__3__r__23354)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__23354)
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__23354,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__23349)))
& VX23350 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__23348,Vvar__1__p__23349,Vvar__2__q__23353,Vvar__3__r__23354) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__33004,Vvar__1__F__33005] :
( cType___24t(Vvar__0__T__33004)
=> ( t(Vvar__1__F__33005,Vvar__0__T__33004)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__33004,Vvar__1__F__33005)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__39070,Vvar__1__F__39071] :
( cType___24t(Vvar__0__T__39070)
=> ( t(Vvar__1__F__39071,Vvar__0__T__39070)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__39070,Vvar__1__F__39071)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX6393] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX6393)
=> ( VX6393 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__6394] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6394)
& ? [Vvar__1___24Anonymous__6395] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__6395)
& VX6393 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__6394,Vvar__1___24Anonymous__6395) ) )
| ? [Vvar__0___24Anonymous__6396] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6396)
& ? [Vvar__1___24Anonymous__6397] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__6397)
& VX6393 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__6396,Vvar__1___24Anonymous__6397) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__6179,VX6180] :
( cType___24t(Vvar__0__C__6179)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,VX6180)
=> ( ? [Vvar__1___24Anonymous__6182] :
( t(Vvar__1___24Anonymous__6182,Vvar__0__C__6179)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__6179,Vvar__1___24Anonymous__6182) )
| ? [Vvar__1___24Anonymous__6184] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6184)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__6179,Vvar__1___24Anonymous__6184) )
| ? [Vvar__1___24Anonymous__6186] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__1___24Anonymous__6186)
& ? [Vvar__2___24Anonymous__6187] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__2___24Anonymous__6187)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__6179,Vvar__1___24Anonymous__6186,Vvar__2___24Anonymous__6187) ) )
| ? [Vvar__1___24Anonymous__6189] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__1___24Anonymous__6189)
& ? [Vvar__2___24Anonymous__6190] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__2___24Anonymous__6190)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__6179,Vvar__1___24Anonymous__6189,Vvar__2___24Anonymous__6190) ) )
| ? [Vvar__1___24Anonymous__6192] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__1___24Anonymous__6192)
& ? [Vvar__2___24Anonymous__6193] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__2___24Anonymous__6193)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__6179,Vvar__1___24Anonymous__6192,Vvar__2___24Anonymous__6193) ) )
| ? [Vvar__1___24Anonymous__6195] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__1___24Anonymous__6195)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__6179,Vvar__1___24Anonymous__6195) )
| ? [Vvar__1___24Anonymous__6197] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__6179,Vvar__1___24Anonymous__6197)
& ? [Vvar__2___24Anonymous__6198] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6198)
& VX6180 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__6179,Vvar__1___24Anonymous__6197,Vvar__2___24Anonymous__6198) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__6343,VX6344] :
( cType___24t(Vvar__0__C__6343)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6343,VX6344)
=> ( ? [Vvar__1___24Anonymous__6346] :
( t(Vvar__1___24Anonymous__6346,Vvar__0__C__6343)
& VX6344 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__6343,Vvar__1___24Anonymous__6346) )
| ? [Vvar__1___24Anonymous__6348] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6348)
& ? [Vvar__2___24Anonymous__6349] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6343,Vvar__2___24Anonymous__6349)
& VX6344 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__6343,Vvar__1___24Anonymous__6348,Vvar__2___24Anonymous__6349) ) )
| ? [Vvar__1___24Anonymous__6351] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6343,Vvar__1___24Anonymous__6351)
& ? [Vvar__2___24Anonymous__6352] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__6352)
& ? [Vvar__3___24Anonymous__6353] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__6343,Vvar__3___24Anonymous__6353)
& VX6344 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__6343,Vvar__1___24Anonymous__6351,Vvar__2___24Anonymous__6352,Vvar__3___24Anonymous__6353) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662] :
( cType___24t(Vvar__0__R__8631)
=> ( t(Vvar__1__rO__8632,Vvar__0__R__8631)
=> ( t(Vvar__2__rI__8633,Vvar__0__R__8631)
=> ( c_24__type__9063___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__3__rplus__8634)
=> ( c_24__type__9164___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__4__rtimes__8639)
=> ( c_24__type__9265___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__5__rminus__8644)
=> ( c_24__type__9355___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__6__ropp__8649)
=> ( c_24__type__9456___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__7__req__8652)
=> ( c_24__type__9557___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__8__rle__8657)
=> ( c_24__type__9658___24t(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662,Vvar__9__rlt__8662)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652,Vvar__8__rle__8657,Vvar__9__rlt__8662)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__8631,Vvar__7__req__8652)
& ! [Vvar__var__var__var__var__11__x1__8706__8712__8817__8823__8829] :
( t(Vvar__var__var__var__var__11__x1__8706__8712__8817__8823__8829,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__12__x2__8707__8713__8818__8824__8830] :
( t(Vvar__var__var__var__var__12__x2__8707__8713__8818__8824__8830,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__11__x1__8706__8712__8817__8823__8829),Vvar__var__var__var__var__12__x2__8707__8713__8818__8824__8830))
=> ! [Vvar__var__var__var__var__14__y1__8708__8714__8819__8825__8831] :
( t(Vvar__var__var__var__var__14__y1__8708__8714__8819__8825__8831,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__15__y2__8709__8715__8820__8826__8832] :
( t(Vvar__var__var__var__var__15__y2__8709__8715__8820__8826__8832,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__14__y1__8708__8714__8819__8825__8831),Vvar__var__var__var__var__15__y2__8709__8715__8820__8826__8832))
=> p(happ(happ(Vvar__7__req__8652,happ(happ(Vvar__3__rplus__8634,Vvar__var__var__var__var__11__x1__8706__8712__8817__8823__8829),Vvar__var__var__var__var__14__y1__8708__8714__8819__8825__8831)),happ(happ(Vvar__3__rplus__8634,Vvar__var__var__var__var__12__x2__8707__8713__8818__8824__8830),Vvar__var__var__var__var__15__y2__8709__8715__8820__8826__8832))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__8719__8725__8835__8841__8847] :
( t(Vvar__var__var__var__var__12__x1__8719__8725__8835__8841__8847,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__13__x2__8720__8726__8836__8842__8848] :
( t(Vvar__var__var__var__var__13__x2__8720__8726__8836__8842__8848,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__12__x1__8719__8725__8835__8841__8847),Vvar__var__var__var__var__13__x2__8720__8726__8836__8842__8848))
=> ! [Vvar__var__var__var__var__15__y1__8721__8727__8837__8843__8849] :
( t(Vvar__var__var__var__var__15__y1__8721__8727__8837__8843__8849,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__16__y2__8722__8728__8838__8844__8850] :
( t(Vvar__var__var__var__var__16__y2__8722__8728__8838__8844__8850,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__15__y1__8721__8727__8837__8843__8849),Vvar__var__var__var__var__16__y2__8722__8728__8838__8844__8850))
=> p(happ(happ(Vvar__7__req__8652,happ(happ(Vvar__4__rtimes__8639,Vvar__var__var__var__var__12__x1__8719__8725__8835__8841__8847),Vvar__var__var__var__var__15__y1__8721__8727__8837__8843__8849)),happ(happ(Vvar__4__rtimes__8639,Vvar__var__var__var__var__13__x2__8720__8726__8836__8842__8848),Vvar__var__var__var__var__16__y2__8722__8728__8838__8844__8850))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__8732__8735__8853__8856__8859] :
( t(Vvar__var__var__var__var__13__x1__8732__8735__8853__8856__8859,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__14__x2__8733__8736__8854__8857__8860] :
( t(Vvar__var__var__var__var__14__x2__8733__8736__8854__8857__8860,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__13__x1__8732__8735__8853__8856__8859),Vvar__var__var__var__var__14__x2__8733__8736__8854__8857__8860))
=> p(happ(happ(Vvar__7__req__8652,happ(Vvar__6__ropp__8649,Vvar__var__var__var__var__13__x1__8732__8735__8853__8856__8859)),happ(Vvar__6__ropp__8649,Vvar__var__var__var__var__14__x2__8733__8736__8854__8857__8860))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__8739__8745__8862__8868__8874] :
( t(Vvar__var__var__var__var__14__x1__8739__8745__8862__8868__8874,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__15__x2__8740__8746__8863__8869__8875] :
( t(Vvar__var__var__var__var__15__x2__8740__8746__8863__8869__8875,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__14__x1__8739__8745__8862__8868__8874),Vvar__var__var__var__var__15__x2__8740__8746__8863__8869__8875))
=> ! [Vvar__var__var__var__var__17__y1__8741__8747__8864__8870__8876] :
( t(Vvar__var__var__var__var__17__y1__8741__8747__8864__8870__8876,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__18__y2__8742__8748__8865__8871__8877] :
( t(Vvar__var__var__var__var__18__y2__8742__8748__8865__8871__8877,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__17__y1__8741__8747__8864__8870__8876),Vvar__var__var__var__var__18__y2__8742__8748__8865__8871__8877))
=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__var__14__x1__8739__8745__8862__8868__8874),Vvar__var__var__var__var__17__y1__8741__8747__8864__8870__8876))
<=> p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__var__15__x2__8740__8746__8863__8869__8875),Vvar__var__var__var__var__18__y2__8742__8748__8865__8871__8877)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__8752__8758__8880__8886__8892] :
( t(Vvar__var__var__var__var__15__x1__8752__8758__8880__8886__8892,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__16__x2__8753__8759__8881__8887__8893] :
( t(Vvar__var__var__var__var__16__x2__8753__8759__8881__8887__8893,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__15__x1__8752__8758__8880__8886__8892),Vvar__var__var__var__var__16__x2__8753__8759__8881__8887__8893))
=> ! [Vvar__var__var__var__var__18__y1__8754__8760__8882__8888__8894] :
( t(Vvar__var__var__var__var__18__y1__8754__8760__8882__8888__8894,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__19__y2__8755__8761__8883__8889__8895] :
( t(Vvar__var__var__var__var__19__y2__8755__8761__8883__8889__8895,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__18__y1__8754__8760__8882__8888__8894),Vvar__var__var__var__var__19__y2__8755__8761__8883__8889__8895))
=> ( p(happ(happ(Vvar__9__rlt__8662,Vvar__var__var__var__var__15__x1__8752__8758__8880__8886__8892),Vvar__var__var__var__var__18__y1__8754__8760__8882__8888__8894))
<=> p(happ(happ(Vvar__9__rlt__8662,Vvar__var__var__var__var__16__x2__8753__8759__8881__8887__8893),Vvar__var__var__var__var__19__y2__8755__8761__8883__8889__8895)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__8631,Vvar__1__rO__8632,Vvar__2__rI__8633,Vvar__3__rplus__8634,Vvar__4__rtimes__8639,Vvar__5__rminus__8644,Vvar__6__ropp__8649,Vvar__7__req__8652)
& ! [Vvar__var__var__var__17__n__8766__8767__8898__8899] :
( t(Vvar__var__var__var__17__n__8766__8767__8898__8899,Vvar__0__R__8631)
=> p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__17__n__8766__8767__8898__8899),Vvar__var__var__var__17__n__8766__8767__8898__8899)) )
& ! [Vvar__var__var__var__var__18__n__8769__8773__8900__8904__8908] :
( t(Vvar__var__var__var__var__18__n__8769__8773__8900__8904__8908,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__19__m__8770__8774__8901__8905__8909] :
( t(Vvar__var__var__var__var__19__m__8770__8774__8901__8905__8909,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__var__18__n__8769__8773__8900__8904__8908),Vvar__var__var__var__var__19__m__8770__8774__8901__8905__8909))
=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__var__19__m__8770__8774__8901__8905__8909),Vvar__var__var__var__var__18__n__8769__8773__8900__8904__8908))
=> p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__18__n__8769__8773__8900__8904__8908),Vvar__var__var__var__var__19__m__8770__8774__8901__8905__8909)) ) ) ) )
& ! [Vvar__var__var__var__19__n__8778__8783__8912__8917] :
( t(Vvar__var__var__var__19__n__8778__8783__8912__8917,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__20__m__8779__8784__8913__8918] :
( t(Vvar__var__var__var__20__m__8779__8784__8913__8918,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__21__p__8780__8785__8914__8919] :
( t(Vvar__var__var__var__21__p__8780__8785__8914__8919,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__19__n__8778__8783__8912__8917),Vvar__var__var__var__20__m__8779__8784__8913__8918))
=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__20__m__8779__8784__8913__8918),Vvar__var__var__var__21__p__8780__8785__8914__8919))
=> p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__19__n__8778__8783__8912__8917),Vvar__var__var__var__21__p__8780__8785__8914__8919)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__8789__8791__8922__8924__8926__8928] :
( t(Vvar__var__var__var__var__var__20__n__8789__8791__8922__8924__8926__8928,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__var__21__m__8790__8792__8923__8925__8927__8929] :
( t(Vvar__var__var__var__var__var__21__m__8790__8792__8923__8925__8927__8929,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__9__rlt__8662,Vvar__var__var__var__var__var__20__n__8789__8791__8922__8924__8926__8928),Vvar__var__var__var__var__var__21__m__8790__8792__8923__8925__8927__8929))
<=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__var__var__20__n__8789__8791__8922__8924__8926__8928),Vvar__var__var__var__var__var__21__m__8790__8792__8923__8925__8927__8929))
& ~ p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__var__20__n__8789__8791__8922__8924__8926__8928),Vvar__var__var__var__var__var__21__m__8790__8792__8923__8925__8927__8929)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__8794__8796__8930__8932__8934] :
( t(Vvar__var__var__var__var__21__n__8794__8796__8930__8932__8934,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__22__m__8795__8797__8931__8933__8935] :
( t(Vvar__var__var__var__var__22__m__8795__8797__8931__8933__8935,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__9__rlt__8662,Vvar__var__var__var__var__21__n__8794__8796__8930__8932__8934),Vvar__var__var__var__var__22__m__8795__8797__8931__8933__8935))
| p(happ(happ(Vvar__7__req__8652,Vvar__var__var__var__var__21__n__8794__8796__8930__8932__8934),Vvar__var__var__var__var__22__m__8795__8797__8931__8933__8935))
| p(happ(happ(Vvar__9__rlt__8662,Vvar__var__var__var__var__22__m__8795__8797__8931__8933__8935),Vvar__var__var__var__var__21__n__8794__8796__8930__8932__8934)) ) ) )
& ! [Vvar__var__var__var__var__22__n__8799__8803__8936__8940__8944] :
( t(Vvar__var__var__var__var__22__n__8799__8803__8936__8940__8944,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__23__m__8800__8804__8937__8941__8945] :
( t(Vvar__var__var__var__var__23__m__8800__8804__8937__8941__8945,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__24__p__8801__8805__8938__8942__8946] :
( t(Vvar__var__var__var__var__24__p__8801__8805__8938__8942__8946,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__8__rle__8657,Vvar__var__var__var__var__22__n__8799__8803__8936__8940__8944),Vvar__var__var__var__var__23__m__8800__8804__8937__8941__8945))
=> p(happ(happ(Vvar__8__rle__8657,happ(happ(Vvar__3__rplus__8634,Vvar__var__var__var__var__24__p__8801__8805__8938__8942__8946),Vvar__var__var__var__var__22__n__8799__8803__8936__8940__8944)),happ(happ(Vvar__3__rplus__8634,Vvar__var__var__var__var__24__p__8801__8805__8938__8942__8946),Vvar__var__var__var__var__23__m__8800__8804__8937__8941__8945))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__8808__8812__8948__8952__8956__8960] :
( t(Vvar__var__var__var__var__var__23__n__8808__8812__8948__8952__8956__8960,Vvar__0__R__8631)
=> ! [Vvar__var__var__var__var__var__24__m__8809__8813__8949__8953__8957__8961] :
( t(Vvar__var__var__var__var__var__24__m__8809__8813__8949__8953__8957__8961,Vvar__0__R__8631)
=> ( p(happ(happ(Vvar__9__rlt__8662,Vvar__1__rO__8632),Vvar__var__var__var__var__var__23__n__8808__8812__8948__8952__8956__8960))
=> ( p(happ(happ(Vvar__9__rlt__8662,Vvar__1__rO__8632),Vvar__var__var__var__var__var__24__m__8809__8813__8949__8953__8957__8961))
=> p(happ(happ(Vvar__9__rlt__8662,Vvar__1__rO__8632),happ(happ(Vvar__4__rtimes__8639,Vvar__var__var__var__var__var__23__n__8808__8812__8948__8952__8956__8960),Vvar__var__var__var__var__var__24__m__8809__8813__8949__8953__8957__8961))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__8652,Vvar__1__rO__8632),Vvar__2__rI__8633))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX9925] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX9925)
=> ( VX9925 = cCoq_2emicromega_2eRMicromega_2eC0
| VX9925 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__9926] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__9926)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__9926) )
| ? [Vvar__0__r__9927] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__9927)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__9927) )
| ? [Vvar__0__r1__9928] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9928)
& ? [Vvar__1__r2__9929] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__9929)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__9928,Vvar__1__r2__9929) ) )
| ? [Vvar__0__r1__9930] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9930)
& ? [Vvar__1__r2__9931] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__9931)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__9930,Vvar__1__r2__9931) ) )
| ? [Vvar__0__r1__9932] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9932)
& ? [Vvar__1__r2__9933] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__9933)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__9932,Vvar__1__r2__9933) ) )
| ? [Vvar__0__r1__9934] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__9934)
& ? [Vvar__1__z__9935] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__9935)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__9934,Vvar__1__z__9935) ) )
| ? [Vvar__0__r__9936] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__9936)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__9936) )
| ? [Vvar__0__r__9937] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__9937)
& VX9925 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__9937) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__15638,VX15639] :
( cType___24t(Vvar__0__T__15638)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__15638,VX15639)
=> ? [Vvar__1__Flhs__15641] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__15638,Vvar__1__Flhs__15641)
& ? [Vvar__2__Fop__15642] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__15642)
& ? [Vvar__3__Frhs__15643] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__15638,Vvar__3__Frhs__15643)
& VX15639 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__15638,Vvar__1__Flhs__15641,Vvar__2__Fop__15642,Vvar__3__Frhs__15643) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX15490] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX15490)
=> ( VX15490 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX15490 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX15490 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX15490 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX15637] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX15637)
=> ( VX15637 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX15637 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX15637 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX15637 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX15637 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX15637 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__15491,VX15492] :
( cType___24t(Vvar__0__C__15491)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15491,VX15492)
=> ( ? [Vvar__1___24Anonymous__15494] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__15494)
& VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__15491,Vvar__1___24Anonymous__15494) )
| ? [Vvar__1___24Anonymous__15496] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__15491,Vvar__1___24Anonymous__15496)
& VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__15491,Vvar__1___24Anonymous__15496) )
| ? [Vvar__1___24Anonymous__15498] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__15491,Vvar__1___24Anonymous__15498)
& ? [Vvar__2___24Anonymous__15499] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15491,Vvar__2___24Anonymous__15499)
& VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__15491,Vvar__1___24Anonymous__15498,Vvar__2___24Anonymous__15499) ) )
| ? [Vvar__1___24Anonymous__15501] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15491,Vvar__1___24Anonymous__15501)
& ? [Vvar__2___24Anonymous__15502] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15491,Vvar__2___24Anonymous__15502)
& VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__15491,Vvar__1___24Anonymous__15501,Vvar__2___24Anonymous__15502) ) )
| ? [Vvar__1___24Anonymous__15504] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15491,Vvar__1___24Anonymous__15504)
& ? [Vvar__2___24Anonymous__15505] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__15491,Vvar__2___24Anonymous__15505)
& VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__15491,Vvar__1___24Anonymous__15504,Vvar__2___24Anonymous__15505) ) )
| ? [Vvar__1___24Anonymous__15507] :
( t(Vvar__1___24Anonymous__15507,Vvar__0__C__15491)
& VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__15491,Vvar__1___24Anonymous__15507) )
| VX15492 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__15491) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266] :
( cType___24t(Vvar__0__R__10197)
=> ( t(Vvar__1__rO__10198,Vvar__0__R__10197)
=> ( t(Vvar__2__rI__10199,Vvar__0__R__10197)
=> ( c_24__type__10730___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__3__rplus__10200)
=> ( c_24__type__11076___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__4__rtimes__10205)
=> ( c_24__type__11422___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__5__rminus__10210)
=> ( c_24__type__11745___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__6__ropp__10215)
=> ( c_24__type__12091___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__7__req__10218)
=> ( c_24__type__12437___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__8__rle__10223)
=> ( cType___24t(Vvar__9__C__10228)
=> ( t(Vvar__10__cO__10229,Vvar__9__C__10228)
=> ( t(Vvar__11__cI__10230,Vvar__9__C__10228)
=> ( c_24__type__12783___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__12__cplus__10231)
=> ( c_24__type__13129___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__13__ctimes__10236)
=> ( c_24__type__13475___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__14__cminus__10241)
=> ( c_24__type__13798___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__15__copp__10246)
=> ( c_24__type__14144___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__16__ceqb__10249)
=> ( c_24__type__14490___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__17__cleb__10254)
=> ( c_24__type__14813___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__18__phi__10259)
=> ( cType___24t(Vvar__19__E__10262)
=> ( c_24__type__15136___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__20__pow__phi__10263)
=> ( c_24__type__15482___24t(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266,Vvar__21__rpow__10266)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__8__rle__10223,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__17__cleb__10254,Vvar__18__phi__10259,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__10197,Vvar__1__rO__10198,Vvar__2__rI__10199,Vvar__3__rplus__10200,Vvar__4__rtimes__10205,Vvar__5__rminus__10210,Vvar__6__ropp__10215,Vvar__7__req__10218,Vvar__9__C__10228,Vvar__10__cO__10229,Vvar__11__cI__10230,Vvar__12__cplus__10231,Vvar__13__ctimes__10236,Vvar__14__cminus__10241,Vvar__15__copp__10246,Vvar__16__ceqb__10249,Vvar__18__phi__10259)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__10197,Vvar__2__rI__10199,Vvar__4__rtimes__10205,Vvar__7__req__10218,Vvar__19__E__10262,Vvar__20__pow__phi__10263,Vvar__21__rpow__10266)
& ! [Vvar__var__var__var__var__var__24__x__10349__10352__10362__10365__10368__10371] :
( t(Vvar__var__var__var__var__var__24__x__10349__10352__10362__10365__10368__10371,Vvar__9__C__10228)
=> ! [Vvar__var__var__var__var__var__25__y__10350__10353__10363__10366__10369__10372] :
( t(Vvar__var__var__var__var__var__25__y__10350__10353__10363__10366__10369__10372,Vvar__9__C__10228)
=> ( happ(happ(Vvar__16__ceqb__10249,Vvar__var__var__var__var__var__24__x__10349__10352__10362__10365__10368__10371),Vvar__var__var__var__var__var__25__y__10350__10353__10363__10366__10369__10372) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__10218,happ(Vvar__18__phi__10259,Vvar__var__var__var__var__var__24__x__10349__10352__10362__10365__10368__10371)),happ(Vvar__18__phi__10259,Vvar__var__var__var__var__var__25__y__10350__10353__10363__10366__10369__10372))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__10356__10359__10374__10377__10380__10383] :
( t(Vvar__var__var__var__var__var__25__x__10356__10359__10374__10377__10380__10383,Vvar__9__C__10228)
=> ! [Vvar__var__var__var__var__var__26__y__10357__10360__10375__10378__10381__10384] :
( t(Vvar__var__var__var__var__var__26__y__10357__10360__10375__10378__10381__10384,Vvar__9__C__10228)
=> ( happ(happ(Vvar__17__cleb__10254,Vvar__var__var__var__var__var__25__x__10356__10359__10374__10377__10380__10383),Vvar__var__var__var__var__var__26__y__10357__10360__10375__10378__10381__10384) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__10223,happ(Vvar__18__phi__10259,Vvar__var__var__var__var__var__25__x__10356__10359__10374__10377__10380__10383)),happ(Vvar__18__phi__10259,Vvar__var__var__var__var__var__26__y__10357__10360__10375__10378__10381__10384))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,VX22658] :
( cType___24t(Vvar__0__TA__22654)
=> ( cType___24t(Vvar__1__TX__22655)
=> ( cType___24t(Vvar__2__AA__22656)
=> ( cType___24t(Vvar__3__AF__22657)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,VX22658)
=> ( VX22658 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657)
| VX22658 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657)
| ? [Vvar__4___24Anonymous__22671] :
( t(Vvar__4___24Anonymous__22671,Vvar__1__TX__22655)
& VX22658 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22671) )
| ? [Vvar__4___24Anonymous__22676] :
( t(Vvar__4___24Anonymous__22676,Vvar__0__TA__22654)
& ? [Vvar__5___24Anonymous__22677] :
( t(Vvar__5___24Anonymous__22677,Vvar__2__AA__22656)
& VX22658 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22676,Vvar__5___24Anonymous__22677) ) )
| ? [Vvar__4___24Anonymous__22682] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22682)
& ? [Vvar__5___24Anonymous__22683] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__5___24Anonymous__22683)
& VX22658 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22682,Vvar__5___24Anonymous__22683) ) )
| ? [Vvar__4___24Anonymous__22688] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22688)
& ? [Vvar__5___24Anonymous__22689] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__5___24Anonymous__22689)
& VX22658 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22688,Vvar__5___24Anonymous__22689) ) )
| ? [Vvar__4___24Anonymous__22694] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22694)
& VX22658 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22694) )
| ? [Vvar__4___24Anonymous__22699] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22699)
& ? [Vvar__5___24Anonymous__22700] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__22657,Vvar__5___24Anonymous__22700)
& ? [Vvar__6___24Anonymous__22701] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__6___24Anonymous__22701)
& VX22658 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__22654,Vvar__1__TX__22655,Vvar__2__AA__22656,Vvar__3__AF__22657,Vvar__4___24Anonymous__22699,Vvar__5___24Anonymous__22700,Vvar__6___24Anonymous__22701) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__37280,VX37281] :
( cType___24t(Vvar__0__A__37280)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__37280,VX37281)
=> ( VX37281 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37280)
| ? [Vvar__1___24Anonymous__37284] :
( t(Vvar__1___24Anonymous__37284,Vvar__0__A__37280)
& VX37281 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37280,Vvar__1___24Anonymous__37284) )
| ? [Vvar__1___24Anonymous__37286] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__37280,Vvar__1___24Anonymous__37286)
& ? [Vvar__2___24Anonymous__37287] :
( t(Vvar__2___24Anonymous__37287,Vvar__0__A__37280)
& ? [Vvar__3___24Anonymous__37288] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__37280,Vvar__3___24Anonymous__37288)
& VX37281 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__37280,Vvar__1___24Anonymous__37286,Vvar__2___24Anonymous__37287,Vvar__3___24Anonymous__37288) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__40240] :
( cProp___24t(Vvar__0___24Anonymous__40240)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__40240)
=> ( ? [Vvar__0__P__40242] :
( cProp___24t(Vvar__0__P__40242)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__40242)
& Vvar__0___24Anonymous__40240 = Vvar__0__P__40242 )
| ? [Vvar__0__s__40244] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__40244)
& Vvar__0___24Anonymous__40240 = c_24__prop__40253___24a2(Vvar__0___24Anonymous__40240,Vvar__0__s__40244) )
| ? [Vvar__0__s1__40246] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__40246)
& ? [Vvar__1__s2__40247] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__40247)
& Vvar__0___24Anonymous__40240 = c_24__prop__40254___24a3(Vvar__0___24Anonymous__40240,Vvar__0__s1__40246,Vvar__1__s2__40247) ) )
| ? [Vvar__0__s1__40250] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__40250)
& ? [Vvar__1__s2__40251] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__40251)
& Vvar__0___24Anonymous__40240 = c_24__prop__40255___24a3(Vvar__0___24Anonymous__40240,Vvar__0__s1__40250,Vvar__1__s2__40251) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__23388] :
( cProp___24t(Vvar__0___24Anonymous__23388)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__23388)
=> ( ? [Vvar__0__S__23390] :
( cType___24t(Vvar__0__S__23390)
& ? [Vvar__1__x__23391] :
( t(Vvar__1__x__23391,Vvar__0__S__23390)
& ? [Vvar__2__y__23392] :
( t(Vvar__2__y__23392,Vvar__0__S__23390)
& Vvar__0___24Anonymous__23388 = c_24__prop__23412___24a4(Vvar__0___24Anonymous__23388,Vvar__0__S__23390,Vvar__1__x__23391,Vvar__2__y__23392) ) ) )
| ? [Vvar__0__x__23393] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__23393)
& ? [Vvar__1__y__23394] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__23394)
& Vvar__0___24Anonymous__23388 = c_24__prop__23413___24a3(Vvar__0___24Anonymous__23388,Vvar__0__x__23393,Vvar__1__y__23394) ) )
| ? [Vvar__0__x__23395] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__23395)
& ? [Vvar__1__s__23396] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__23396)
& Vvar__0___24Anonymous__23388 = c_24__prop__23414___24a3(Vvar__0___24Anonymous__23388,Vvar__0__x__23395,Vvar__1__s__23396) ) )
| Vvar__0___24Anonymous__23388 = c_24True
| Vvar__0___24Anonymous__23388 = c_24False
| ? [Vvar__0__P__23397] :
( cProp___24t(Vvar__0__P__23397)
& ? [Vvar__1__Q__23398] :
( cProp___24t(Vvar__1__Q__23398)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__23397)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__23398)
& Vvar__0___24Anonymous__23388 = c_24__prop__23415___24a3(Vvar__0___24Anonymous__23388,Vvar__0__P__23397,Vvar__1__Q__23398) ) )
| ? [Vvar__0__P__23401] :
( cProp___24t(Vvar__0__P__23401)
& ? [Vvar__1__Q__23402] :
( cProp___24t(Vvar__1__Q__23402)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__23401)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__23402)
& Vvar__0___24Anonymous__23388 = c_24__prop__23416___24a3(Vvar__0___24Anonymous__23388,Vvar__0__P__23401,Vvar__1__Q__23402) ) )
| ? [Vvar__0__P__23405] :
( cProp___24t(Vvar__0__P__23405)
& ? [Vvar__1__Q__23406] :
( cProp___24t(Vvar__1__Q__23406)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__23405)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__23406)
& Vvar__0___24Anonymous__23388 = c_24__prop__23417___24a3(Vvar__0___24Anonymous__23388,Vvar__0__P__23405,Vvar__1__Q__23406) ) )
| ? [Vvar__0__P__23410] :
( cProp___24t(Vvar__0__P__23410)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__23410)
& Vvar__0___24Anonymous__23388 = c_24__prop__23418___24a2(Vvar__0___24Anonymous__23388,Vvar__0__P__23410) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX23162] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX23162)
=> ( VX23162 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__23163] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__23163)
& ? [Vvar__1___24Anonymous__23164] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__23164)
& VX23162 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__23163,Vvar__1___24Anonymous__23164) ) )
| ? [Vvar__0___24Anonymous__23165] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__23165)
& ? [Vvar__1___24Anonymous__23166] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__23166)
& VX23162 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__23165,Vvar__1___24Anonymous__23166) ) )
| ? [Vvar__0___24Anonymous__23167] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__23167)
& ? [Vvar__1___24Anonymous__23168] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__23168)
& ? [Vvar__2___24Anonymous__23169] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__23169)
& VX23162 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__23167,Vvar__1___24Anonymous__23168,Vvar__2___24Anonymous__23169) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__23205,Vvar__1__env__23206,Vvar__2__env_27__23209,Vvar__3__x__23212] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__23205)
=> ( c_24__type__23233___24t(Vvar__0__fr__23205,Vvar__1__env__23206,Vvar__2__env_27__23209,Vvar__3__x__23212,Vvar__1__env__23206)
=> ( c_24__type__23242___24t(Vvar__0__fr__23205,Vvar__1__env__23206,Vvar__2__env_27__23209,Vvar__3__x__23212,Vvar__2__env_27__23209)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__23212)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__23205,Vvar__1__env__23206,Vvar__2__env_27__23209,Vvar__3__x__23212)
=> ( happ(Vvar__1__env__23206,Vvar__3__x__23212) = happ(Vvar__2__env_27__23209,Vvar__3__x__23212)
& happ(Vvar__1__env__23206,Vvar__3__x__23212) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__23209,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__23205,Vvar__3__x__23212))),happ(Vvar__2__env_27__23209,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__23205,Vvar__3__x__23212))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__23209,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__23205,Vvar__3__x__23212))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__23209,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__23205,Vvar__3__x__23212))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__7197,VX7198] :
( cType___24t(Vvar__0__C__7197)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,VX7198)
=> ( VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__7197)
| VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__7197)
| ? [Vvar__1___24Anonymous__7202] :
( t(Vvar__1___24Anonymous__7202,Vvar__0__C__7197)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__7197,Vvar__1___24Anonymous__7202) )
| ? [Vvar__1___24Anonymous__7204] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__7204)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__7197,Vvar__1___24Anonymous__7204) )
| ? [Vvar__1___24Anonymous__7206] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7206)
& ? [Vvar__2___24Anonymous__7207] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__2___24Anonymous__7207)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__7197,Vvar__1___24Anonymous__7206,Vvar__2___24Anonymous__7207) ) )
| ? [Vvar__1___24Anonymous__7209] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7209)
& ? [Vvar__2___24Anonymous__7210] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__2___24Anonymous__7210)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__7197,Vvar__1___24Anonymous__7209,Vvar__2___24Anonymous__7210) ) )
| ? [Vvar__1___24Anonymous__7212] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7212)
& ? [Vvar__2___24Anonymous__7213] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__2___24Anonymous__7213)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__7197,Vvar__1___24Anonymous__7212,Vvar__2___24Anonymous__7213) ) )
| ? [Vvar__1___24Anonymous__7215] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7215)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__7197,Vvar__1___24Anonymous__7215) )
| ? [Vvar__1___24Anonymous__7217] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7217)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__7197,Vvar__1___24Anonymous__7217) )
| ? [Vvar__1___24Anonymous__7219] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7219)
& ? [Vvar__2___24Anonymous__7220] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__2___24Anonymous__7220)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__7197,Vvar__1___24Anonymous__7219,Vvar__2___24Anonymous__7220) ) )
| ? [Vvar__1___24Anonymous__7222] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__7197,Vvar__1___24Anonymous__7222)
& ? [Vvar__2___24Anonymous__7223] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__7223)
& VX7198 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__7197,Vvar__1___24Anonymous__7222,Vvar__2___24Anonymous__7223) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490] :
( cType___24t(Vvar__0__R__6461)
=> ( t(Vvar__1__rO__6462,Vvar__0__R__6461)
=> ( t(Vvar__2__rI__6463,Vvar__0__R__6461)
=> ( c_24__type__6655___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__3__radd__6464)
=> ( c_24__type__6748___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__4__rmul__6469)
=> ( c_24__type__6841___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__5__rsub__6474)
=> ( c_24__type__6923___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__6__ropp__6479)
=> ( c_24__type__7016___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__7__rdiv__6482)
=> ( c_24__type__7098___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__8__rinv__6487)
=> ( c_24__type__7191___24t(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490,Vvar__9__req__6490)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__7__rdiv__6482,Vvar__8__rinv__6487,Vvar__9__req__6490)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__6461,Vvar__1__rO__6462,Vvar__2__rI__6463,Vvar__3__radd__6464,Vvar__4__rmul__6469,Vvar__5__rsub__6474,Vvar__6__ropp__6479,Vvar__9__req__6490)
& ~ p(happ(happ(Vvar__9__req__6490,Vvar__2__rI__6463),Vvar__1__rO__6462))
& ! [Vvar__var__var__var__var__var__var__12__p__6533__6535__6542__6544__6546__6548__6550] :
( t(Vvar__var__var__var__var__var__var__12__p__6533__6535__6542__6544__6546__6548__6550,Vvar__0__R__6461)
=> ! [Vvar__var__var__var__var__var__var__13__q__6534__6536__6543__6545__6547__6549__6551] :
( t(Vvar__var__var__var__var__var__var__13__q__6534__6536__6543__6545__6547__6549__6551,Vvar__0__R__6461)
=> p(happ(happ(Vvar__9__req__6490,happ(happ(Vvar__7__rdiv__6482,Vvar__var__var__var__var__var__var__12__p__6533__6535__6542__6544__6546__6548__6550),Vvar__var__var__var__var__var__var__13__q__6534__6536__6543__6545__6547__6549__6551)),happ(happ(Vvar__4__rmul__6469,Vvar__var__var__var__var__var__var__12__p__6533__6535__6542__6544__6546__6548__6550),happ(Vvar__8__rinv__6487,Vvar__var__var__var__var__var__var__13__q__6534__6536__6543__6545__6547__6549__6551)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__6538__6540__6552__6554__6556__6558__6560__6562] :
( t(Vvar__var__var__var__var__var__var__var__13__p__6538__6540__6552__6554__6556__6558__6560__6562,Vvar__0__R__6461)
=> ( ~ p(happ(happ(Vvar__9__req__6490,Vvar__var__var__var__var__var__var__var__13__p__6538__6540__6552__6554__6556__6558__6560__6562),Vvar__1__rO__6462))
=> p(happ(happ(Vvar__9__req__6490,happ(happ(Vvar__4__rmul__6469,happ(Vvar__8__rinv__6487,Vvar__var__var__var__var__var__var__var__13__p__6538__6540__6552__6554__6556__6558__6560__6562)),Vvar__var__var__var__var__var__var__var__13__p__6538__6540__6552__6554__6556__6558__6560__6562)),Vvar__2__rI__6463)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581] :
( cType___24t(Vvar__0__R__7552)
=> ( t(Vvar__1__rO__7553,Vvar__0__R__7552)
=> ( t(Vvar__2__rI__7554,Vvar__0__R__7552)
=> ( c_24__type__7746___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__3__radd__7555)
=> ( c_24__type__7839___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__4__rmul__7560)
=> ( c_24__type__7932___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__5__rsub__7565)
=> ( c_24__type__8014___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__6__ropp__7570)
=> ( c_24__type__8107___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__7__rdiv__7573)
=> ( c_24__type__8189___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__8__rinv__7578)
=> ( c_24__type__8282___24t(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581,Vvar__9__req__7581)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__7__rdiv__7573,Vvar__8__rinv__7578,Vvar__9__req__7581)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__7552,Vvar__1__rO__7553,Vvar__2__rI__7554,Vvar__3__radd__7555,Vvar__4__rmul__7560,Vvar__5__rsub__7565,Vvar__6__ropp__7570,Vvar__9__req__7581)
& ~ p(happ(happ(Vvar__9__req__7581,Vvar__2__rI__7554),Vvar__1__rO__7553))
& ! [Vvar__var__var__var__var__var__var__12__p__7624__7626__7633__7635__7637__7639__7641] :
( t(Vvar__var__var__var__var__var__var__12__p__7624__7626__7633__7635__7637__7639__7641,Vvar__0__R__7552)
=> ! [Vvar__var__var__var__var__var__var__13__q__7625__7627__7634__7636__7638__7640__7642] :
( t(Vvar__var__var__var__var__var__var__13__q__7625__7627__7634__7636__7638__7640__7642,Vvar__0__R__7552)
=> p(happ(happ(Vvar__9__req__7581,happ(happ(Vvar__7__rdiv__7573,Vvar__var__var__var__var__var__var__12__p__7624__7626__7633__7635__7637__7639__7641),Vvar__var__var__var__var__var__var__13__q__7625__7627__7634__7636__7638__7640__7642)),happ(happ(Vvar__4__rmul__7560,Vvar__var__var__var__var__var__var__12__p__7624__7626__7633__7635__7637__7639__7641),happ(Vvar__8__rinv__7578,Vvar__var__var__var__var__var__var__13__q__7625__7627__7634__7636__7638__7640__7642)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__7629__7631__7643__7645__7647__7649__7651__7653] :
( t(Vvar__var__var__var__var__var__var__var__13__p__7629__7631__7643__7645__7647__7649__7651__7653,Vvar__0__R__7552)
=> ( ~ p(happ(happ(Vvar__9__req__7581,Vvar__var__var__var__var__var__var__var__13__p__7629__7631__7643__7645__7647__7649__7651__7653),Vvar__1__rO__7553))
=> p(happ(happ(Vvar__9__req__7581,happ(happ(Vvar__4__rmul__7560,happ(Vvar__8__rinv__7578,Vvar__var__var__var__var__var__var__var__13__p__7629__7631__7643__7645__7647__7649__7651__7653)),Vvar__var__var__var__var__var__var__var__13__p__7629__7631__7643__7645__7647__7649__7651__7653)),Vvar__2__rI__7554)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__7524,VX7525] :
( cType___24t(Vvar__0__C__7524)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__7524,VX7525)
=> ? [Vvar__1__num__7527] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7524,Vvar__1__num__7527)
& ? [Vvar__2__denum__7528] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7524,Vvar__2__denum__7528)
& ? [Vvar__3__condition__7529] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__7524),Vvar__3__condition__7529)
& VX7525 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__7524,Vvar__1__num__7527,Vvar__2__denum__7528,Vvar__3__condition__7529) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__7538,VX7539] :
( cType___24t(Vvar__0__C__7538)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__7538,VX7539)
=> ? [Vvar__1__rsplit__left__7541] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7538,Vvar__1__rsplit__left__7541)
& ? [Vvar__2__rsplit__common__7542] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7538,Vvar__2__rsplit__common__7542)
& ? [Vvar__3__rsplit__right__7543] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__7538,Vvar__3__rsplit__right__7543)
& VX7539 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__7538,Vvar__1__rsplit__left__7541,Vvar__2__rsplit__common__7542,Vvar__3__rsplit__right__7543) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096] :
( cType___24t(Vvar__0__R__39075)
=> ( t(Vvar__1__rO__39076,Vvar__0__R__39075)
=> ( t(Vvar__2__rI__39077,Vvar__0__R__39075)
=> ( c_24__type__39223___24t(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096,Vvar__3__radd__39078)
=> ( c_24__type__39286___24t(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096,Vvar__4__rmul__39083)
=> ( c_24__type__39349___24t(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096,Vvar__5__rdiv__39088)
=> ( c_24__type__39403___24t(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096,Vvar__6__rinv__39093)
=> ( c_24__type__39466___24t(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096,Vvar__7__req__39096)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__5__rdiv__39088,Vvar__6__rinv__39093,Vvar__7__req__39096)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__39075,Vvar__1__rO__39076,Vvar__2__rI__39077,Vvar__3__radd__39078,Vvar__4__rmul__39083,Vvar__7__req__39096)
& ~ p(happ(happ(Vvar__7__req__39096,Vvar__2__rI__39077),Vvar__1__rO__39076))
& ! [Vvar__var__var__var__var__var__var__10__p__39131__39133__39140__39142__39144__39146__39148] :
( t(Vvar__var__var__var__var__var__var__10__p__39131__39133__39140__39142__39144__39146__39148,Vvar__0__R__39075)
=> ! [Vvar__var__var__var__var__var__var__11__q__39132__39134__39141__39143__39145__39147__39149] :
( t(Vvar__var__var__var__var__var__var__11__q__39132__39134__39141__39143__39145__39147__39149,Vvar__0__R__39075)
=> p(happ(happ(Vvar__7__req__39096,happ(happ(Vvar__5__rdiv__39088,Vvar__var__var__var__var__var__var__10__p__39131__39133__39140__39142__39144__39146__39148),Vvar__var__var__var__var__var__var__11__q__39132__39134__39141__39143__39145__39147__39149)),happ(happ(Vvar__4__rmul__39083,Vvar__var__var__var__var__var__var__10__p__39131__39133__39140__39142__39144__39146__39148),happ(Vvar__6__rinv__39093,Vvar__var__var__var__var__var__var__11__q__39132__39134__39141__39143__39145__39147__39149)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__39136__39138__39150__39152__39154__39156__39158__39160] :
( t(Vvar__var__var__var__var__var__var__var__11__p__39136__39138__39150__39152__39154__39156__39158__39160,Vvar__0__R__39075)
=> ( ~ p(happ(happ(Vvar__7__req__39096,Vvar__var__var__var__var__var__var__var__11__p__39136__39138__39150__39152__39154__39156__39158__39160),Vvar__1__rO__39076))
=> p(happ(happ(Vvar__7__req__39096,happ(happ(Vvar__4__rmul__39083,happ(Vvar__6__rinv__39093,Vvar__var__var__var__var__var__var__var__11__p__39136__39138__39150__39152__39154__39156__39158__39160)),Vvar__var__var__var__var__var__var__var__11__p__39136__39138__39150__39152__39154__39156__39158__39160)),Vvar__2__rI__39077)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX39472] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX39472)
=> ? [Vvar__0__hypo__type__39473] :
( cType___24t(Vvar__0__hypo__type__39473)
& ? [Vvar__1__hypo__proof__39474] :
( t(Vvar__1__hypo__proof__39474,Vvar__0__hypo__type__39473)
& VX39472 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__39473,Vvar__1__hypo__proof__39474) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX15699] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX15699)
=> ( VX15699 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__15700] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15700)
& ? [Vvar__1___24Anonymous__15701] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__15701)
& VX15699 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__15700,Vvar__1___24Anonymous__15701) ) )
| ? [Vvar__0___24Anonymous__15702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15702)
& ? [Vvar__1___24Anonymous__15703] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__15703)
& VX15699 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__15702,Vvar__1___24Anonymous__15703) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__15720,VX15721] :
( cType___24t(Vvar__0__C__15720)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,VX15721)
=> ( VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__15720)
| VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__15720)
| ? [Vvar__1___24Anonymous__15725] :
( t(Vvar__1___24Anonymous__15725,Vvar__0__C__15720)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__15720,Vvar__1___24Anonymous__15725) )
| ? [Vvar__1___24Anonymous__15727] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15727)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__15720,Vvar__1___24Anonymous__15727) )
| ? [Vvar__1___24Anonymous__15729] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__1___24Anonymous__15729)
& ? [Vvar__2___24Anonymous__15730] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__2___24Anonymous__15730)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__15720,Vvar__1___24Anonymous__15729,Vvar__2___24Anonymous__15730) ) )
| ? [Vvar__1___24Anonymous__15732] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__1___24Anonymous__15732)
& ? [Vvar__2___24Anonymous__15733] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__2___24Anonymous__15733)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__15720,Vvar__1___24Anonymous__15732,Vvar__2___24Anonymous__15733) ) )
| ? [Vvar__1___24Anonymous__15735] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__1___24Anonymous__15735)
& ? [Vvar__2___24Anonymous__15736] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__2___24Anonymous__15736)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__15720,Vvar__1___24Anonymous__15735,Vvar__2___24Anonymous__15736) ) )
| ? [Vvar__1___24Anonymous__15738] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__1___24Anonymous__15738)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__15720,Vvar__1___24Anonymous__15738) )
| ? [Vvar__1___24Anonymous__15740] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15720,Vvar__1___24Anonymous__15740)
& ? [Vvar__2___24Anonymous__15741] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__15741)
& VX15721 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__15720,Vvar__1___24Anonymous__15740,Vvar__2___24Anonymous__15741) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__15652,VX15653] :
( cType___24t(Vvar__0__C__15652)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15652,VX15653)
=> ( ? [Vvar__1___24Anonymous__15655] :
( t(Vvar__1___24Anonymous__15655,Vvar__0__C__15652)
& VX15653 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__15652,Vvar__1___24Anonymous__15655) )
| ? [Vvar__1___24Anonymous__15657] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15657)
& ? [Vvar__2___24Anonymous__15658] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15652,Vvar__2___24Anonymous__15658)
& VX15653 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__15652,Vvar__1___24Anonymous__15657,Vvar__2___24Anonymous__15658) ) )
| ? [Vvar__1___24Anonymous__15660] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15652,Vvar__1___24Anonymous__15660)
& ? [Vvar__2___24Anonymous__15661] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15661)
& ? [Vvar__3___24Anonymous__15662] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__15652,Vvar__3___24Anonymous__15662)
& VX15653 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__15652,Vvar__1___24Anonymous__15660,Vvar__2___24Anonymous__15661,Vvar__3___24Anonymous__15662) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291] :
( cType___24t(Vvar__0__R__16270)
=> ( t(Vvar__1__rO__16271,Vvar__0__R__16270)
=> ( t(Vvar__2__rI__16272,Vvar__0__R__16270)
=> ( c_24__type__16519___24t(Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291,Vvar__3__radd__16273)
=> ( c_24__type__16582___24t(Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291,Vvar__4__rmul__16278)
=> ( c_24__type__16645___24t(Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291,Vvar__5__rsub__16283)
=> ( c_24__type__16699___24t(Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291,Vvar__6__ropp__16288)
=> ( c_24__type__16762___24t(Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291,Vvar__7__req__16291)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__16270,Vvar__1__rO__16271,Vvar__2__rI__16272,Vvar__3__radd__16273,Vvar__4__rmul__16278,Vvar__5__rsub__16283,Vvar__6__ropp__16288,Vvar__7__req__16291)
=> ( ! [Vvar__var__var__var__var__var__8__x__16324__16325__16378__16379__16380__16381] :
( t(Vvar__var__var__var__var__var__8__x__16324__16325__16378__16379__16380__16381,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__3__radd__16273,Vvar__1__rO__16271),Vvar__var__var__var__var__var__8__x__16324__16325__16378__16379__16380__16381)),Vvar__var__var__var__var__var__8__x__16324__16325__16378__16379__16380__16381)) )
& ! [Vvar__var__var__var__var__9__x__16327__16329__16382__16384__16386] :
( t(Vvar__var__var__var__var__9__x__16327__16329__16382__16384__16386,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__10__y__16328__16330__16383__16385__16387] :
( t(Vvar__var__var__var__var__10__y__16328__16330__16383__16385__16387,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__9__x__16327__16329__16382__16384__16386),Vvar__var__var__var__var__10__y__16328__16330__16383__16385__16387)),happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__10__y__16328__16330__16383__16385__16387),Vvar__var__var__var__var__9__x__16327__16329__16382__16384__16386))) ) )
& ! [Vvar__var__var__var__var__10__x__16332__16335__16388__16391__16394] :
( t(Vvar__var__var__var__var__10__x__16332__16335__16388__16391__16394,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__11__y__16333__16336__16389__16392__16395] :
( t(Vvar__var__var__var__var__11__y__16333__16336__16389__16392__16395,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__12__z__16334__16337__16390__16393__16396] :
( t(Vvar__var__var__var__var__12__z__16334__16337__16390__16393__16396,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__10__x__16332__16335__16388__16391__16394),happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__11__y__16333__16336__16389__16392__16395),Vvar__var__var__var__var__12__z__16334__16337__16390__16393__16396))),happ(happ(Vvar__3__radd__16273,happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__10__x__16332__16335__16388__16391__16394),Vvar__var__var__var__var__11__y__16333__16336__16389__16392__16395)),Vvar__var__var__var__var__12__z__16334__16337__16390__16393__16396))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__16339__16340__16397__16398__16399__16400] :
( t(Vvar__var__var__var__var__var__11__x__16339__16340__16397__16398__16399__16400,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__4__rmul__16278,Vvar__2__rI__16272),Vvar__var__var__var__var__var__11__x__16339__16340__16397__16398__16399__16400)),Vvar__var__var__var__var__var__11__x__16339__16340__16397__16398__16399__16400)) )
& ! [Vvar__var__var__var__var__var__12__x__16342__16343__16401__16402__16403__16404] :
( t(Vvar__var__var__var__var__var__12__x__16342__16343__16401__16402__16403__16404,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__4__rmul__16278,Vvar__1__rO__16271),Vvar__var__var__var__var__var__12__x__16342__16343__16401__16402__16403__16404)),Vvar__1__rO__16271)) )
& ! [Vvar__var__var__var__var__13__x__16345__16347__16405__16407__16409] :
( t(Vvar__var__var__var__var__13__x__16345__16347__16405__16407__16409,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__14__y__16346__16348__16406__16408__16410] :
( t(Vvar__var__var__var__var__14__y__16346__16348__16406__16408__16410,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__13__x__16345__16347__16405__16407__16409),Vvar__var__var__var__var__14__y__16346__16348__16406__16408__16410)),happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__14__y__16346__16348__16406__16408__16410),Vvar__var__var__var__var__13__x__16345__16347__16405__16407__16409))) ) )
& ! [Vvar__var__var__var__var__14__x__16350__16353__16411__16414__16417] :
( t(Vvar__var__var__var__var__14__x__16350__16353__16411__16414__16417,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__15__y__16351__16354__16412__16415__16418] :
( t(Vvar__var__var__var__var__15__y__16351__16354__16412__16415__16418,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__16__z__16352__16355__16413__16416__16419] :
( t(Vvar__var__var__var__var__16__z__16352__16355__16413__16416__16419,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__14__x__16350__16353__16411__16414__16417),happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__15__y__16351__16354__16412__16415__16418),Vvar__var__var__var__var__16__z__16352__16355__16413__16416__16419))),happ(happ(Vvar__4__rmul__16278,happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__14__x__16350__16353__16411__16414__16417),Vvar__var__var__var__var__15__y__16351__16354__16412__16415__16418)),Vvar__var__var__var__var__16__z__16352__16355__16413__16416__16419))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__16357__16360__16420__16423__16426__16429] :
( t(Vvar__var__var__var__var__var__15__x__16357__16360__16420__16423__16426__16429,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__var__16__y__16358__16361__16421__16424__16427__16430] :
( t(Vvar__var__var__var__var__var__16__y__16358__16361__16421__16424__16427__16430,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__var__17__z__16359__16362__16422__16425__16428__16431] :
( t(Vvar__var__var__var__var__var__17__z__16359__16362__16422__16425__16428__16431,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__4__rmul__16278,happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__var__15__x__16357__16360__16420__16423__16426__16429),Vvar__var__var__var__var__var__16__y__16358__16361__16421__16424__16427__16430)),Vvar__var__var__var__var__var__17__z__16359__16362__16422__16425__16428__16431)),happ(happ(Vvar__3__radd__16273,happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__var__15__x__16357__16360__16420__16423__16426__16429),Vvar__var__var__var__var__var__17__z__16359__16362__16422__16425__16428__16431)),happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__var__16__y__16358__16361__16421__16424__16427__16430),Vvar__var__var__var__var__var__17__z__16359__16362__16422__16425__16428__16431)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__16364__16366__16432__16434__16436__16438] :
( t(Vvar__var__var__var__var__var__16__x__16364__16366__16432__16434__16436__16438,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__var__17__y__16365__16367__16433__16435__16437__16439] :
( t(Vvar__var__var__var__var__var__17__y__16365__16367__16433__16435__16437__16439,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(Vvar__6__ropp__16288,happ(happ(Vvar__4__rmul__16278,Vvar__var__var__var__var__var__16__x__16364__16366__16432__16434__16436__16438),Vvar__var__var__var__var__var__17__y__16365__16367__16433__16435__16437__16439))),happ(happ(Vvar__4__rmul__16278,happ(Vvar__6__ropp__16288,Vvar__var__var__var__var__var__16__x__16364__16366__16432__16434__16436__16438)),Vvar__var__var__var__var__var__17__y__16365__16367__16433__16435__16437__16439))) ) )
& ! [Vvar__var__var__var__var__var__17__x__16369__16371__16440__16442__16444__16446] :
( t(Vvar__var__var__var__var__var__17__x__16369__16371__16440__16442__16444__16446,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__var__18__y__16370__16372__16441__16443__16445__16447] :
( t(Vvar__var__var__var__var__var__18__y__16370__16372__16441__16443__16445__16447,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(Vvar__6__ropp__16288,happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__var__17__x__16369__16371__16440__16442__16444__16446),Vvar__var__var__var__var__var__18__y__16370__16372__16441__16443__16445__16447))),happ(happ(Vvar__3__radd__16273,happ(Vvar__6__ropp__16288,Vvar__var__var__var__var__var__17__x__16369__16371__16440__16442__16444__16446)),happ(Vvar__6__ropp__16288,Vvar__var__var__var__var__var__18__y__16370__16372__16441__16443__16445__16447)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__16374__16376__16448__16450__16452__16454__16456] :
( t(Vvar__var__var__var__var__var__var__18__x__16374__16376__16448__16450__16452__16454__16456,Vvar__0__R__16270)
=> ! [Vvar__var__var__var__var__var__var__19__y__16375__16377__16449__16451__16453__16455__16457] :
( t(Vvar__var__var__var__var__var__var__19__y__16375__16377__16449__16451__16453__16455__16457,Vvar__0__R__16270)
=> p(happ(happ(Vvar__7__req__16291,happ(happ(Vvar__5__rsub__16283,Vvar__var__var__var__var__var__var__18__x__16374__16376__16448__16450__16452__16454__16456),Vvar__var__var__var__var__var__var__19__y__16375__16377__16449__16451__16453__16455__16457)),happ(happ(Vvar__3__radd__16273,Vvar__var__var__var__var__var__var__18__x__16374__16376__16448__16450__16452__16454__16456),happ(Vvar__6__ropp__16288,Vvar__var__var__var__var__var__var__19__y__16375__16377__16449__16451__16453__16455__16457)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353] :
( cType___24t(Vvar__0__R__21333)
=> ( c_24__type__21473___24t(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353,Vvar__1__req__21334)
=> ( cType___24t(Vvar__2__C__21339)
=> ( c_24__type__21523___24t(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353,Vvar__3__cadd__21340)
=> ( c_24__type__21573___24t(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353,Vvar__4__cmul__21345)
=> ( c_24__type__21615___24t(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353,Vvar__5__phi__21350)
=> ( c_24__type__21665___24t(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353,Vvar__6__cdiv__21353)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__21385__21390__21395__21400__21405__21410__21415__21420] :
( t(Vvar__var__var__var__var__var__var__var__7__a__21385__21390__21395__21400__21405__21410__21415__21420,Vvar__2__C__21339)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__21386__21391__21396__21401__21406__21411__21416__21421] :
( t(Vvar__var__var__var__var__var__var__var__8__b__21386__21391__21396__21401__21406__21411__21416__21421,Vvar__2__C__21339)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2421728___24a9(Vvar__0__R__21333,Vvar__1__req__21334,Vvar__2__C__21339,Vvar__3__cadd__21340,Vvar__4__cmul__21345,Vvar__5__phi__21350,Vvar__6__cdiv__21353,Vvar__var__var__var__var__var__var__var__7__a__21385__21390__21395__21400__21405__21410__21415__21420,Vvar__var__var__var__var__var__var__var__8__b__21386__21391__21396__21401__21406__21411__21416__21421) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__3__req__21758,Vvar__4__Cpow__21763,Vvar__5__Cp__phi__21764,Vvar__6__rpow__21767] :
( cType___24t(Vvar__0__R__21751)
=> ( t(Vvar__1__rI__21752,Vvar__0__R__21751)
=> ( c_24__type__21853___24t(Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__3__req__21758,Vvar__4__Cpow__21763,Vvar__5__Cp__phi__21764,Vvar__6__rpow__21767,Vvar__2__rmul__21753)
=> ( c_24__type__21897___24t(Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__3__req__21758,Vvar__4__Cpow__21763,Vvar__5__Cp__phi__21764,Vvar__6__rpow__21767,Vvar__3__req__21758)
=> ( cType___24t(Vvar__4__Cpow__21763)
=> ( c_24__type__21933___24t(Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__3__req__21758,Vvar__4__Cpow__21763,Vvar__5__Cp__phi__21764,Vvar__6__rpow__21767,Vvar__5__Cp__phi__21764)
=> ( c_24__type__21977___24t(Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__3__req__21758,Vvar__4__Cpow__21763,Vvar__5__Cp__phi__21764,Vvar__6__rpow__21767,Vvar__6__rpow__21767)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__3__req__21758,Vvar__4__Cpow__21763,Vvar__5__Cp__phi__21764,Vvar__6__rpow__21767)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__21795__21797__21799__21801__21803__21805__21807__21809] :
( t(Vvar__var__var__var__var__var__var__var__7__r__21795__21797__21799__21801__21803__21805__21807__21809,Vvar__0__R__21751)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__21796__21798__21800__21802__21804__21806__21808__21810] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__21796__21798__21800__21802__21804__21806__21808__21810)
=> p(happ(happ(Vvar__3__req__21758,happ(happ(Vvar__6__rpow__21767,Vvar__var__var__var__var__var__var__var__7__r__21795__21797__21799__21801__21803__21805__21807__21809),happ(Vvar__5__Cp__phi__21764,Vvar__var__var__var__var__var__var__var__8__n__21796__21798__21800__21802__21804__21806__21808__21810))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__21751,Vvar__1__rI__21752,Vvar__2__rmul__21753,Vvar__var__var__var__var__var__var__var__7__r__21795__21797__21799__21801__21803__21805__21807__21809,Vvar__var__var__var__var__var__var__var__8__n__21796__21798__21800__21802__21804__21806__21808__21810))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535] :
( cType___24t(Vvar__0__R__17521)
=> ( c_24__type__17626___24t(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535,Vvar__1__radd__17522)
=> ( c_24__type__17656___24t(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535,Vvar__2__rmul__17527)
=> ( c_24__type__17680___24t(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535,Vvar__3__ropp__17532)
=> ( c_24__type__17710___24t(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535,Vvar__4__req__17535)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17740___24a5(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17521,c_24__type__17764___24a5(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535),Vvar__4__req__17535,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17521,Vvar__0__R__17521,Vvar__4__req__17535,Vvar__4__req__17535)),Vvar__1__radd__17522)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17797___24a5(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17521,c_24__type__17821___24a5(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535),Vvar__4__req__17535,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17521,Vvar__0__R__17521,Vvar__4__req__17535,Vvar__4__req__17535)),Vvar__2__rmul__17527)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17848___24a5(Vvar__0__R__17521,Vvar__1__radd__17522,Vvar__2__rmul__17527,Vvar__3__ropp__17532,Vvar__4__req__17535),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17521,Vvar__0__R__17521,Vvar__4__req__17535,Vvar__4__req__17535),Vvar__3__ropp__17532)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX21982] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX21982)
=> ( VX21982 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__21983] :
( cType___24t(Vvar__0__R__21983)
& ? [Vvar__1__req__21984] :
( c_24__type__50___24t(Vvar__0__R__21983,Vvar__1__req__21984)
& ? [Vvar__2__reqb__21989] :
( c_24__type__22063___24t(Vvar__0__R__21983,Vvar__2__reqb__21989)
& ! [Vvar__var__3__x__21995__21998] :
( t(Vvar__var__3__x__21995__21998,Vvar__0__R__21983)
=> ! [Vvar__var__4__y__21996__21999] :
( t(Vvar__var__4__y__21996__21999,Vvar__0__R__21983)
=> ( happ(happ(Vvar__2__reqb__21989,Vvar__var__3__x__21995__21998),Vvar__var__4__y__21996__21999) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__21984,Vvar__var__3__x__21995__21998),Vvar__var__4__y__21996__21999)) ) ) )
& VX21982 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__21983,Vvar__1__req__21984,Vvar__2__reqb__21989) ) ) )
| ? [Vvar__0__R__22001] :
( cType___24t(Vvar__0__R__22001)
& ? [Vvar__1__rO__22002] :
( t(Vvar__1__rO__22002,Vvar__0__R__22001)
& ? [Vvar__2__rI__22003] :
( t(Vvar__2__rI__22003,Vvar__0__R__22001)
& ? [Vvar__3__radd__22004] :
( c_24__type__8334___24t(Vvar__0__R__22001,Vvar__3__radd__22004)
& ? [Vvar__4__rmul__22009] :
( c_24__type__8334___24t(Vvar__0__R__22001,Vvar__4__rmul__22009)
& ? [Vvar__5__rsub__22014] :
( c_24__type__8334___24t(Vvar__0__R__22001,Vvar__5__rsub__22014)
& ? [Vvar__6__ropp__22019] :
( c_24__type__912___24t(Vvar__0__R__22001,Vvar__6__ropp__22019)
& ? [Vvar__7__req__22022] :
( c_24__type__50___24t(Vvar__0__R__22001,Vvar__7__req__22022)
& ? [Vvar__8__C__22027] :
( cType___24t(Vvar__8__C__22027)
& ? [Vvar__9__cO__22028] :
( t(Vvar__9__cO__22028,Vvar__8__C__22027)
& ? [Vvar__10__cI__22029] :
( t(Vvar__10__cI__22029,Vvar__8__C__22027)
& ? [Vvar__11__cadd__22030] :
( c_24__type__22086___24t(Vvar__0__R__22001,Vvar__8__C__22027,Vvar__11__cadd__22030)
& ? [Vvar__12__cmul__22035] :
( c_24__type__22086___24t(Vvar__0__R__22001,Vvar__8__C__22027,Vvar__12__cmul__22035)
& ? [Vvar__13__csub__22040] :
( c_24__type__22086___24t(Vvar__0__R__22001,Vvar__8__C__22027,Vvar__13__csub__22040)
& ? [Vvar__14__copp__22045] :
( c_24__type__4435___24t(Vvar__0__R__22001,Vvar__8__C__22027,Vvar__14__copp__22045)
& ? [Vvar__15__ceqb__22048] :
( c_24__type__22105___24t(Vvar__0__R__22001,Vvar__8__C__22027,Vvar__15__ceqb__22048)
& ? [Vvar__16__phi__22053] :
( c_24__type__22109___24t(Vvar__0__R__22001,Vvar__8__C__22027,Vvar__16__phi__22053)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__22001,Vvar__1__rO__22002,Vvar__2__rI__22003,Vvar__3__radd__22004,Vvar__4__rmul__22009,Vvar__5__rsub__22014,Vvar__6__ropp__22019,Vvar__7__req__22022,Vvar__8__C__22027,Vvar__9__cO__22028,Vvar__10__cI__22029,Vvar__11__cadd__22030,Vvar__12__cmul__22035,Vvar__13__csub__22040,Vvar__14__copp__22045,Vvar__15__ceqb__22048,Vvar__16__phi__22053)
& VX21982 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__22001,Vvar__1__rO__22002,Vvar__2__rI__22003,Vvar__3__radd__22004,Vvar__4__rmul__22009,Vvar__5__rsub__22014,Vvar__6__ropp__22019,Vvar__7__req__22022,Vvar__8__C__22027,Vvar__9__cO__22028,Vvar__10__cI__22029,Vvar__11__cadd__22030,Vvar__12__cmul__22035,Vvar__13__csub__22040,Vvar__14__copp__22045,Vvar__15__ceqb__22048,Vvar__16__phi__22053) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901] :
( cType___24t(Vvar__0__R__18849)
=> ( t(Vvar__1__rO__18850,Vvar__0__R__18849)
=> ( t(Vvar__2__rI__18851,Vvar__0__R__18849)
=> ( c_24__type__19245___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__3__radd__18852)
=> ( c_24__type__19458___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__4__rmul__18857)
=> ( c_24__type__19671___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__5__rsub__18862)
=> ( c_24__type__19866___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__6__ropp__18867)
=> ( c_24__type__20079___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__7__req__18870)
=> ( cType___24t(Vvar__8__C__18875)
=> ( t(Vvar__9__cO__18876,Vvar__8__C__18875)
=> ( t(Vvar__10__cI__18877,Vvar__8__C__18875)
=> ( c_24__type__20292___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__11__cadd__18878)
=> ( c_24__type__20505___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__12__cmul__18883)
=> ( c_24__type__20718___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__13__csub__18888)
=> ( c_24__type__20913___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__14__copp__18893)
=> ( c_24__type__21126___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__15__ceqb__18896)
=> ( c_24__type__21321___24t(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901,Vvar__16__phi__18901)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__18849,Vvar__1__rO__18850,Vvar__2__rI__18851,Vvar__3__radd__18852,Vvar__4__rmul__18857,Vvar__5__rsub__18862,Vvar__6__ropp__18867,Vvar__7__req__18870,Vvar__8__C__18875,Vvar__9__cO__18876,Vvar__10__cI__18877,Vvar__11__cadd__18878,Vvar__12__cmul__18883,Vvar__13__csub__18888,Vvar__14__copp__18893,Vvar__15__ceqb__18896,Vvar__16__phi__18901)
=> ( p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,Vvar__9__cO__18876)),Vvar__1__rO__18850))
& p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,Vvar__10__cI__18877)),Vvar__2__rI__18851))
& ! [Vvar__var__var__var__var__var__var__19__x__18963__18965__18987__18989__18991__18993__18995] :
( t(Vvar__var__var__var__var__var__var__19__x__18963__18965__18987__18989__18991__18993__18995,Vvar__8__C__18875)
=> ! [Vvar__var__var__var__var__var__var__20__y__18964__18966__18988__18990__18992__18994__18996] :
( t(Vvar__var__var__var__var__var__var__20__y__18964__18966__18988__18990__18992__18994__18996,Vvar__8__C__18875)
=> p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,happ(happ(Vvar__11__cadd__18878,Vvar__var__var__var__var__var__var__19__x__18963__18965__18987__18989__18991__18993__18995),Vvar__var__var__var__var__var__var__20__y__18964__18966__18988__18990__18992__18994__18996))),happ(happ(Vvar__3__radd__18852,happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__19__x__18963__18965__18987__18989__18991__18993__18995)),happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__20__y__18964__18966__18988__18990__18992__18994__18996)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__18968__18970__18997__18999__19001__19003__19005] :
( t(Vvar__var__var__var__var__var__var__20__x__18968__18970__18997__18999__19001__19003__19005,Vvar__8__C__18875)
=> ! [Vvar__var__var__var__var__var__var__21__y__18969__18971__18998__19000__19002__19004__19006] :
( t(Vvar__var__var__var__var__var__var__21__y__18969__18971__18998__19000__19002__19004__19006,Vvar__8__C__18875)
=> p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,happ(happ(Vvar__13__csub__18888,Vvar__var__var__var__var__var__var__20__x__18968__18970__18997__18999__19001__19003__19005),Vvar__var__var__var__var__var__var__21__y__18969__18971__18998__19000__19002__19004__19006))),happ(happ(Vvar__5__rsub__18862,happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__20__x__18968__18970__18997__18999__19001__19003__19005)),happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__21__y__18969__18971__18998__19000__19002__19004__19006)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__18973__18975__19007__19009__19011__19013__19015] :
( t(Vvar__var__var__var__var__var__var__21__x__18973__18975__19007__19009__19011__19013__19015,Vvar__8__C__18875)
=> ! [Vvar__var__var__var__var__var__var__22__y__18974__18976__19008__19010__19012__19014__19016] :
( t(Vvar__var__var__var__var__var__var__22__y__18974__18976__19008__19010__19012__19014__19016,Vvar__8__C__18875)
=> p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,happ(happ(Vvar__12__cmul__18883,Vvar__var__var__var__var__var__var__21__x__18973__18975__19007__19009__19011__19013__19015),Vvar__var__var__var__var__var__var__22__y__18974__18976__19008__19010__19012__19014__19016))),happ(happ(Vvar__4__rmul__18857,happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__21__x__18973__18975__19007__19009__19011__19013__19015)),happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__22__y__18974__18976__19008__19010__19012__19014__19016)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__18978__18979__19017__19018__19019__19020__19021] :
( t(Vvar__var__var__var__var__var__var__22__x__18978__18979__19017__19018__19019__19020__19021,Vvar__8__C__18875)
=> p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,happ(Vvar__14__copp__18893,Vvar__var__var__var__var__var__var__22__x__18978__18979__19017__19018__19019__19020__19021))),happ(Vvar__6__ropp__18867,happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__var__22__x__18978__18979__19017__19018__19019__19020__19021)))) )
& ! [Vvar__var__var__var__var__var__23__x__18981__18984__19022__19025__19028__19031] :
( t(Vvar__var__var__var__var__var__23__x__18981__18984__19022__19025__19028__19031,Vvar__8__C__18875)
=> ! [Vvar__var__var__var__var__var__24__y__18982__18985__19023__19026__19029__19032] :
( t(Vvar__var__var__var__var__var__24__y__18982__18985__19023__19026__19029__19032,Vvar__8__C__18875)
=> ( happ(happ(Vvar__15__ceqb__18896,Vvar__var__var__var__var__var__23__x__18981__18984__19022__19025__19028__19031),Vvar__var__var__var__var__var__24__y__18982__18985__19023__19026__19029__19032) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__18870,happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__23__x__18981__18984__19022__19025__19028__19031)),happ(Vvar__16__phi__18901,Vvar__var__var__var__var__var__24__y__18982__18985__19023__19026__19029__19032))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833] :
( cType___24t(Vvar__0__R__16812)
=> ( t(Vvar__1__rO__16813,Vvar__0__R__16812)
=> ( t(Vvar__2__rI__16814,Vvar__0__R__16812)
=> ( c_24__type__17036___24t(Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833,Vvar__3__radd__16815)
=> ( c_24__type__17099___24t(Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833,Vvar__4__rmul__16820)
=> ( c_24__type__17162___24t(Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833,Vvar__5__rsub__16825)
=> ( c_24__type__17216___24t(Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833,Vvar__6__ropp__16830)
=> ( c_24__type__17279___24t(Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833,Vvar__7__req__16833)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__16812,Vvar__1__rO__16813,Vvar__2__rI__16814,Vvar__3__radd__16815,Vvar__4__rmul__16820,Vvar__5__rsub__16825,Vvar__6__ropp__16830,Vvar__7__req__16833)
=> ( ! [Vvar__var__var__var__var__var__8__x__16866__16867__16910__16911__16912__16913] :
( t(Vvar__var__var__var__var__var__8__x__16866__16867__16910__16911__16912__16913,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__3__radd__16815,Vvar__1__rO__16813),Vvar__var__var__var__var__var__8__x__16866__16867__16910__16911__16912__16913)),Vvar__var__var__var__var__var__8__x__16866__16867__16910__16911__16912__16913)) )
& ! [Vvar__var__var__var__var__9__x__16869__16871__16914__16916__16918] :
( t(Vvar__var__var__var__var__9__x__16869__16871__16914__16916__16918,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__10__y__16870__16872__16915__16917__16919] :
( t(Vvar__var__var__var__var__10__y__16870__16872__16915__16917__16919,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__9__x__16869__16871__16914__16916__16918),Vvar__var__var__var__var__10__y__16870__16872__16915__16917__16919)),happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__10__y__16870__16872__16915__16917__16919),Vvar__var__var__var__var__9__x__16869__16871__16914__16916__16918))) ) )
& ! [Vvar__var__var__var__var__10__x__16874__16877__16920__16923__16926] :
( t(Vvar__var__var__var__var__10__x__16874__16877__16920__16923__16926,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__11__y__16875__16878__16921__16924__16927] :
( t(Vvar__var__var__var__var__11__y__16875__16878__16921__16924__16927,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__12__z__16876__16879__16922__16925__16928] :
( t(Vvar__var__var__var__var__12__z__16876__16879__16922__16925__16928,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__10__x__16874__16877__16920__16923__16926),happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__11__y__16875__16878__16921__16924__16927),Vvar__var__var__var__var__12__z__16876__16879__16922__16925__16928))),happ(happ(Vvar__3__radd__16815,happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__10__x__16874__16877__16920__16923__16926),Vvar__var__var__var__var__11__y__16875__16878__16921__16924__16927)),Vvar__var__var__var__var__12__z__16876__16879__16922__16925__16928))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__16881__16882__16929__16930__16931__16932] :
( t(Vvar__var__var__var__var__var__11__x__16881__16882__16929__16930__16931__16932,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__4__rmul__16820,Vvar__2__rI__16814),Vvar__var__var__var__var__var__11__x__16881__16882__16929__16930__16931__16932)),Vvar__var__var__var__var__var__11__x__16881__16882__16929__16930__16931__16932)) )
& ! [Vvar__var__var__var__var__12__x__16884__16886__16933__16935__16937] :
( t(Vvar__var__var__var__var__12__x__16884__16886__16933__16935__16937,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__13__y__16885__16887__16934__16936__16938] :
( t(Vvar__var__var__var__var__13__y__16885__16887__16934__16936__16938,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__12__x__16884__16886__16933__16935__16937),Vvar__var__var__var__var__13__y__16885__16887__16934__16936__16938)),happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__13__y__16885__16887__16934__16936__16938),Vvar__var__var__var__var__12__x__16884__16886__16933__16935__16937))) ) )
& ! [Vvar__var__var__var__var__13__x__16889__16892__16939__16942__16945] :
( t(Vvar__var__var__var__var__13__x__16889__16892__16939__16942__16945,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__14__y__16890__16893__16940__16943__16946] :
( t(Vvar__var__var__var__var__14__y__16890__16893__16940__16943__16946,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__15__z__16891__16894__16941__16944__16947] :
( t(Vvar__var__var__var__var__15__z__16891__16894__16941__16944__16947,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__13__x__16889__16892__16939__16942__16945),happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__14__y__16890__16893__16940__16943__16946),Vvar__var__var__var__var__15__z__16891__16894__16941__16944__16947))),happ(happ(Vvar__4__rmul__16820,happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__13__x__16889__16892__16939__16942__16945),Vvar__var__var__var__var__14__y__16890__16893__16940__16943__16946)),Vvar__var__var__var__var__15__z__16891__16894__16941__16944__16947))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__16896__16899__16948__16951__16954__16957] :
( t(Vvar__var__var__var__var__var__14__x__16896__16899__16948__16951__16954__16957,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__var__15__y__16897__16900__16949__16952__16955__16958] :
( t(Vvar__var__var__var__var__var__15__y__16897__16900__16949__16952__16955__16958,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__var__16__z__16898__16901__16950__16953__16956__16959] :
( t(Vvar__var__var__var__var__var__16__z__16898__16901__16950__16953__16956__16959,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__4__rmul__16820,happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__var__14__x__16896__16899__16948__16951__16954__16957),Vvar__var__var__var__var__var__15__y__16897__16900__16949__16952__16955__16958)),Vvar__var__var__var__var__var__16__z__16898__16901__16950__16953__16956__16959)),happ(happ(Vvar__3__radd__16815,happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__var__14__x__16896__16899__16948__16951__16954__16957),Vvar__var__var__var__var__var__16__z__16898__16901__16950__16953__16956__16959)),happ(happ(Vvar__4__rmul__16820,Vvar__var__var__var__var__var__15__y__16897__16900__16949__16952__16955__16958),Vvar__var__var__var__var__var__16__z__16898__16901__16950__16953__16956__16959)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__16903__16905__16960__16962__16964__16966__16968] :
( t(Vvar__var__var__var__var__var__var__15__x__16903__16905__16960__16962__16964__16966__16968,Vvar__0__R__16812)
=> ! [Vvar__var__var__var__var__var__var__16__y__16904__16906__16961__16963__16965__16967__16969] :
( t(Vvar__var__var__var__var__var__var__16__y__16904__16906__16961__16963__16965__16967__16969,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__5__rsub__16825,Vvar__var__var__var__var__var__var__15__x__16903__16905__16960__16962__16964__16966__16968),Vvar__var__var__var__var__var__var__16__y__16904__16906__16961__16963__16965__16967__16969)),happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__var__var__15__x__16903__16905__16960__16962__16964__16966__16968),happ(Vvar__6__ropp__16830,Vvar__var__var__var__var__var__var__16__y__16904__16906__16961__16963__16965__16967__16969)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__16908__16909__16970__16971__16972__16973__16974] :
( t(Vvar__var__var__var__var__var__var__16__x__16908__16909__16970__16971__16972__16973__16974,Vvar__0__R__16812)
=> p(happ(happ(Vvar__7__req__16833,happ(happ(Vvar__3__radd__16815,Vvar__var__var__var__var__var__var__16__x__16908__16909__16970__16971__16972__16973__16974),happ(Vvar__6__ropp__16830,Vvar__var__var__var__var__var__var__16__x__16908__16909__16970__16971__16972__16973__16974))),Vvar__1__rO__16813)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887] :
( cType___24t(Vvar__0__R__17851)
=> ( t(Vvar__1__rO__17852,Vvar__0__R__17851)
=> ( t(Vvar__2__rI__17853,Vvar__0__R__17851)
=> ( c_24__type__18104___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__3__radd__17854)
=> ( c_24__type__18229___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__4__rmul__17859)
=> ( c_24__type__18354___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__5__req__17864)
=> ( cType___24t(Vvar__6__C__17869)
=> ( t(Vvar__7__cO__17870,Vvar__6__C__17869)
=> ( t(Vvar__8__cI__17871,Vvar__6__C__17869)
=> ( c_24__type__18479___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__9__cadd__17872)
=> ( c_24__type__18604___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__10__cmul__17877)
=> ( c_24__type__18729___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__11__ceqb__17882)
=> ( c_24__type__18840___24t(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887,Vvar__12__phi__17887)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__17851,Vvar__1__rO__17852,Vvar__2__rI__17853,Vvar__3__radd__17854,Vvar__4__rmul__17859,Vvar__5__req__17864,Vvar__6__C__17869,Vvar__7__cO__17870,Vvar__8__cI__17871,Vvar__9__cadd__17872,Vvar__10__cmul__17877,Vvar__11__ceqb__17882,Vvar__12__phi__17887)
=> ( p(happ(happ(Vvar__5__req__17864,happ(Vvar__12__phi__17887,Vvar__7__cO__17870)),Vvar__1__rO__17852))
& p(happ(happ(Vvar__5__req__17864,happ(Vvar__12__phi__17887,Vvar__8__cI__17871)),Vvar__2__rI__17853))
& ! [Vvar__var__var__var__var__var__var__15__x__17933__17935__17949__17951__17953__17955__17957] :
( t(Vvar__var__var__var__var__var__var__15__x__17933__17935__17949__17951__17953__17955__17957,Vvar__6__C__17869)
=> ! [Vvar__var__var__var__var__var__var__16__y__17934__17936__17950__17952__17954__17956__17958] :
( t(Vvar__var__var__var__var__var__var__16__y__17934__17936__17950__17952__17954__17956__17958,Vvar__6__C__17869)
=> p(happ(happ(Vvar__5__req__17864,happ(Vvar__12__phi__17887,happ(happ(Vvar__9__cadd__17872,Vvar__var__var__var__var__var__var__15__x__17933__17935__17949__17951__17953__17955__17957),Vvar__var__var__var__var__var__var__16__y__17934__17936__17950__17952__17954__17956__17958))),happ(happ(Vvar__3__radd__17854,happ(Vvar__12__phi__17887,Vvar__var__var__var__var__var__var__15__x__17933__17935__17949__17951__17953__17955__17957)),happ(Vvar__12__phi__17887,Vvar__var__var__var__var__var__var__16__y__17934__17936__17950__17952__17954__17956__17958)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__17938__17940__17959__17961__17963__17965__17967] :
( t(Vvar__var__var__var__var__var__var__16__x__17938__17940__17959__17961__17963__17965__17967,Vvar__6__C__17869)
=> ! [Vvar__var__var__var__var__var__var__17__y__17939__17941__17960__17962__17964__17966__17968] :
( t(Vvar__var__var__var__var__var__var__17__y__17939__17941__17960__17962__17964__17966__17968,Vvar__6__C__17869)
=> p(happ(happ(Vvar__5__req__17864,happ(Vvar__12__phi__17887,happ(happ(Vvar__10__cmul__17877,Vvar__var__var__var__var__var__var__16__x__17938__17940__17959__17961__17963__17965__17967),Vvar__var__var__var__var__var__var__17__y__17939__17941__17960__17962__17964__17966__17968))),happ(happ(Vvar__4__rmul__17859,happ(Vvar__12__phi__17887,Vvar__var__var__var__var__var__var__16__x__17938__17940__17959__17961__17963__17965__17967)),happ(Vvar__12__phi__17887,Vvar__var__var__var__var__var__var__17__y__17939__17941__17960__17962__17964__17966__17968)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__17943__17946__17969__17972__17975__17978] :
( t(Vvar__var__var__var__var__var__17__x__17943__17946__17969__17972__17975__17978,Vvar__6__C__17869)
=> ! [Vvar__var__var__var__var__var__18__y__17944__17947__17970__17973__17976__17979] :
( t(Vvar__var__var__var__var__var__18__y__17944__17947__17970__17973__17976__17979,Vvar__6__C__17869)
=> ( happ(happ(Vvar__11__ceqb__17882,Vvar__var__var__var__var__var__17__x__17943__17946__17969__17972__17975__17978),Vvar__var__var__var__var__var__18__y__17944__17947__17970__17973__17976__17979) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__17864,happ(Vvar__12__phi__17887,Vvar__var__var__var__var__var__17__x__17943__17946__17969__17972__17975__17978)),happ(Vvar__12__phi__17887,Vvar__var__var__var__var__var__18__y__17944__17947__17970__17973__17976__17979))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__16006,Vvar__1__rO__16007,Vvar__2__rI__16008,Vvar__3__radd__16009,Vvar__4__rmul__16014,Vvar__5__req__16019] :
( cType___24t(Vvar__0__R__16006)
=> ( t(Vvar__1__rO__16007,Vvar__0__R__16006)
=> ( t(Vvar__2__rI__16008,Vvar__0__R__16006)
=> ( c_24__type__16174___24t(Vvar__0__R__16006,Vvar__1__rO__16007,Vvar__2__rI__16008,Vvar__3__radd__16009,Vvar__4__rmul__16014,Vvar__5__req__16019,Vvar__3__radd__16009)
=> ( c_24__type__16213___24t(Vvar__0__R__16006,Vvar__1__rO__16007,Vvar__2__rI__16008,Vvar__3__radd__16009,Vvar__4__rmul__16014,Vvar__5__req__16019,Vvar__4__rmul__16014)
=> ( c_24__type__16252___24t(Vvar__0__R__16006,Vvar__1__rO__16007,Vvar__2__rI__16008,Vvar__3__radd__16009,Vvar__4__rmul__16014,Vvar__5__req__16019,Vvar__5__req__16019)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__16006,Vvar__1__rO__16007,Vvar__2__rI__16008,Vvar__3__radd__16009,Vvar__4__rmul__16014,Vvar__5__req__16019)
=> ( ! [Vvar__var__var__var__var__var__6__n__16044__16045__16083__16084__16085__16086] :
( t(Vvar__var__var__var__var__var__6__n__16044__16045__16083__16084__16085__16086,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__3__radd__16009,Vvar__1__rO__16007),Vvar__var__var__var__var__var__6__n__16044__16045__16083__16084__16085__16086)),Vvar__var__var__var__var__var__6__n__16044__16045__16083__16084__16085__16086)) )
& ! [Vvar__var__var__var__var__7__n__16047__16049__16087__16089__16091] :
( t(Vvar__var__var__var__var__7__n__16047__16049__16087__16089__16091,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__8__m__16048__16050__16088__16090__16092] :
( t(Vvar__var__var__var__var__8__m__16048__16050__16088__16090__16092,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__3__radd__16009,Vvar__var__var__var__var__7__n__16047__16049__16087__16089__16091),Vvar__var__var__var__var__8__m__16048__16050__16088__16090__16092)),happ(happ(Vvar__3__radd__16009,Vvar__var__var__var__var__8__m__16048__16050__16088__16090__16092),Vvar__var__var__var__var__7__n__16047__16049__16087__16089__16091))) ) )
& ! [Vvar__var__var__var__var__8__n__16052__16055__16093__16096__16099] :
( t(Vvar__var__var__var__var__8__n__16052__16055__16093__16096__16099,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__9__m__16053__16056__16094__16097__16100] :
( t(Vvar__var__var__var__var__9__m__16053__16056__16094__16097__16100,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__10__p__16054__16057__16095__16098__16101] :
( t(Vvar__var__var__var__var__10__p__16054__16057__16095__16098__16101,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__3__radd__16009,Vvar__var__var__var__var__8__n__16052__16055__16093__16096__16099),happ(happ(Vvar__3__radd__16009,Vvar__var__var__var__var__9__m__16053__16056__16094__16097__16100),Vvar__var__var__var__var__10__p__16054__16057__16095__16098__16101))),happ(happ(Vvar__3__radd__16009,happ(happ(Vvar__3__radd__16009,Vvar__var__var__var__var__8__n__16052__16055__16093__16096__16099),Vvar__var__var__var__var__9__m__16053__16056__16094__16097__16100)),Vvar__var__var__var__var__10__p__16054__16057__16095__16098__16101))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__16059__16060__16102__16103__16104__16105] :
( t(Vvar__var__var__var__var__var__9__n__16059__16060__16102__16103__16104__16105,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__4__rmul__16014,Vvar__2__rI__16008),Vvar__var__var__var__var__var__9__n__16059__16060__16102__16103__16104__16105)),Vvar__var__var__var__var__var__9__n__16059__16060__16102__16103__16104__16105)) )
& ! [Vvar__var__var__var__var__var__10__n__16062__16063__16106__16107__16108__16109] :
( t(Vvar__var__var__var__var__var__10__n__16062__16063__16106__16107__16108__16109,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__4__rmul__16014,Vvar__1__rO__16007),Vvar__var__var__var__var__var__10__n__16062__16063__16106__16107__16108__16109)),Vvar__1__rO__16007)) )
& ! [Vvar__var__var__var__var__11__n__16065__16067__16110__16112__16114] :
( t(Vvar__var__var__var__var__11__n__16065__16067__16110__16112__16114,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__12__m__16066__16068__16111__16113__16115] :
( t(Vvar__var__var__var__var__12__m__16066__16068__16111__16113__16115,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__11__n__16065__16067__16110__16112__16114),Vvar__var__var__var__var__12__m__16066__16068__16111__16113__16115)),happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__12__m__16066__16068__16111__16113__16115),Vvar__var__var__var__var__11__n__16065__16067__16110__16112__16114))) ) )
& ! [Vvar__var__var__var__var__12__n__16070__16073__16116__16119__16122] :
( t(Vvar__var__var__var__var__12__n__16070__16073__16116__16119__16122,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__13__m__16071__16074__16117__16120__16123] :
( t(Vvar__var__var__var__var__13__m__16071__16074__16117__16120__16123,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__14__p__16072__16075__16118__16121__16124] :
( t(Vvar__var__var__var__var__14__p__16072__16075__16118__16121__16124,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__12__n__16070__16073__16116__16119__16122),happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__13__m__16071__16074__16117__16120__16123),Vvar__var__var__var__var__14__p__16072__16075__16118__16121__16124))),happ(happ(Vvar__4__rmul__16014,happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__12__n__16070__16073__16116__16119__16122),Vvar__var__var__var__var__13__m__16071__16074__16117__16120__16123)),Vvar__var__var__var__var__14__p__16072__16075__16118__16121__16124))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__16077__16080__16125__16128__16131__16134] :
( t(Vvar__var__var__var__var__var__13__n__16077__16080__16125__16128__16131__16134,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__var__14__m__16078__16081__16126__16129__16132__16135] :
( t(Vvar__var__var__var__var__var__14__m__16078__16081__16126__16129__16132__16135,Vvar__0__R__16006)
=> ! [Vvar__var__var__var__var__var__15__p__16079__16082__16127__16130__16133__16136] :
( t(Vvar__var__var__var__var__var__15__p__16079__16082__16127__16130__16133__16136,Vvar__0__R__16006)
=> p(happ(happ(Vvar__5__req__16019,happ(happ(Vvar__4__rmul__16014,happ(happ(Vvar__3__radd__16009,Vvar__var__var__var__var__var__13__n__16077__16080__16125__16128__16131__16134),Vvar__var__var__var__var__var__14__m__16078__16081__16126__16129__16132__16135)),Vvar__var__var__var__var__var__15__p__16079__16082__16127__16130__16133__16136)),happ(happ(Vvar__3__radd__16009,happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__var__13__n__16077__16080__16125__16128__16131__16134),Vvar__var__var__var__var__var__15__p__16079__16082__16127__16130__16133__16136)),happ(happ(Vvar__4__rmul__16014,Vvar__var__var__var__var__var__14__m__16078__16081__16126__16129__16132__16135),Vvar__var__var__var__var__var__15__p__16079__16082__16127__16130__16133__16136)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__34392,Vvar__1__copp__34393,Vvar__2__ceqb__34396,Vvar__3__get__sign__34401] :
( cType___24t(Vvar__0__C__34392)
=> ( c_24__type__34448___24t(Vvar__0__C__34392,Vvar__1__copp__34393,Vvar__2__ceqb__34396,Vvar__3__get__sign__34401,Vvar__1__copp__34393)
=> ( c_24__type__34467___24t(Vvar__0__C__34392,Vvar__1__copp__34393,Vvar__2__ceqb__34396,Vvar__3__get__sign__34401,Vvar__2__ceqb__34396)
=> ( c_24__type__34481___24t(Vvar__0__C__34392,Vvar__1__copp__34393,Vvar__2__ceqb__34396,Vvar__3__get__sign__34401,Vvar__3__get__sign__34401)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__34392,Vvar__1__copp__34393,Vvar__2__ceqb__34396,Vvar__3__get__sign__34401)
=> ( ! [Vvar__var__var__var__var__var__4__c__34418__34421__34424__34427__34430__34433] :
( t(Vvar__var__var__var__var__var__4__c__34418__34421__34424__34427__34430__34433,Vvar__0__C__34392)
=> ! [Vvar__var__var__var__var__var__5__c_27__34419__34422__34425__34428__34431__34434] :
( t(Vvar__var__var__var__var__var__5__c_27__34419__34422__34425__34428__34431__34434,Vvar__0__C__34392)
=> ( happ(Vvar__3__get__sign__34401,Vvar__var__var__var__var__var__4__c__34418__34421__34424__34427__34430__34433) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__34392,Vvar__var__var__var__var__var__5__c_27__34419__34422__34425__34428__34431__34434)
=> happ(happ(Vvar__2__ceqb__34396,Vvar__var__var__var__var__var__4__c__34418__34421__34424__34427__34430__34433),happ(Vvar__1__copp__34393,Vvar__var__var__var__var__var__5__c_27__34419__34422__34425__34428__34431__34434)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310] :
( cType___24t(Vvar__0__R__17299)
=> ( c_24__type__17385___24t(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310,Vvar__1__radd__17300)
=> ( c_24__type__17408___24t(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310,Vvar__2__rmul__17305)
=> ( c_24__type__17431___24t(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310,Vvar__3__req__17310)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17454___24a4(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17299,c_24__type__17472___24a4(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310),Vvar__3__req__17310,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17299,Vvar__0__R__17299,Vvar__3__req__17310,Vvar__3__req__17310)),Vvar__1__radd__17300)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17498___24a4(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17299,c_24__type__17516___24a4(Vvar__0__R__17299,Vvar__1__radd__17300,Vvar__2__rmul__17305,Vvar__3__req__17310),Vvar__3__req__17310,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__17299,Vvar__0__R__17299,Vvar__3__req__17310,Vvar__3__req__17310)),Vvar__2__rmul__17305)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX39535] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX39535)
=> ( VX39535 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX39535 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction',axiom,
! [Vvar__0__X__164,Vvar__1__P__165,Vvar__2__x__168] :
( cType___24t(Vvar__0__X__164)
=> ( c_24__type__180___24t(Vvar__0__X__164,Vvar__1__P__165,Vvar__2__x__168,Vvar__1__P__165)
=> ( t(Vvar__2__x__168,Vvar__0__X__164)
=> ( cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(Vvar__0__X__164,Vvar__1__P__165,Vvar__2__x__168)
=> ( p(happ(Vvar__1__P__165,Vvar__2__x__168))
& p(c_24True) ) ) ) ) ) ).
fof('$_lam_105',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__105___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(happ(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ).
fof('$_lam_117',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__117___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> happ(Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__4) ) ).
fof('$_lam_159857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__159857___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__159858] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__159858)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__159858)
& c_24__lam__159857___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__159858) ) ) ) ).
fof('$_lam_159864',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__159864___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__159865] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__159865)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__159865)
& c_24__lam__159864___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__159865) ) ) ) ).
fof('$_lam_159868',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__159868___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__159869] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__159869)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__159869)
& c_24__lam__159868___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_lam_163830',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__163830___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),cQuotients_2eequiv__classes___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2) ) ).
fof('$_lam_163945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__163945___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_163950',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__163950___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_178372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__178372___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ? [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
& cQuotients_2equotient__projection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6) = Vv__CANONICAL__4
& happ(Vv__CANONICAL__3,Vv__CANONICAL__6) = Vv__CANONICAL__5 ) ) ).
fof('$_lam_178387',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__178387___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ? [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
& cQuotients_2equotient__projection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6) = Vv__CANONICAL__4
& happ(Vv__CANONICAL__3,Vv__CANONICAL__6) = Vv__CANONICAL__5 ) ) ).
fof('$_lam_178456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__178456___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ? [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
& cQuotients_2equotient__projection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6) = Vv__CANONICAL__4
& happ(Vv__CANONICAL__3,Vv__CANONICAL__6) = Vv__CANONICAL__5 ) ) ).
fof('$_lam_4325',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__4325___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('$_lam_4329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__4329___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__859___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_925',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__925___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_prop_23412',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__S__23390,Vvar__1__x__23391,Vvar__2__y__23392] :
( p(c_24__prop__23412___24a4(Vvar__0___24Anonymous__23388,Vvar__0__S__23390,Vvar__1__x__23391,Vvar__2__y__23392))
<=> Vvar__1__x__23391 = Vvar__2__y__23392 ) ).
fof('$_prop_23413',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__x__23393,Vvar__1__y__23394] :
( p(c_24__prop__23413___24a3(Vvar__0___24Anonymous__23388,Vvar__0__x__23393,Vvar__1__y__23394))
<=> Vvar__0__x__23393 = Vvar__1__y__23394 ) ).
fof('$_prop_23414',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__x__23395,Vvar__1__s__23396] :
( p(c_24__prop__23414___24a3(Vvar__0___24Anonymous__23388,Vvar__0__x__23395,Vvar__1__s__23396))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__23395,Vvar__1__s__23396) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_23415',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__P__23397,Vvar__1__Q__23398] :
( p(c_24__prop__23415___24a3(Vvar__0___24Anonymous__23388,Vvar__0__P__23397,Vvar__1__Q__23398))
<=> ( p(Vvar__0__P__23397)
& p(Vvar__1__Q__23398) ) ) ).
fof('$_prop_23416',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__P__23401,Vvar__1__Q__23402] :
( p(c_24__prop__23416___24a3(Vvar__0___24Anonymous__23388,Vvar__0__P__23401,Vvar__1__Q__23402))
<=> ( p(Vvar__0__P__23401)
| p(Vvar__1__Q__23402) ) ) ).
fof('$_prop_23417',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__P__23405,Vvar__1__Q__23406] :
( p(c_24__prop__23417___24a3(Vvar__0___24Anonymous__23388,Vvar__0__P__23405,Vvar__1__Q__23406))
<=> ( p(Vvar__0__P__23405)
=> p(Vvar__1__Q__23406) ) ) ).
fof('$_prop_23418',axiom,
! [Vvar__0___24Anonymous__23388,Vvar__0__P__23410] :
( p(c_24__prop__23418___24a2(Vvar__0___24Anonymous__23388,Vvar__0__P__23410))
<=> ~ p(Vvar__0__P__23410) ) ).
fof('$_prop_23626',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__23626___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_31844',axiom,
! [V7__A] :
( p(c_24__prop__31844___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_40253',axiom,
! [Vvar__0___24Anonymous__40240,Vvar__0__s__40244] :
( p(c_24__prop__40253___24a2(Vvar__0___24Anonymous__40240,Vvar__0__s__40244))
<=> ! [Vvar__1__a__40245] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__40245)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__40245,Vvar__0__s__40244) ) ) ).
fof('$_prop_40254',axiom,
! [Vvar__0___24Anonymous__40240,Vvar__0__s1__40246,Vvar__1__s2__40247] :
( p(c_24__prop__40254___24a3(Vvar__0___24Anonymous__40240,Vvar__0__s1__40246,Vvar__1__s2__40247))
<=> ! [Vvar__2__a__40248] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__40248)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__40248,Vvar__0__s1__40246)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__40248,Vvar__1__s2__40247) ) ) ) ).
fof('$_prop_40255',axiom,
! [Vvar__0___24Anonymous__40240,Vvar__0__s1__40250,Vvar__1__s2__40251] :
( p(c_24__prop__40255___24a3(Vvar__0___24Anonymous__40240,Vvar__0__s1__40250,Vvar__1__s2__40251))
<=> ! [Vvar__2__a__40252] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__40252)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__40252,Vvar__0__s1__40250)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__40252,Vvar__1__s2__40251) ) ) ) ).
fof('$_prop_5913',axiom,
! [V1__A] :
( p(c_24__prop__5913___24a1(V1__A))
<=> ( p(V1__A)
=> p(V1__A) ) ) ).
fof('$_prop_87237',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__87237___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_type_10071',axiom,
! [Vvar__10072] :
( c_24__type__10071___24t(Vvar__10072)
<=> ! [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__10072,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10075',axiom,
! [Vvar__10076] :
( c_24__type__10075___24t(Vvar__10076)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10076,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10077',axiom,
! [Vvar__10078] :
( c_24__type__10077___24t(Vvar__10078)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__10078,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10105',axiom,
! [Vvar__10106] :
( c_24__type__10105___24t(Vvar__10106)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__10106,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10163',axiom,
! [Vvar__10164] :
( c_24__type__10163___24t(Vvar__10164)
<=> ! [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__10164,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__10731] :
( c_24__type__10730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__10731)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10731,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11076',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__11077] :
( c_24__type__11076___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__11077)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11077,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11422',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11423] :
( c_24__type__11422___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__11423)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11423,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11745',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__11746] :
( c_24__type__11745___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__11746)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__11746,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_1193',axiom,
! [Vvar__1194] :
( c_24__type__1193___24t(Vvar__1194)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1194,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1206',axiom,
! [Vvar__1207] :
( c_24__type__1206___24t(Vvar__1207)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1207,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1208',axiom,
! [Vvar__1209] :
( c_24__type__1208___24t(Vvar__1209)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__1209,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12091',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__12092] :
( c_24__type__12091___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__12092)
<=> ! [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__12092,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_1234',axiom,
! [Vvar__1235] :
( c_24__type__1234___24t(Vvar__1235)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1235,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12437',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__12438] :
( c_24__type__12437___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__12438)
<=> ! [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__12438,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_1246',axiom,
! [Vvar__1247] :
( c_24__type__1246___24t(Vvar__1247)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1247,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1259',axiom,
! [Vvar__1260] :
( c_24__type__1259___24t(Vvar__1260)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1260,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1267',axiom,
! [Vvar__1268] :
( c_24__type__1267___24t(Vvar__1268)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__1268,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12783',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__12784] :
( c_24__type__12783___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__12784)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__12784,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_13129',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13130] :
( c_24__type__13129___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13130)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__13130,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_13475',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__13476] :
( c_24__type__13475___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__13476)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__13476,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_13798',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13799] :
( c_24__type__13798___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__13799)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__13799,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_14',axiom,
! [Vvar__15] :
( c_24__type__14___24t(Vvar__15)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__15,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14144',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14145] :
( c_24__type__14144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14145)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__14145,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_14490',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__14491] :
( c_24__type__14490___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__14491)
<=> ! [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__14491,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_14813',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14814] :
( c_24__type__14813___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__14814)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__14814,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_15136',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__15137] :
( c_24__type__15136___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__15137)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__15137,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_15482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15483] :
( c_24__type__15482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15483)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__15483,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15942',axiom,
! [Vvar__15943] :
( c_24__type__15942___24t(Vvar__15943)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__15943,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15945',axiom,
! [Vvar__15946] :
( c_24__type__15945___24t(Vvar__15946)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__15946,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15948',axiom,
! [Vvar__15949] :
( c_24__type__15948___24t(Vvar__15949)
<=> ! [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__15949,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15953',axiom,
! [Vvar__15954] :
( c_24__type__15953___24t(Vvar__15954)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__15954,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15962',axiom,
! [Vvar__15963] :
( c_24__type__15962___24t(Vvar__15963)
<=> ! [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__15963,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159716',axiom,
! [Vvar__159717] :
( c_24__type__159716___24t(Vvar__159717)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__159717,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_159721',axiom,
! [Vvar__159722] :
( c_24__type__159721___24t(Vvar__159722)
<=> ! [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__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__159722,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_159724',axiom,
! [Vvar__159725] :
( c_24__type__159724___24t(Vvar__159725)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__159725,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159727',axiom,
! [Vvar__159728] :
( c_24__type__159727___24t(Vvar__159728)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__159728,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159732',axiom,
! [Vvar__159733] :
( c_24__type__159732___24t(Vvar__159733)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__159733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_159740',axiom,
! [Vvar__159741] :
( c_24__type__159740___24t(Vvar__159741)
<=> ! [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__159741,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_159747',axiom,
! [Vvar__159748] :
( c_24__type__159747___24t(Vvar__159748)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__159748,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159752',axiom,
! [Vvar__159753] :
( c_24__type__159752___24t(Vvar__159753)
<=> ! [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__159753,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_159784',axiom,
! [Vvar__159785] :
( c_24__type__159784___24t(Vvar__159785)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__159785,Vv__CANONICAL__0)) ) ) ).
fof('$_type_159786',axiom,
! [Vvar__159787] :
( c_24__type__159786___24t(Vvar__159787)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__159787,Vv__CANONICAL__0)) ) ) ).
fof('$_type_159789',axiom,
! [Vvar__159790] :
( c_24__type__159789___24t(Vvar__159790)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__159790,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159793',axiom,
! [Vvar__159794] :
( c_24__type__159793___24t(Vvar__159794)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__159794,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15980',axiom,
! [Vvar__15981] :
( c_24__type__15980___24t(Vvar__15981)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8334___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__15981,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_159835',axiom,
! [Vvar__159836] :
( c_24__type__159835___24t(Vvar__159836)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8334___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)
=> t(happ(happ(happ(happ(Vvar__159836,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_159871',axiom,
! [Vvar__159872] :
( c_24__type__159871___24t(Vvar__159872)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__159872,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_159874',axiom,
! [Vvar__159875] :
( c_24__type__159874___24t(Vvar__159875)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__159875,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16001',axiom,
! [Vvar__16002] :
( c_24__type__16001___24t(Vvar__16002)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8334___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__16002,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_16174',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16175] :
( c_24__type__16174___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16175)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16175,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16213',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16214] :
( c_24__type__16213___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16214)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16214,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16252',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16253] :
( c_24__type__16252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__16253)
<=> ! [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__16253,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_163663',axiom,
! [Vvar__163664] :
( c_24__type__163663___24t(Vvar__163664)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cB___24t(happ(Vvar__163664,Vv__CANONICAL__0)) ) ) ).
fof('$_type_163834',axiom,
! [Vvar__163835] :
( c_24__type__163834___24t(Vvar__163835)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cQuotients_2equotient___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__163835,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_163839',axiom,
! [Vvar__163840] :
( c_24__type__163839___24t(Vvar__163840)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__163840,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_163842',axiom,
! [Vvar__163843] :
( c_24__type__163842___24t(Vvar__163843)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),happ(happ(Vvar__163843,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_163850',axiom,
! [Vvar__163851] :
( c_24__type__163850___24t(Vvar__163851)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__163851,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_163939',axiom,
! [Vvar__163940] :
( c_24__type__163939___24t(Vvar__163940)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eLogic_2eex___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eLogic_2eunique___24a2(Vv__CANONICAL__0,c_24__lam__163945___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__163950___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__163940,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_16519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16520] :
( c_24__type__16519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16520)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16520,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16582',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__16583] :
( c_24__type__16582___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__16583)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16583,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16646] :
( c_24__type__16645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16646)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16646,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16699',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__16700] :
( c_24__type__16699___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__16700)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__16700,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_16762',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16763] :
( c_24__type__16762___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__16763)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__16763,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_17036',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__17037] :
( c_24__type__17036___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__17037)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17037,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__17100] :
( c_24__type__17099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__17100)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17100,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17162',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__17163] :
( c_24__type__17162___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__17163)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17163,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17216',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__17217] :
( c_24__type__17216___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__17217)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__17217,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_17279',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__17280] :
( c_24__type__17279___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__17280)
<=> ! [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__17280,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_17385',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17386] :
( c_24__type__17385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17386)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17386,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17408',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17409] :
( c_24__type__17408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17409)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17409,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17431',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17432] :
( c_24__type__17431___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17432)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__17432,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_17454',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17455] :
( c_24__type__17454___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17455)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17455,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17472',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17473] :
( c_24__type__17472___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17473)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__17473,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_17498',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17499] :
( c_24__type__17498___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17499)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17499,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17517] :
( c_24__type__17516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__17517)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__17517,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_17626',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17627] :
( c_24__type__17626___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17627)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17627,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17656',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17657] :
( c_24__type__17656___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17657)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17657,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17681] :
( c_24__type__17680___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17681)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17681,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_17710',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17711] :
( c_24__type__17710___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17711)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__17711,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_17740',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17741] :
( c_24__type__17740___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17741)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17741,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17764',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17765] :
( c_24__type__17764___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17765)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17765,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_17797',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17798] :
( c_24__type__17797___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17798)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17798,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17821',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17822] :
( c_24__type__17821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17822)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17822,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_178336',axiom,
! [Vvar__178337] :
( c_24__type__178336___24t(Vvar__178337)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cQuotients_2equotient___24t(cB,cS,happ(Vvar__178337,Vv__CANONICAL__0)) ) ) ).
fof('$_type_178346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__178347] :
( c_24__type__178346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__178347)
<=> ! [Vv__CANONICAL__3] :
( cQuotients_2equotient___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> t(happ(Vvar__178347,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_178430',axiom,
! [Vvar__178431] :
( c_24__type__178430___24t(Vvar__178431)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__92___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__5),Vv__CANONICAL__6))
=> happ(Vv__CANONICAL__3,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) )
=> ! [Vv__CANONICAL__6] :
( cQuotients_2equotient___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(Vvar__178431,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__6),Vv__CANONICAL__1) ) ) ) ) ) ) ) ) ).
fof('$_type_17848',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17849] :
( c_24__type__17848___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__17849)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__17849,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__181] :
( c_24__type__180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__181)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__181,Vv__CANONICAL__3)) ) ) ).
fof('$_type_18104',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18105] :
( c_24__type__18104___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18105)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18105,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18229',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,Vvar__18230] :
( c_24__type__18229___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,Vvar__18230)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__18230,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18354',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18355] :
( c_24__type__18354___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18355)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18355,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_18479',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,Vvar__18480] :
( c_24__type__18479___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,Vvar__18480)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__18480,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_18604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18605] :
( c_24__type__18604___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18605)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__18605,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_18729',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,Vvar__18730] :
( c_24__type__18729___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,Vvar__18730)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__18730,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_18840',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18841] :
( c_24__type__18840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__18841)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__18841,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_19245',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__19246] :
( c_24__type__19245___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__19246)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19246,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19458',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19459] :
( c_24__type__19458___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19459)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19459,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19671',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__19672] :
( c_24__type__19671___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__19672)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19672,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19866',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19867] :
( c_24__type__19866___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__19867)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__19867,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_2',axiom,
! [Vv__CANONICAL__0,Vvar__3] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vvar__3)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3,Vv__CANONICAL__1)) ) ) ).
fof('$_type_20079',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20080] :
( c_24__type__20079___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20080)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20080,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_20292',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__20293] :
( c_24__type__20292___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__20293)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20293,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20506] :
( c_24__type__20505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20506)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20506,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20718',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__20719] :
( c_24__type__20718___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__20719)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__20719,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_20913',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20914] :
( c_24__type__20913___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__20914)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__20914,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_21126',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__21127] :
( c_24__type__21126___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__21127)
<=> ! [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__21127,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_21321',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21322] :
( c_24__type__21321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__21322)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__21322,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_214',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__215] :
( c_24__type__214___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__215)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__215,Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ).
fof('$_type_21473',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21474] :
( c_24__type__21473___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21474)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21474,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21523',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21524] :
( c_24__type__21523___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21524)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__21524,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_21573',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21574] :
( c_24__type__21573___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21574)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__21574,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_21615',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21616] :
( c_24__type__21615___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21616)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__21616,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_21665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21666] :
( c_24__type__21665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21666)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__21666,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21741',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21742] :
( c_24__type__21741___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21742)
<=> ! [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__21742,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_21749',axiom,
! [Vvar__21750] :
( c_24__type__21749___24t(Vvar__21750)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21750,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21853',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21854] :
( c_24__type__21853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21854)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__21854,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_21897',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21898] :
( c_24__type__21897___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21898)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__21898,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_21933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21934] :
( c_24__type__21933___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21934)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__21934,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_21977',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21978] :
( c_24__type__21977___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__21978)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__21978,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22063',axiom,
! [Vv__CANONICAL__0,Vvar__22064] :
( c_24__type__22063___24t(Vv__CANONICAL__0,Vvar__22064)
<=> ! [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__22064,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_22086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22087] :
( c_24__type__22086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22087)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__22087,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_22105',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22106] :
( c_24__type__22105___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22106)
<=> ! [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__22106,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_22109',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22110] :
( c_24__type__22109___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22110)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__22110,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_22239',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22240] :
( c_24__type__22239___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22240)
<=> ! [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__22240,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22274',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22275] :
( c_24__type__22274___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22275)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22275,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22315] :
( c_24__type__22314___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22315)
<=> ! [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__22315,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22353',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22354] :
( c_24__type__22353___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__22354)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22354,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_22388',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22389] :
( c_24__type__22388___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22389)
<=> ! [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__22389,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22423',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22424] :
( c_24__type__22423___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22424)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__22424,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_22439',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22440] :
( c_24__type__22439___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22440)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22440,Vv__CANONICAL__2)) ) ) ).
fof('$_type_22443',axiom,
! [Vvar__22444] :
( c_24__type__22443___24t(Vvar__22444)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22461',axiom,
! [Vvar__22462] :
( c_24__type__22461___24t(Vvar__22462)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___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__22462,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_22488',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22489] :
( c_24__type__22488___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22489)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22489,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22496',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22497] :
( c_24__type__22496___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22497)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22497,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22504',axiom,
! [Vvar__22505] :
( c_24__type__22504___24t(Vvar__22505)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__22505,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22534',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22535] :
( c_24__type__22534___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22535)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22535,Vv__CANONICAL__2)) ) ) ).
fof('$_type_22538',axiom,
! [Vvar__22539] :
( c_24__type__22538___24t(Vvar__22539)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22539,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22556',axiom,
! [Vvar__22557] :
( c_24__type__22556___24t(Vvar__22557)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4013___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__22557,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22584] :
( c_24__type__22583___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22584)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22584,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22591',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22592] :
( c_24__type__22591___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__22592)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22592,Vv__CANONICAL__3)) ) ) ).
fof('$_type_22599',axiom,
! [Vvar__22600] :
( c_24__type__22599___24t(Vvar__22600)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4013___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__22600,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22625',axiom,
! [Vvar__22626] :
( c_24__type__22625___24t(Vvar__22626)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22626,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22708',axiom,
! [Vvar__22709] :
( c_24__type__22708___24t(Vvar__22709)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__22709,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_23106',axiom,
! [Vvar__23107] :
( c_24__type__23106___24t(Vvar__23107)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__23107,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23158',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23159] :
( c_24__type__23158___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23159)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23159,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_23233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23234] :
( c_24__type__23233___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23234)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23234,Vv__CANONICAL__4)) ) ) ).
fof('$_type_23242',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23243] :
( c_24__type__23242___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23243)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23243,Vv__CANONICAL__4)) ) ) ).
fof('$_type_23370',axiom,
! [Vvar__23371] :
( c_24__type__23370___24t(Vvar__23371)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__23371,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23423',axiom,
! [Vvar__23424] :
( c_24__type__23423___24t(Vvar__23424)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__23424,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23426',axiom,
! [Vvar__23427] :
( c_24__type__23426___24t(Vvar__23427)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__23427,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23432',axiom,
! [Vvar__23433] :
( c_24__type__23432___24t(Vvar__23433)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23434___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23434___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23433,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23434',axiom,
! [Vvar__23435] :
( c_24__type__23434___24t(Vvar__23435)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__23435,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23454',axiom,
! [Vvar__23455] :
( c_24__type__23454___24t(Vvar__23455)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__23455,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23458',axiom,
! [Vvar__23459] :
( c_24__type__23458___24t(Vvar__23459)
<=> ! [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__23459,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23472',axiom,
! [Vvar__23473] :
( c_24__type__23472___24t(Vvar__23473)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8334___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__23473,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23557',axiom,
! [Vvar__23558] :
( c_24__type__23557___24t(Vvar__23558)
<=> ! [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__23558,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23584',axiom,
! [Vvar__23585] :
( c_24__type__23584___24t(Vvar__23585)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23585,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23588',axiom,
! [Vvar__23589] :
( c_24__type__23588___24t(Vvar__23589)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__23589,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23610',axiom,
! [Vvar__23611] :
( c_24__type__23610___24t(Vvar__23611)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__23611,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23629',axiom,
! [Vvar__23630] :
( c_24__type__23629___24t(Vvar__23630)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23610___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23610___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23630,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24065',axiom,
! [Vvar__24066] :
( c_24__type__24065___24t(Vvar__24066)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24066,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24163',axiom,
! [Vvar__24164] :
( c_24__type__24163___24t(Vvar__24164)
<=> ! [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__24164,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24324',axiom,
! [Vvar__24325] :
( c_24__type__24324___24t(Vvar__24325)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__24325,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25117',axiom,
! [Vvar__25118] :
( c_24__type__25117___24t(Vvar__25118)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22063___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__25118,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27857] :
( c_24__type__27856___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27857)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__27857,Vv__CANONICAL__2)) ) ) ).
fof('$_type_27862',axiom,
! [Vvar__27863] :
( c_24__type__27862___24t(Vvar__27863)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__27863,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_27879',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27880] :
( c_24__type__27879___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27880)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__27880,Vv__CANONICAL__2)) ) ) ).
fof('$_type_27885',axiom,
! [Vvar__27886] :
( c_24__type__27885___24t(Vvar__27886)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__27886,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_29399',axiom,
! [Vvar__29400] :
( c_24__type__29399___24t(Vvar__29400)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__29400,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31112',axiom,
! [Vvar__31113] :
( c_24__type__31112___24t(Vvar__31113)
<=> ! [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__31113,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31648',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31649] :
( c_24__type__31648___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31649)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__31649,Vv__CANONICAL__3)) ) ) ).
fof('$_type_31669',axiom,
! [Vv__CANONICAL__0,Vvar__31670] :
( c_24__type__31669___24t(Vv__CANONICAL__0,Vvar__31670)
<=> ( p(Vv__CANONICAL__0)
=> cProp___24t(Vvar__31670) ) ) ).
fof('$_type_31679',axiom,
! [Vvar__31680] :
( c_24__type__31679___24t(Vvar__31680)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__31680,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31721',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31722] :
( c_24__type__31721___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31722)
<=> ( p(happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2))
=> cProp___24t(Vvar__31722) ) ) ).
fof('$_type_31846',axiom,
! [Vvar__31847] :
( c_24__type__31846___24t(Vvar__31847)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__31847,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31853',axiom,
! [Vvar__31854] :
( c_24__type__31853___24t(Vvar__31854)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__31857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__31854,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31858] :
( c_24__type__31857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31858)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__31858) ) ) ).
fof('$_type_31860',axiom,
! [Vvar__31861] :
( c_24__type__31860___24t(Vvar__31861)
<=> ! [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__31861,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31891',axiom,
! [Vvar__31892] :
( c_24__type__31891___24t(Vvar__31892)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__31892,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_31895',axiom,
! [Vvar__31896] :
( c_24__type__31895___24t(Vvar__31896)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__31896,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31972',axiom,
! [Vvar__31973] :
( c_24__type__31972___24t(Vvar__31973)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__31973,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32790',axiom,
! [Vv__CANONICAL__0,Vvar__32791] :
( c_24__type__32790___24t(Vv__CANONICAL__0,Vvar__32791)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__32791,Vv__CANONICAL__1)) ) ) ).
fof('$_type_32803',axiom,
! [Vvar__32804] :
( c_24__type__32803___24t(Vvar__32804)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__8293___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__32808___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__32804,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32808',axiom,
! [Vv__CANONICAL__0,Vvar__32809] :
( c_24__type__32808___24t(Vv__CANONICAL__0,Vvar__32809)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__32809,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_34448',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34449] :
( c_24__type__34448___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34449)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__34449,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_34467',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34468] :
( c_24__type__34467___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34468)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34468,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34482] :
( c_24__type__34481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34482)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__34482,Vv__CANONICAL__4)) ) ) ).
fof('$_type_34574',axiom,
! [Vvar__34575] :
( c_24__type__34574___24t(Vvar__34575)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__50___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__34584___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__34575,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34584',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34585] :
( c_24__type__34584___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34585)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34585,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_37109',axiom,
! [Vvar__37110] :
( c_24__type__37109___24t(Vvar__37110)
<=> ! [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__37110,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_37126',axiom,
! [Vvar__37127] :
( c_24__type__37126___24t(Vvar__37127)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__37127,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_37429',axiom,
! [Vvar__37430] :
( c_24__type__37429___24t(Vvar__37430)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__37430,Vv__CANONICAL__0)) ) ) ).
fof('$_type_378',axiom,
! [Vvar__379] :
( c_24__type__378___24t(Vvar__379)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__379,Vv__CANONICAL__0)) ) ) ).
fof('$_type_380',axiom,
! [Vvar__381] :
( c_24__type__380___24t(Vvar__381)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__381,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38072',axiom,
! [Vvar__38073] :
( c_24__type__38072___24t(Vvar__38073)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__38073,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3847',axiom,
! [Vvar__3848] :
( c_24__type__3847___24t(Vvar__3848)
<=> ! [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__3848,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3869',axiom,
! [Vvar__3870] :
( c_24__type__3869___24t(Vvar__3870)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__3870,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3874',axiom,
! [Vvar__3875] :
( c_24__type__3874___24t(Vvar__3875)
<=> ! [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__3875,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38751',axiom,
! [Vvar__38752] :
( c_24__type__38751___24t(Vvar__38752)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__38752,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3890',axiom,
! [Vvar__3891] :
( c_24__type__3890___24t(Vvar__3891)
<=> ! [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__3891,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3893',axiom,
! [Vvar__3894] :
( c_24__type__3893___24t(Vvar__3894)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3894,Vv__CANONICAL__0)) ) ) ).
fof('$_type_38945',axiom,
! [Vvar__38946] :
( c_24__type__38945___24t(Vvar__38946)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5865___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__38946,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_38958',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38959] :
( c_24__type__38958___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38959)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(Vvar__38959,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_38965',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38966] :
( c_24__type__38965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__38966)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__38966,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_38969',axiom,
! [Vvar__38970] :
( c_24__type__38969___24t(Vvar__38970)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__38970,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_38975',axiom,
! [Vv__CANONICAL__0,Vvar__38976] :
( c_24__type__38975___24t(Vv__CANONICAL__0,Vvar__38976)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__38976,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_39223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__39224] :
( c_24__type__39223___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__39224)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39224,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39286',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__39287] :
( c_24__type__39286___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__39287)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39287,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39349',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__39350] :
( c_24__type__39349___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__39350)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__39350,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_39403',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__39404] :
( c_24__type__39403___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__39404)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__39404,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_39466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__39467] :
( c_24__type__39466___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__39467)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__39467,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_4',axiom,
! [Vvar__5] :
( c_24__type__4___24t(Vvar__5)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__5,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__4001] :
( c_24__type__4000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__4001)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__4001,Vv__CANONICAL__6)) ) ) ).
fof('$_type_40123',axiom,
! [Vvar__40124] :
( c_24__type__40123___24t(Vvar__40124)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__8334___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)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__40124,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_4013',axiom,
! [Vv__CANONICAL__0,Vvar__4014] :
( c_24__type__4013___24t(Vv__CANONICAL__0,Vvar__4014)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__4014,Vv__CANONICAL__1)) ) ) ).
fof('$_type_40221',axiom,
! [Vvar__40222] :
( c_24__type__40221___24t(Vvar__40222)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__40222,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4083',axiom,
! [Vvar__4084] :
( c_24__type__4083___24t(Vvar__4084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__92___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__4084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4186',axiom,
! [Vvar__4187] :
( c_24__type__4186___24t(Vvar__4187)
<=> ! [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__4187,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4202',axiom,
! [Vvar__4203] :
( c_24__type__4202___24t(Vvar__4203)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4203,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4209',axiom,
! [Vvar__4210] :
( c_24__type__4209___24t(Vvar__4210)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4210,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4271',axiom,
! [Vvar__4272] :
( c_24__type__4271___24t(Vvar__4272)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4272,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4358',axiom,
! [Vvar__4359] :
( c_24__type__4358___24t(Vvar__4359)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4359,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_438',axiom,
! [Vvar__439] :
( c_24__type__438___24t(Vvar__439)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__439,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4399',axiom,
! [Vvar__4400] :
( c_24__type__4399___24t(Vvar__4400)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__50___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__4400,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4409',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4410] :
( c_24__type__4409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4410)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__4410,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_4435',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4436] :
( c_24__type__4435___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4436)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__4436,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_4495',axiom,
! [Vvar__4496] :
( c_24__type__4495___24t(Vvar__4496)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__4496,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4518',axiom,
! [Vvar__4519] :
( c_24__type__4518___24t(Vvar__4519)
<=> ! [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__4519,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_4523',axiom,
! [Vvar__4524] :
( c_24__type__4523___24t(Vvar__4524)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__4524,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_4579',axiom,
! [Vvar__4580] :
( c_24__type__4579___24t(Vvar__4580)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__50___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4580,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4697',axiom,
! [Vvar__4698] :
( c_24__type__4697___24t(Vvar__4698)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__4698,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4706',axiom,
! [Vvar__4707] :
( c_24__type__4706___24t(Vvar__4707)
<=> ! [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__4707,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4750',axiom,
! [Vvar__4751] :
( c_24__type__4750___24t(Vvar__4751)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__4751,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4901',axiom,
! [Vvar__4902] :
( c_24__type__4901___24t(Vvar__4902)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__4902,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4905',axiom,
! [Vvar__4906] :
( c_24__type__4905___24t(Vvar__4906)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__4750___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4750___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__4906,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4943',axiom,
! [Vvar__4944] :
( c_24__type__4943___24t(Vvar__4944)
<=> ! [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__4944,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4983',axiom,
! [Vvar__4984] :
( c_24__type__4983___24t(Vvar__4984)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__4984,Vv__CANONICAL__0)) ) ) ).
fof('$_type_50',axiom,
! [Vv__CANONICAL__0,Vvar__51] :
( c_24__type__50___24t(Vv__CANONICAL__0,Vvar__51)
<=> ! [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__51,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_5025',axiom,
! [Vvar__5026] :
( c_24__type__5025___24t(Vvar__5026)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5026,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_52652',axiom,
! [Vvar__52653] :
( c_24__type__52652___24t(Vvar__52653)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(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)
=> t(happ(happ(happ(happ(Vvar__52653,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_53',axiom,
! [Vvar__54] :
( c_24__type__53___24t(Vvar__54)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__54,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5596',axiom,
! [Vvar__5597] :
( c_24__type__5596___24t(Vvar__5597)
<=> ! [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__5597,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5700',axiom,
! [Vvar__5701] :
( c_24__type__5700___24t(Vvar__5701)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5701,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5703',axiom,
! [Vvar__5704] :
( c_24__type__5703___24t(Vvar__5704)
<=> ! [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__5704,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5720',axiom,
! [Vvar__5721] :
( c_24__type__5720___24t(Vvar__5721)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__5721,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5724',axiom,
! [Vvar__5725] :
( c_24__type__5724___24t(Vvar__5725)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__5725,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5754',axiom,
! [Vvar__5755] :
( c_24__type__5754___24t(Vvar__5755)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__5755,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5758',axiom,
! [Vvar__5759] :
( c_24__type__5758___24t(Vvar__5759)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__5759,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5763',axiom,
! [Vvar__5764] :
( c_24__type__5763___24t(Vvar__5764)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__5764,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5782',axiom,
! [Vvar__5783] :
( c_24__type__5782___24t(Vvar__5783)
<=> ! [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__5783,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5833',axiom,
! [Vvar__5834] :
( c_24__type__5833___24t(Vvar__5834)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__5834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_5835',axiom,
! [Vvar__5836] :
( c_24__type__5835___24t(Vvar__5836)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5836,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5846',axiom,
! [Vvar__5847] :
( c_24__type__5846___24t(Vvar__5847)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__5847,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5865',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5866] :
( c_24__type__5865___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__5866)
<=> ! [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__5866,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_5872',axiom,
! [Vvar__5873] :
( c_24__type__5872___24t(Vvar__5873)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5878',axiom,
! [Vvar__5879] :
( c_24__type__5878___24t(Vvar__5879)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5879,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5992',axiom,
! [Vvar__5993] :
( c_24__type__5992___24t(Vvar__5993)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__5993,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5994',axiom,
! [Vvar__5995] :
( c_24__type__5994___24t(Vvar__5995)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__5995,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6006',axiom,
! [Vvar__6007] :
( c_24__type__6006___24t(Vvar__6007)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__6007,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6048',axiom,
! [Vvar__6049] :
( c_24__type__6048___24t(Vvar__6049)
<=> ! [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__6049,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6060',axiom,
! [Vvar__6061] :
( c_24__type__6060___24t(Vvar__6061)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__6061,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_6072',axiom,
! [Vvar__6073] :
( c_24__type__6072___24t(Vvar__6073)
<=> ! [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__6073,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_6084',axiom,
! [Vvar__6085] :
( c_24__type__6084___24t(Vvar__6085)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__6085,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6126',axiom,
! [Vvar__6127] :
( c_24__type__6126___24t(Vvar__6127)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__6127,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6177',axiom,
! [Vv__CANONICAL__0,Vvar__6178] :
( c_24__type__6177___24t(Vv__CANONICAL__0,Vvar__6178)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__6178,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_6391',axiom,
! [Vvar__6392] :
( c_24__type__6391___24t(Vvar__6392)
<=> ! [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__6392,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6443',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__6444] :
( c_24__type__6443___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__6444)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__6444,Vv__CANONICAL__6)) ) ) ).
fof('$_type_6451',axiom,
! [Vvar__6452] :
( c_24__type__6451___24t(Vvar__6452)
<=> ! [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__1 = Vv__CANONICAL__2
=> cProp___24t(happ(happ(happ(Vvar__6452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_6655',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6656] :
( c_24__type__6655___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6656)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6656,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6748',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__6749] :
( c_24__type__6748___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__6749)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6749,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6842] :
( c_24__type__6841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6842)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6842,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6923',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__6924] :
( c_24__type__6923___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__6924)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__6924,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_7016',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7017] :
( c_24__type__7016___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7017)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7017,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7098',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__7099] :
( c_24__type__7098___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__7099)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__7099,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_7191',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7192] :
( c_24__type__7191___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7192)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__7192,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_772',axiom,
! [Vvar__773] :
( c_24__type__772___24t(Vvar__773)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___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)
=> cProp___24t(happ(happ(happ(happ(Vvar__773,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_7746',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7747] :
( c_24__type__7746___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7747)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7747,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7839',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__7840] :
( c_24__type__7839___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__7840)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7840,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_784',axiom,
! [Vvar__785] :
( c_24__type__784___24t(Vvar__785)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__785,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_788',axiom,
! [Vvar__789] :
( c_24__type__788___24t(Vvar__789)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__789,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7932',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7933] :
( c_24__type__7932___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__7933)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7933,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8014',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__8015] :
( c_24__type__8014___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__8015)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__8015,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_8107',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8108] :
( c_24__type__8107___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__8108)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8108,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8189',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__8190] :
( c_24__type__8189___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__8190)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__8190,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_827',axiom,
! [Vv__CANONICAL__0,Vvar__828] :
( c_24__type__827___24t(Vv__CANONICAL__0,Vvar__828)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__828,Vv__CANONICAL__1)) ) ) ).
fof('$_type_8282',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__8283] :
( c_24__type__8282___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__8283)
<=> ! [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__8283,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_8293',axiom,
! [Vvar__8294] :
( c_24__type__8293___24t(Vvar__8294)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__8294,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8329',axiom,
! [Vvar__8330] :
( c_24__type__8329___24t(Vvar__8330)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8334___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__8334___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__8330,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8334',axiom,
! [Vv__CANONICAL__0,Vvar__8335] :
( c_24__type__8334___24t(Vv__CANONICAL__0,Vvar__8335)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8335,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8383',axiom,
! [Vvar__8384] :
( c_24__type__8383___24t(Vvar__8384)
<=> ! [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)
=> t(happ(happ(happ(Vvar__8384,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_8395',axiom,
! [Vvar__8396] :
( c_24__type__8395___24t(Vvar__8396)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__8396,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_840',axiom,
! [Vvar__841] :
( c_24__type__840___24t(Vvar__841)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__842___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__847___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__841,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8419',axiom,
! [Vvar__8420] :
( c_24__type__8419___24t(Vvar__8420)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8426___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__8420,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_842',axiom,
! [Vvar__843] :
( c_24__type__842___24t(Vvar__843)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__843,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8426',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8427] :
( c_24__type__8426___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8427)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__8427,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8450',axiom,
! [Vvar__8451] :
( c_24__type__8450___24t(Vvar__8451)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__8457___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__8451,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_8457',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8458] :
( c_24__type__8457___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8458)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8458,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_847',axiom,
! [Vv__CANONICAL__0,Vvar__848] :
( c_24__type__847___24t(Vv__CANONICAL__0,Vvar__848)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__848,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_8504',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8505] :
( c_24__type__8504___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8505)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8505,Vv__CANONICAL__3)) ) ) ).
fof('$_type_852',axiom,
! [Vv__CANONICAL__0,Vvar__853] :
( c_24__type__852___24t(Vv__CANONICAL__0,Vvar__853)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__853,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_854',axiom,
! [Vvar__855] :
( c_24__type__854___24t(Vvar__855)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__855,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8551',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8552] :
( c_24__type__8551___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__8552)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__8552,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_8586',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8587] :
( c_24__type__8586___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8587)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8587,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_86187',axiom,
! [Vvar__86188] :
( c_24__type__86187___24t(Vvar__86188)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__86188,Vv__CANONICAL__0)) ) ) ).
fof('$_type_87031',axiom,
! [Vvar__87032] :
( c_24__type__87031___24t(Vvar__87032)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__380___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__87032,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_87045',axiom,
! [Vvar__87046] :
( c_24__type__87045___24t(Vvar__87046)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4013___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))
=> cProp___24t(happ(happ(happ(happ(Vvar__87046,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_87080',axiom,
! [Vvar__87081] :
( c_24__type__87080___24t(Vvar__87081)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__87081,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_871',axiom,
! [Vvar__872] :
( c_24__type__871___24t(Vvar__872)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__872,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_87245',axiom,
! [Vvar__87246] :
( c_24__type__87245___24t(Vvar__87246)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__87246,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_876',axiom,
! [Vv__CANONICAL__0,Vvar__877] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vvar__877)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__877,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_889',axiom,
! [Vv__CANONICAL__0,Vvar__890] :
( c_24__type__889___24t(Vv__CANONICAL__0,Vvar__890)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__890,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_9',axiom,
! [Vvar__10] :
( c_24__type__9___24t(Vvar__10)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__10,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_900',axiom,
! [Vv__CANONICAL__0,Vvar__901] :
( c_24__type__900___24t(Vv__CANONICAL__0,Vvar__901)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__876___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__901,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9063',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__9064] :
( c_24__type__9063___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__9064)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9064,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_909',axiom,
! [Vv__CANONICAL__0,Vvar__910] :
( c_24__type__909___24t(Vv__CANONICAL__0,Vvar__910)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__910,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_912',axiom,
! [Vv__CANONICAL__0,Vvar__913] :
( c_24__type__912___24t(Vv__CANONICAL__0,Vvar__913)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__913,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_9164',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9165] :
( c_24__type__9164___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9165)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9165,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_92',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__93] :
( c_24__type__92___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__93)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__93,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_9265',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9266] :
( c_24__type__9265___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9266)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9266,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9355',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__9356] :
( c_24__type__9355___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__9356)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__9356,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_937',axiom,
! [Vvar__938] :
( c_24__type__937___24t(Vvar__938)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__942___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__938,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_942',axiom,
! [Vv__CANONICAL__0,Vvar__943] :
( c_24__type__942___24t(Vv__CANONICAL__0,Vvar__943)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__943,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9457] :
( c_24__type__9456___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9457)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9457,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_955',axiom,
! [Vv__CANONICAL__0,Vvar__956] :
( c_24__type__955___24t(Vv__CANONICAL__0,Vvar__956)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__942___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__956,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_9557',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9558] :
( c_24__type__9557___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9558)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9558,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_9658',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__9659] :
( c_24__type__9658___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__9659)
<=> ! [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__9659,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_966',axiom,
! [Vv__CANONICAL__0,Vvar__967] :
( c_24__type__966___24t(Vv__CANONICAL__0,Vvar__967)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__967,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_975',axiom,
! [Vv__CANONICAL__0,Vvar__976] :
( c_24__type__975___24t(Vv__CANONICAL__0,Vvar__976)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__976,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_9782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9783] :
( c_24__type__9782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9783)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9783,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_9801',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9802] :
( c_24__type__9801___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9802)
<=> ! [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__9802,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_9821',axiom,
! [Vvar__9822] :
( c_24__type__9821___24t(Vvar__9822)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__50___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__50___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__9822,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_9904',axiom,
! [Vvar__9905] :
( c_24__type__9904___24t(Vvar__9905)
<=> ! [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__9905,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9909',axiom,
! [Vvar__9910] :
( c_24__type__9909___24t(Vvar__9910)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__9910,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9914',axiom,
! [Vvar__9915] :
( c_24__type__9914___24t(Vvar__9915)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__9915,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9916',axiom,
! [Vvar__9917] :
( c_24__type__9916___24t(Vvar__9917)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__9917,Vv__CANONICAL__0)) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_B',axiom,
cType___24t(cB) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__4271___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__4901___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__4271___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__4271___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__4905___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__937___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__4186___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__5835___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__3847___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__5846___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__8293___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__4750___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__5703___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__5700___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__23557___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_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__5703___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__5596___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_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.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.x00',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).
fof('$_typeof_Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).
fof('$_typeof_Coq.Init.Byte.x02',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).
fof('$_typeof_Coq.Init.Byte.x03',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).
fof('$_typeof_Coq.Init.Byte.x04',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).
fof('$_typeof_Coq.Init.Byte.x05',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).
fof('$_typeof_Coq.Init.Byte.x06',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).
fof('$_typeof_Coq.Init.Byte.x07',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).
fof('$_typeof_Coq.Init.Byte.x08',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).
fof('$_typeof_Coq.Init.Byte.x09',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).
fof('$_typeof_Coq.Init.Byte.x0a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).
fof('$_typeof_Coq.Init.Byte.x0b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).
fof('$_typeof_Coq.Init.Byte.x0c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).
fof('$_typeof_Coq.Init.Byte.x0d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).
fof('$_typeof_Coq.Init.Byte.x0e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).
fof('$_typeof_Coq.Init.Byte.x0f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).
fof('$_typeof_Coq.Init.Byte.x10',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).
fof('$_typeof_Coq.Init.Byte.x11',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).
fof('$_typeof_Coq.Init.Byte.x12',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).
fof('$_typeof_Coq.Init.Byte.x13',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).
fof('$_typeof_Coq.Init.Byte.x14',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).
fof('$_typeof_Coq.Init.Byte.x15',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).
fof('$_typeof_Coq.Init.Byte.x16',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).
fof('$_typeof_Coq.Init.Byte.x17',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).
fof('$_typeof_Coq.Init.Byte.x18',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).
fof('$_typeof_Coq.Init.Byte.x19',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).
fof('$_typeof_Coq.Init.Byte.x1a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).
fof('$_typeof_Coq.Init.Byte.x1b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).
fof('$_typeof_Coq.Init.Byte.x1c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).
fof('$_typeof_Coq.Init.Byte.x1d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).
fof('$_typeof_Coq.Init.Byte.x1e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).
fof('$_typeof_Coq.Init.Byte.x1f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).
fof('$_typeof_Coq.Init.Byte.x20',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).
fof('$_typeof_Coq.Init.Byte.x21',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).
fof('$_typeof_Coq.Init.Byte.x22',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).
fof('$_typeof_Coq.Init.Byte.x23',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).
fof('$_typeof_Coq.Init.Byte.x24',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).
fof('$_typeof_Coq.Init.Byte.x25',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).
fof('$_typeof_Coq.Init.Byte.x26',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).
fof('$_typeof_Coq.Init.Byte.x27',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).
fof('$_typeof_Coq.Init.Byte.x28',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).
fof('$_typeof_Coq.Init.Byte.x29',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).
fof('$_typeof_Coq.Init.Byte.x2a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).
fof('$_typeof_Coq.Init.Byte.x2b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).
fof('$_typeof_Coq.Init.Byte.x2c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).
fof('$_typeof_Coq.Init.Byte.x2d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).
fof('$_typeof_Coq.Init.Byte.x2e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).
fof('$_typeof_Coq.Init.Byte.x2f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).
fof('$_typeof_Coq.Init.Byte.x30',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).
fof('$_typeof_Coq.Init.Byte.x31',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).
fof('$_typeof_Coq.Init.Byte.x32',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).
fof('$_typeof_Coq.Init.Byte.x33',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).
fof('$_typeof_Coq.Init.Byte.x34',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).
fof('$_typeof_Coq.Init.Byte.x35',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).
fof('$_typeof_Coq.Init.Byte.x36',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).
fof('$_typeof_Coq.Init.Byte.x37',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).
fof('$_typeof_Coq.Init.Byte.x38',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).
fof('$_typeof_Coq.Init.Byte.x39',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).
fof('$_typeof_Coq.Init.Byte.x3a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).
fof('$_typeof_Coq.Init.Byte.x3b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).
fof('$_typeof_Coq.Init.Byte.x3c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).
fof('$_typeof_Coq.Init.Byte.x3d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).
fof('$_typeof_Coq.Init.Byte.x3e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).
fof('$_typeof_Coq.Init.Byte.x3f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).
fof('$_typeof_Coq.Init.Byte.x40',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).
fof('$_typeof_Coq.Init.Byte.x41',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).
fof('$_typeof_Coq.Init.Byte.x42',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).
fof('$_typeof_Coq.Init.Byte.x43',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).
fof('$_typeof_Coq.Init.Byte.x44',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).
fof('$_typeof_Coq.Init.Byte.x45',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).
fof('$_typeof_Coq.Init.Byte.x46',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).
fof('$_typeof_Coq.Init.Byte.x47',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).
fof('$_typeof_Coq.Init.Byte.x48',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).
fof('$_typeof_Coq.Init.Byte.x49',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).
fof('$_typeof_Coq.Init.Byte.x4a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).
fof('$_typeof_Coq.Init.Byte.x4b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).
fof('$_typeof_Coq.Init.Byte.x4c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).
fof('$_typeof_Coq.Init.Byte.x4d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).
fof('$_typeof_Coq.Init.Byte.x4e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).
fof('$_typeof_Coq.Init.Byte.x4f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).
fof('$_typeof_Coq.Init.Byte.x50',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).
fof('$_typeof_Coq.Init.Byte.x51',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).
fof('$_typeof_Coq.Init.Byte.x52',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).
fof('$_typeof_Coq.Init.Byte.x53',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).
fof('$_typeof_Coq.Init.Byte.x54',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).
fof('$_typeof_Coq.Init.Byte.x55',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).
fof('$_typeof_Coq.Init.Byte.x56',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).
fof('$_typeof_Coq.Init.Byte.x57',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).
fof('$_typeof_Coq.Init.Byte.x58',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).
fof('$_typeof_Coq.Init.Byte.x59',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).
fof('$_typeof_Coq.Init.Byte.x5a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).
fof('$_typeof_Coq.Init.Byte.x5b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).
fof('$_typeof_Coq.Init.Byte.x5c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).
fof('$_typeof_Coq.Init.Byte.x5d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).
fof('$_typeof_Coq.Init.Byte.x5e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).
fof('$_typeof_Coq.Init.Byte.x5f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).
fof('$_typeof_Coq.Init.Byte.x60',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).
fof('$_typeof_Coq.Init.Byte.x61',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).
fof('$_typeof_Coq.Init.Byte.x62',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).
fof('$_typeof_Coq.Init.Byte.x63',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).
fof('$_typeof_Coq.Init.Byte.x64',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).
fof('$_typeof_Coq.Init.Byte.x65',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).
fof('$_typeof_Coq.Init.Byte.x66',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).
fof('$_typeof_Coq.Init.Byte.x67',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).
fof('$_typeof_Coq.Init.Byte.x68',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).
fof('$_typeof_Coq.Init.Byte.x69',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).
fof('$_typeof_Coq.Init.Byte.x6a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).
fof('$_typeof_Coq.Init.Byte.x6b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).
fof('$_typeof_Coq.Init.Byte.x6c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).
fof('$_typeof_Coq.Init.Byte.x6d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).
fof('$_typeof_Coq.Init.Byte.x6e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).
fof('$_typeof_Coq.Init.Byte.x6f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).
fof('$_typeof_Coq.Init.Byte.x70',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).
fof('$_typeof_Coq.Init.Byte.x71',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).
fof('$_typeof_Coq.Init.Byte.x72',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).
fof('$_typeof_Coq.Init.Byte.x73',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).
fof('$_typeof_Coq.Init.Byte.x74',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).
fof('$_typeof_Coq.Init.Byte.x75',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).
fof('$_typeof_Coq.Init.Byte.x76',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).
fof('$_typeof_Coq.Init.Byte.x77',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).
fof('$_typeof_Coq.Init.Byte.x78',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).
fof('$_typeof_Coq.Init.Byte.x79',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).
fof('$_typeof_Coq.Init.Byte.x7a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).
fof('$_typeof_Coq.Init.Byte.x7b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).
fof('$_typeof_Coq.Init.Byte.x7c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).
fof('$_typeof_Coq.Init.Byte.x7d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).
fof('$_typeof_Coq.Init.Byte.x7e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).
fof('$_typeof_Coq.Init.Byte.x7f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).
fof('$_typeof_Coq.Init.Byte.x80',axiom,
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fof('$_typeof_Coq.Init.Byte.x81',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).
fof('$_typeof_Coq.Init.Byte.x82',axiom,
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fof('$_typeof_Coq.Init.Byte.x83',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).
fof('$_typeof_Coq.Init.Byte.x84',axiom,
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fof('$_typeof_Coq.Init.Byte.x85',axiom,
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fof('$_typeof_Coq.Init.Byte.x86',axiom,
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fof('$_typeof_Coq.Init.Byte.x87',axiom,
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fof('$_typeof_Coq.Init.Byte.x88',axiom,
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fof('$_typeof_Coq.Init.Byte.x89',axiom,
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fof('$_typeof_Coq.Init.Byte.x8a',axiom,
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fof('$_typeof_Coq.Init.Byte.x8b',axiom,
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fof('$_typeof_Coq.Init.Byte.x8c',axiom,
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fof('$_typeof_Coq.Init.Byte.x8d',axiom,
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fof('$_typeof_Coq.Init.Byte.x8e',axiom,
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fof('$_typeof_Coq.Init.Byte.x8f',axiom,
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fof('$_typeof_Coq.Init.Byte.x90',axiom,
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fof('$_typeof_Coq.Init.Byte.x91',axiom,
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fof('$_typeof_Coq.Init.Byte.x92',axiom,
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fof('$_typeof_Coq.Init.Byte.x93',axiom,
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fof('$_typeof_Coq.Init.Byte.x94',axiom,
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fof('$_typeof_Coq.Init.Byte.x95',axiom,
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fof('$_typeof_Coq.Init.Byte.x96',axiom,
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fof('$_typeof_Coq.Init.Byte.x97',axiom,
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fof('$_typeof_Coq.Init.Byte.x98',axiom,
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fof('$_typeof_Coq.Init.Byte.x99',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).
fof('$_typeof_Coq.Init.Byte.x9a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).
fof('$_typeof_Coq.Init.Byte.x9b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).
fof('$_typeof_Coq.Init.Byte.x9c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).
fof('$_typeof_Coq.Init.Byte.x9d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).
fof('$_typeof_Coq.Init.Byte.x9e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).
fof('$_typeof_Coq.Init.Byte.x9f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).
fof('$_typeof_Coq.Init.Byte.xa0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).
fof('$_typeof_Coq.Init.Byte.xa1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).
fof('$_typeof_Coq.Init.Byte.xa2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).
fof('$_typeof_Coq.Init.Byte.xa3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).
fof('$_typeof_Coq.Init.Byte.xa4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).
fof('$_typeof_Coq.Init.Byte.xa5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).
fof('$_typeof_Coq.Init.Byte.xa6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).
fof('$_typeof_Coq.Init.Byte.xa7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).
fof('$_typeof_Coq.Init.Byte.xa8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).
fof('$_typeof_Coq.Init.Byte.xa9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa9) ).
fof('$_typeof_Coq.Init.Byte.xaa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaa) ).
fof('$_typeof_Coq.Init.Byte.xab',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exab) ).
fof('$_typeof_Coq.Init.Byte.xac',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exac) ).
fof('$_typeof_Coq.Init.Byte.xad',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exad) ).
fof('$_typeof_Coq.Init.Byte.xae',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exae) ).
fof('$_typeof_Coq.Init.Byte.xaf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaf) ).
fof('$_typeof_Coq.Init.Byte.xb0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb0) ).
fof('$_typeof_Coq.Init.Byte.xb1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb1) ).
fof('$_typeof_Coq.Init.Byte.xb2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb2) ).
fof('$_typeof_Coq.Init.Byte.xb3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb3) ).
fof('$_typeof_Coq.Init.Byte.xb4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb4) ).
fof('$_typeof_Coq.Init.Byte.xb5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb5) ).
fof('$_typeof_Coq.Init.Byte.xb6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb6) ).
fof('$_typeof_Coq.Init.Byte.xb7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).
fof('$_typeof_Coq.Init.Byte.xb8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).
fof('$_typeof_Coq.Init.Byte.xb9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).
fof('$_typeof_Coq.Init.Byte.xba',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).
fof('$_typeof_Coq.Init.Byte.xbb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).
fof('$_typeof_Coq.Init.Byte.xbc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).
fof('$_typeof_Coq.Init.Byte.xbd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).
fof('$_typeof_Coq.Init.Byte.xbe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).
fof('$_typeof_Coq.Init.Byte.xbf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).
fof('$_typeof_Coq.Init.Byte.xc0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).
fof('$_typeof_Coq.Init.Byte.xc1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).
fof('$_typeof_Coq.Init.Byte.xc2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).
fof('$_typeof_Coq.Init.Byte.xc3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).
fof('$_typeof_Coq.Init.Byte.xc4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).
fof('$_typeof_Coq.Init.Byte.xc5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).
fof('$_typeof_Coq.Init.Byte.xc6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).
fof('$_typeof_Coq.Init.Byte.xc7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).
fof('$_typeof_Coq.Init.Byte.xc8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).
fof('$_typeof_Coq.Init.Byte.xc9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).
fof('$_typeof_Coq.Init.Byte.xca',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).
fof('$_typeof_Coq.Init.Byte.xcb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).
fof('$_typeof_Coq.Init.Byte.xcc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).
fof('$_typeof_Coq.Init.Byte.xcd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).
fof('$_typeof_Coq.Init.Byte.xce',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).
fof('$_typeof_Coq.Init.Byte.xcf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).
fof('$_typeof_Coq.Init.Byte.xd0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).
fof('$_typeof_Coq.Init.Byte.xd1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).
fof('$_typeof_Coq.Init.Byte.xd2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).
fof('$_typeof_Coq.Init.Byte.xd3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).
fof('$_typeof_Coq.Init.Byte.xd4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).
fof('$_typeof_Coq.Init.Byte.xd5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).
fof('$_typeof_Coq.Init.Byte.xd6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).
fof('$_typeof_Coq.Init.Byte.xd7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).
fof('$_typeof_Coq.Init.Byte.xd8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).
fof('$_typeof_Coq.Init.Byte.xd9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).
fof('$_typeof_Coq.Init.Byte.xda',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).
fof('$_typeof_Coq.Init.Byte.xdb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).
fof('$_typeof_Coq.Init.Byte.xdc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).
fof('$_typeof_Coq.Init.Byte.xdd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).
fof('$_typeof_Coq.Init.Byte.xde',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).
fof('$_typeof_Coq.Init.Byte.xdf',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).
fof('$_typeof_Coq.Init.Byte.xe0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).
fof('$_typeof_Coq.Init.Byte.xe1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).
fof('$_typeof_Coq.Init.Byte.xe2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).
fof('$_typeof_Coq.Init.Byte.xe3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).
fof('$_typeof_Coq.Init.Byte.xe4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).
fof('$_typeof_Coq.Init.Byte.xe5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).
fof('$_typeof_Coq.Init.Byte.xe6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).
fof('$_typeof_Coq.Init.Byte.xe7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).
fof('$_typeof_Coq.Init.Byte.xe8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).
fof('$_typeof_Coq.Init.Byte.xe9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).
fof('$_typeof_Coq.Init.Byte.xea',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).
fof('$_typeof_Coq.Init.Byte.xeb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).
fof('$_typeof_Coq.Init.Byte.xec',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).
fof('$_typeof_Coq.Init.Byte.xed',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).
fof('$_typeof_Coq.Init.Byte.xee',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).
fof('$_typeof_Coq.Init.Byte.xef',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).
fof('$_typeof_Coq.Init.Byte.xf0',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).
fof('$_typeof_Coq.Init.Byte.xf1',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).
fof('$_typeof_Coq.Init.Byte.xf2',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).
fof('$_typeof_Coq.Init.Byte.xf3',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).
fof('$_typeof_Coq.Init.Byte.xf4',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).
fof('$_typeof_Coq.Init.Byte.xf5',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).
fof('$_typeof_Coq.Init.Byte.xf6',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).
fof('$_typeof_Coq.Init.Byte.xf7',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).
fof('$_typeof_Coq.Init.Byte.xf8',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).
fof('$_typeof_Coq.Init.Byte.xf9',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).
fof('$_typeof_Coq.Init.Byte.xfa',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).
fof('$_typeof_Coq.Init.Byte.xfb',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).
fof('$_typeof_Coq.Init.Byte.xfc',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).
fof('$_typeof_Coq.Init.Byte.xfd',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).
fof('$_typeof_Coq.Init.Byte.xfe',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).
fof('$_typeof_Coq.Init.Byte.xff',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).
fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__31846___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__6126___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).
fof('$_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.ID',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eID) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__5994___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__378___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__5992___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__3847___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__6084___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__3874___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__6060___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__3847___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__159716___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__159721___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__3890___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__4___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__32803___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__1267___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__3869___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__4___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__3847___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__6048___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__6006___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__6072___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__6006___24t(cCoq_2eInit_2eDatatypes_2esum) ).
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.Datatypes.xorb',axiom,
c_24__type__3847___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__5878___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__24163___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__378___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__378___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__4202___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__4750___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__4202___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__378___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__4186___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__4202___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__4271___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__4271___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__4271___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__40221___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__22461___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__22556___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__4518___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__27862___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__27885___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__4523___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__22443___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__22504___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__22538___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__22599___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__4495___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__22625___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__4579___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__8395___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__8419___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__8450___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__8383___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__52652___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__4399___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__4399___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__34574___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__34574___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
c_24__type__38969___24t(cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
c_24__type__5872___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
c_24__type__38945___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
c_24__type__5878___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalDependentChoice_on',axiom,
c_24__type__5878___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
c_24__type__5878___24t(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
c_24__type__5872___24t(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
c_24__type__5872___24t(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.BoolP',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.GodelDummett',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eGodelDummett) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.IndependenceOfGeneralPremises',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.Minimal',axiom,
c_24__type__87031___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimal) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.provable_prop_extensionality',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eprovable__prop__extensionality) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__3893___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.Description.constructive_definite_description',axiom,
c_24__type__163939___24t(cCoq_2eLogic_2eDescription_2econstructive__definite__description) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__87045___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
c_24__type__31853___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__6451___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__4706___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__4706___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__23432___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__4706___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__4706___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.peano_rect',axiom,
c_24__type__840___24t(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__871___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__4697___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__788___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__788___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__23423___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__23434___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__4697___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__4697___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__4697___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__4697___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__788___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__788___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__23423___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__23426___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__4905___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_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__1246___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__1259___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__1259___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__1206___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__1206___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__1234___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__5025___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__5025___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__5025___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__159874___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__4983___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__23458___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__31972___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__23454___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__23472___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__4943___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__4943___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__4943___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__86187___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__86187___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__38072___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__4943___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__1206___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__159871___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__9914___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__9904___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__9909___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__9916___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__24324___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.Rge',axiom,
c_24__type__10075___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__10075___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__9916___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__10075___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__10075___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__10071___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__9916___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__10071___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__10077___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__10163___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__53___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.commut',axiom,
c_24__type__438___24t(cCoq_2eRelations_2eRelation__Definitions_2ecommut) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__53___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__438___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__53___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__4___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__438___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__53___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__53___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__772___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__784___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__53___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Cpo.Chain',axiom,
c_24__type__4___24t(cCoq_2eSets_2eCpo_2eChain) ).
fof('$_typeof_Coq.Sets.Cpo.Cpo',axiom,
c_24__type__4___24t(cCoq_2eSets_2eCpo_2eCpo) ).
fof('$_typeof_Coq.Sets.Ensembles.Ensemble',axiom,
c_24__type__4___24t(cCoq_2eSets_2eEnsembles_2eEnsemble) ).
fof('$_typeof_Coq.Sets.Ensembles.In',axiom,
c_24__type__9___24t(cCoq_2eSets_2eEnsembles_2eIn) ).
fof('$_typeof_Coq.Sets.Ensembles.Included',axiom,
c_24__type__14___24t(cCoq_2eSets_2eEnsembles_2eIncluded) ).
fof('$_typeof_Coq.Sets.Image.injective',axiom,
c_24__type__4083___24t(cCoq_2eSets_2eImage_2einjective) ).
fof('$_typeof_Coq.Sets.Partial_Order.PO',axiom,
c_24__type__4___24t(cCoq_2eSets_2ePartial__Order_2ePO) ).
fof('$_typeof_Coq.Sets.Partial_Order.Rel',axiom,
c_24__type__4___24t(cCoq_2eSets_2ePartial__Order_2eRel) ).
fof('$_typeof_Coq.Sets.Relations_1.Antisymmetric',axiom,
c_24__type__4358___24t(cCoq_2eSets_2eRelations__1_2eAntisymmetric) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__4___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__5833___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('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__29399___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__9821___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__4706___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__4706___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__4271___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__4271___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.eq',axiom,
c_24__type__5025___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
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__5025___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__5025___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
c_24__type__31112___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__1193___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__1193___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).
fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__8293___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__37429___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__23106___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__1193___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__1193___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__23629___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__1193___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__1193___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__1193___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__1193___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__5724___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__5758___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__38751___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__5754___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__23610___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__5782___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__23610___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__23584___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__5763___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__5724___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__5724___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__5720___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__5724___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__5758___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__38751___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__23588___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__5782___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.eqm',axiom,
c_24__type__87245___24t(cCoq_2eZArith_2eZdiv_2eeqm) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__4209___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__4209___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__1208___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
c_24__type__4271___24t(cCoq_2eZArith_2eZnat_2eneq) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__10163___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__23370___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__159727___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__159724___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__159740___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__6391___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__159732___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).
fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).
fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__159793___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
c_24__type__159789___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__159789___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
c_24__type__159793___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).
fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
c_24__type__159789___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).
fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
c_24__type__159784___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__159786___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__10105___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__31891___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_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.PolC',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__37126___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__22708___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__37109___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__6006___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__31860___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__159747___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__87080___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__159752___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__788___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__8329___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__8329___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).
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__15942___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__15942___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__15948___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__15953___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__15945___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__15953___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__15962___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__15953___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__31895___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__25117___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__40123___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__21749___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__21749___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__159835___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__788___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__16001___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__15980___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__24065___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__24065___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_Quotients.InducedFunction2.projf',axiom,
c_24__type__178336___24t(cQuotients_2eInducedFunction2_2eprojf) ).
fof('$_typeof_Quotients.equiv_class',axiom,
c_24__type__163850___24t(cQuotients_2eequiv__class) ).
fof('$_typeof_Quotients.equiv_classes',axiom,
c_24__type__163842___24t(cQuotients_2eequiv__classes) ).
fof('$_typeof_Quotients.induced_function',axiom,
c_24__type__178430___24t(cQuotients_2einduced__function) ).
fof('$_typeof_Quotients.quotient',axiom,
c_24__type__163839___24t(cQuotients_2equotient) ).
fof('$_typeof_Quotients.quotient_projection',axiom,
c_24__type__163834___24t(cQuotients_2equotient__projection) ).
fof('$_typeof_R',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cR) ).
fof('$_typeof_S',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cB,cS) ).
fof('$_typeof_f',axiom,
c_24__type__163663___24t(cf) ).
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.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_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).
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.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.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_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
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.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_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).
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.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.divide_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).
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_le_incl',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_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_stepl',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
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_sym_iff',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.induction',axiom,
! [V0__A] :
( c_24__type__380___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__380,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,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.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_ge_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_2ele___24a2(V1__m,V0__n) ) ) ) ).
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_ind',axiom,
! [V0__A] :
( c_24__type__380___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__380,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eInit_2eDatatypes_2enat,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4271,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__380,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)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V2__m)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V3__n,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)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
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_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_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4271,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__380,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_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_exists_pred',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V1__n)
=> ? [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k)
& cCoq_2eInit_2ePeano_2ele___24a2(V0__z,V3__k) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_ge_cases',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_ind',axiom,
! [V0__A] :
( c_24__type__380___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__380,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)))
=> ( ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eInit_2eDatatypes_2enat,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4271,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__380,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)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m))) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__n,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)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
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_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_l',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),V1__m)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_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_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
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__4271,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__380,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_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.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.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__942___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__942___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__912___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__955___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__966___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__942___24a1(V0__A),c_24__type__975___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__912___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),V1__Aeq))),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( p(c_24False)
=> V0__b = V1__b_27 ) ) ) ).
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.trans_eq_bool',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__380___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.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__975___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_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Logic.ChoiceFacts.proj1_inf',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
& p(V1__B) )
=> p(V0__A) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.BoolP_elim',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ( p(V0__C)
=> ( p(V0__C)
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eBoolP)
=> p(V0__C) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.FalseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.TrueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.aux',axiom,
! [V0__bool] :
( cProp___24t(V0__bool)
=> ( p(V0__bool)
=> ( p(V0__bool)
=> ( ! [V3__C] :
( cProp___24t(V3__C)
=> ( p(V3__C)
=> ( p(V3__C)
=> ( p(V0__bool)
=> p(V3__C) ) ) ) )
=> ( ! [V4__C] :
( cProp___24t(V4__C)
=> ( p(V4__C)
=> ( p(V4__C)
=> c_24Proof = c_24Proof ) ) )
=> ( ! [V5__C] :
( cProp___24t(V5__C)
=> ( p(V5__C)
=> ( p(V5__C)
=> c_24Proof = c_24Proof ) ) )
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
=> ( ! [V7__P] :
( c_24__type__31669___24t(V0__bool,V7__P)
=> ( p(V7__P)
=> ( p(V7__P)
=> ( p(V0__bool)
=> p(V7__P) ) ) ) )
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.boolP_ind',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(V0__P) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.falseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__31679___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__31721___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__31844___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.prop_ext_A_eq_A_imp_A',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ( p(V1__A)
=> c_24__prop__5913___24a1(V1__A) = V1__A ) ) ) ).
fof('Coq.Logic.ClassicalFacts.trueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__2___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.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4013___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.Peirce',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( ( ( p(V0__P)
=> p(c_24False) )
=> p(V0__P) )
=> p(V0__P) ) ) ).
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_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) )
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_and_or2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ( p(V0__P)
| p(V2__R) )
=> ( p(V1__Q)
| p(V2__R) ) ) ) ) ) ) ).
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.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
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.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_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.EqdepFacts.internal_eq_sym_internal',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
=> V2__y = V1__x ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.PI.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.ProofIrrelevanceTheory.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4013___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.ProofIrrelevance.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PredExt_imp_PropFunExt',axiom,
( ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__2___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__2___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
<=> p(happ(V2__Q,V3__x)) ) )
=> V1__P = V2__Q ) ) ) )
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__P] :
( c_24__type__2___24t(V1__A,V2__P)
=> ! [V3__Q] :
( c_24__type__2___24t(V1__A,V3__Q)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> happ(V2__P,V4__x) = happ(V3__Q,V4__x) )
=> V2__P = V3__Q ) ) ) ) ) ).
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.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_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
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.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_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
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_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
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.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.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V0__n) ) ).
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.eq_le_incl',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_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_stepl',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
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_sym_iff',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.induction',axiom,
! [V0__A] :
( c_24__type__854___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__854,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,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.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_antisymm',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_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ge_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_2ele___24a2(V1__m,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_ind',axiom,
! [V0__A] :
( c_24__type__854___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__854,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__A,V2__n))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eNumbers_2eBinNums_2eN,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4706,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__854,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)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eNumbers_2eBinNums_2eN0),V2__m)) )
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V3__n,V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).
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__4706,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__854,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_exists_pred',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__z,V1__n)
=> ? [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__k)
& V1__n = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__k)
& cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__z,V3__k) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ge_cases',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(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ind',axiom,
! [V0__A] :
( c_24__type__854___24t(V0__A)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__854,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e),V0__A)
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__n)))
=> ( ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__n,V4__m)
=> ( p(happ(V0__A,V4__m))
=> p(happ(V0__A,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) )
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__n,V5__m)
=> p(happ(V0__A,V5__m)) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ind_rel',axiom,
! [V0__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cCoq_2eNumbers_2eBinNums_2eN,V0__R)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4706,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__854,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)),V0__R)
=> ( ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> p(happ(happ(V0__R,cCoq_2eNumbers_2eBinNums_2eN0),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__m))) )
=> ( ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V3__n,V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)),cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V4__m))) ) ) ) )
=> ! [V4__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V4__n,V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ) ).
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_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_l',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(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.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.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__4706,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__854,cCoq_2eNArith_2eBinNat_2eN_2eeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,cCoq_2eNArith_2eBinNat_2eN_2eeq,c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2elt) ).
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.peano_ind',axiom,
! [V0__P] :
( c_24__type__854___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.peano_rect_succ',axiom,
! [V0__P] :
( c_24__type__842___24t(V0__P)
=> ! [V1__a] :
( t(V1__a,happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [V2__f] :
( c_24__type__852___24t(V0__P,V2__f)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)) = happ(happ(V2__f,V3__n),cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__876___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__876___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__912___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__889___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__900___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__876___24a1(V0__A),c_24__type__909___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__912___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,V0__A,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),V1__Aeq))),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
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_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).
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.Relations.Operators_Properties.clos_r_clos_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V6__z)
=> p(happ(V3__P,V6__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__2___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( p(happ(V2__P,V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V3__z)
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_is_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_clos_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_is_preorder',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,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_transp_permute',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__R),V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__R),V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.rt1n_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__2___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__y,V3__z)
=> ( p(happ(V2__P,V6__y))
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_PER',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_order',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_antisym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',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_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
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.Relations.Relation_Operators.clos_refl_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__2___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__50___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V2__x),V3__y))
| p(happ(happ(V1__R,V3__y),V2__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V3__y),V4__z))
| p(happ(happ(V1__R,V4__z),V3__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relations.inverse_image_of_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__92___24t(V0__A,V1__B,V2__f)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__117___24a3(V0__A,V1__B,V2__f)) ) ) ) ).
fof('Coq.Relations.Relations.inverse_image_of_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__92___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__105___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___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.Sets.Ensembles.Extensionality_Ensembles',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__A,V2__B)
=> V1__A = V2__B ) ) ) ) ).
fof('Coq.Sets.Ensembles.Full_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Image.Im_def',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__V] :
( cType___24t(V1__V)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__f] :
( c_24__type__92___24t(V0__U,V1__V,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V4__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__V,cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,V2__X,V3__f),happ(V3__f,V4__x)) ) ) ) ) ) ) ).
fof('Coq.Sets.Image.Im_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__V] :
( cType___24t(V1__V)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ! [V3__f] :
( c_24__type__92___24t(V0__U,V1__V,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V4__x)
=> ! [V6__y] :
( t(V6__y,V1__V)
=> ( V6__y = happ(V3__f,V4__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__V,cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,V2__X,V3__f),V6__y) ) ) ) ) ) ) ) ) ).
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.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).
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.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ 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))
=> 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_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
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.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x) ) ).
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.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_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.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,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__23626___24a2(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_stepl',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
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
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.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)
=> 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
| 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)
=> ( 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_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1193,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__4209,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_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)
=> ( 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))
| cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n) ) ) ) ).
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))
=> 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))
=> ( 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_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_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
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_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_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.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__87237___24a2(V0__x,V1__y)) ) ) ).
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.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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___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_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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___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.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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___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.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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___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.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__8334___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__8334___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__912___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_rt',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__8334___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__8334___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__8334___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__912___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__50___24t(V0__R,V7__req)
=> ( ! [V8__x] :
( t(V8__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
=> ( ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
=> ( ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
=> ( ! [V12__x] :
( t(V12__x,V0__R)
=> ! [V13__y] :
( t(V13__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ! [V15__z] :
( t(V15__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
=> ( ! [V14__x] :
( t(V14__x,V0__R)
=> ! [V15__y] :
( t(V15__y,V0__R)
=> ! [V16__z] :
( t(V16__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Quotients.R_impl_equality_of_equiv_class',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> cQuotients_2eequiv__class___24a3(V0__A,V1__R,V3__x) = cQuotients_2eequiv__class___24a3(V0__A,V1__R,V4__y) ) ) ) ) ) ) ).
fof('Quotients.description_of_fbar',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__A,V2__R)
=> ! [V3__f] :
( c_24__type__92___24t(V0__A,V1__B,V3__f)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V6__y))
=> happ(V3__f,V5__x) = happ(V3__f,V6__y) ) ) )
=> ! [V6__xbar] :
( cQuotients_2equotient___24t(V0__A,V2__R,V6__xbar)
=> cCoq_2eInit_2eLogic_2eex___24a2(V1__B,cCoq_2eInit_2eLogic_2eunique___24a2(V1__B,c_24__lam__178456___24a5(V0__A,V1__B,V2__R,V3__f,V6__xbar))) ) ) ) ) ) ) ) ).
fof('Quotients.equality_of_equiv_class_impl_R',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cQuotients_2eequiv__class___24a3(V0__A,V1__R,V3__x) = cQuotients_2eequiv__class___24a3(V0__A,V1__R,V4__y)
=> p(happ(happ(V1__R,V3__x),V4__y)) ) ) ) ) ) ) ).
fof('Quotients.equiv_class_in_quotient',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),cQuotients_2eequiv__classes___24a2(V0__A,V1__R),cQuotients_2eequiv__class___24a3(V0__A,V1__R,V2__x)) ) ) ) ).
fof('Quotients.induced_function_correct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__A,V2__R)
=> ! [V3__f] :
( c_24__type__92___24t(V0__A,V1__B,V3__f)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V6__y))
=> happ(V3__f,V5__x) = happ(V3__f,V6__y) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> cQuotients_2einduced__function___24a5(V0__A,V1__B,V2__R,V3__f,cQuotients_2equotient__projection___24a3(V0__A,V2__R,V6__x)) = happ(V3__f,V6__x) ) ) ) ) ) ) ) ).
fof('Quotients.induced_function_unique',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__A,V2__R)
=> ! [V3__f] :
( c_24__type__92___24t(V0__A,V1__B,V3__f)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V6__y))
=> happ(V3__f,V5__x) = happ(V3__f,V6__y) ) ) )
=> ! [V6__fbar] :
( c_24__type__178346___24t(V0__A,V1__B,V2__R,V6__fbar)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> happ(V6__fbar,cQuotients_2equotient__projection___24a3(V0__A,V2__R,V7__x)) = happ(V3__f,V7__x) )
=> ! [V8__xbar] :
( cQuotients_2equotient___24t(V0__A,V2__R,V8__xbar)
=> happ(V6__fbar,V8__xbar) = cQuotients_2einduced__function___24a5(V0__A,V1__B,V2__R,V3__f,V8__xbar) ) ) ) ) ) ) ) ) ) ).
fof('Quotients.quotient_projection_collapses_R',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> ! [V3__x1] :
( t(V3__x1,V0__A)
=> ! [V4__x2] :
( t(V4__x2,V0__A)
=> ( p(happ(happ(V1__R,V3__x1),V4__x2))
=> cQuotients_2equotient__projection___24a3(V0__A,V1__R,V3__x1) = cQuotients_2equotient__projection___24a3(V0__A,V1__R,V4__x2) ) ) ) ) ) ) ).
fof('Quotients.quotient_projection_correct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__A),c_24__lam__163830___24a2(V0__A,V1__R),cQuotients_2equotient__projection___24a3(V0__A,V1__R,V2__x)) = cQuotients_2eequiv__class___24a3(V0__A,V1__R,V2__x) ) ) ) ).
fof('Quotients.quotient_projection_minimally_collapses_R',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> ! [V3__x1] :
( t(V3__x1,V0__A)
=> ! [V4__x2] :
( t(V4__x2,V0__A)
=> ( cQuotients_2equotient__projection___24a3(V0__A,V1__R,V3__x1) = cQuotients_2equotient__projection___24a3(V0__A,V1__R,V4__x2)
=> p(happ(happ(V1__R,V3__x1),V4__x2)) ) ) ) ) ) ) ).
fof('Quotients.quotient_projection_surjective',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__xbar] :
( cQuotients_2equotient___24t(V0__A,V1__R,V2__xbar)
=> ? [V3__x] :
( t(V3__x,V0__A)
& cQuotients_2equotient__projection___24a3(V0__A,V1__R,V3__x) = V2__xbar ) ) ) ) ).
fof('ZornsLemma.EnsemblesSpec.intro_characteristic_sat',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( c_24__type__2___24t(V0__X,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P),V2__x) ) ) ) ) ).
fof('ZornsLemma.Proj1SigInjective.subset_eq_compatT',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__2___24t(V0__U,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( p(happ(V1__P,V2__x))
=> ( p(happ(V1__P,V3__y))
=> ( V2__x = V3__y
=> cCoq_2eInit_2eSpecif_2eexist___24a3(V0__U,V1__P,V2__x) = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__U,V1__P,V3__y) ) ) ) ) ) ) ) ).
fof(equivR,axiom,
cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(cA,cR) ).
fof(equivS,axiom,
cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(cB,cS) ).
fof(well_defined2,axiom,
! [V0__a1] :
( cA___24t(V0__a1)
=> ! [V1__a2] :
( cA___24t(V1__a2)
=> ( cR___24a2(V0__a1,V1__a2)
=> cS___24a2(cf___24a1(V0__a1),cf___24a1(V1__a2)) ) ) ) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Quotients.quotient_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuotients_2equotient,V_24X1),V_24X2) = cQuotients_2equotient___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Singleton_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Relations.Relation_Definitions.preorder_$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('$adef_Coq.Init.Datatypes.None_$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('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_Coq.ZArith.BinIntDef.Z.modulo_$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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_4325_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__4325,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__4325___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.micromega.DeclConstant.GT_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eGT,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eGT___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$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_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.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_Coq.Sets.Ensembles.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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_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_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_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Partial_Order.Carrier_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eCarrier__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$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.setoid_ring.Ring_polynom.mkmult_pow_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Ensembles.Empty_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Quotients.equiv_class_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuotients_2eequiv__class,V_24X1),V_24X2) = cQuotients_2eequiv__class___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Relations.Relation_Definitions.commut_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ecommut,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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_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.Sets.Ensembles.Singleton_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V_24X1,V_24X2) ).
fof('$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.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_Quotients.quotient_projection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuotients_2equotient__projection,V_24X1),V_24X2),V_24X3) = cQuotients_2equotient__projection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalDependentChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalDependentChoice__on___24a1(V_24X1) ) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_4_P\'_810_$a1',axiom,
! [V_24X1] : happ(c_24__let__4__P_27__810,V_24X1) = c_24__let__4__P_27__810___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___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('$adef_$_lam_859_$a1',axiom,
! [V_24X1] : happ(c_24__lam__859,V_24X1) = c_24__lam__859___24a1(V_24X1) ).
fof('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$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.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_23417_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__23417,V_24X1),V_24X2),V_24X3) = c_24__prop__23417___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Union_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eUnion,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eUnion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$10134_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2410134,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2410134___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Quotients.equiv_classes_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cQuotients_2eequiv__classes,V_24X1),V_24X2) = cQuotients_2eequiv__classes___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_$_prop_40253_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__40253,V_24X1),V_24X2) = c_24__prop__40253___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$10156_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2410156___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Relations_1.Antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eAntisymmetric,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Sets.Finite_sets.cardinal_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eFinite__sets_2ecardinal,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_105_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__105,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__105___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$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_$_lam_178372_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__178372,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__178372___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
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('$adef_Coq.Sets.Partial_Order.covers_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2ecovers,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
<=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).
fof('$adef_Coq.Sets.Ensembles.Inhabited_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eInhabited,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_859_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__859,V_24X1),V_24X2) = c_24__lam__859___24a2(V_24X1,V_24X2) ).
fof('$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.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.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_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_$_prop_23415_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__23415,V_24X1),V_24X2),V_24X3) = c_24__prop__23415___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_159868_$a1',axiom,
! [V_24X1] : happ(c_24__lam__159868,V_24X1) = c_24__lam__159868___24a1(V_24X1) ).
fof('$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.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$23516_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2423516,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2423516___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('$adef_Coq.Init.Nat.pow_$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('$adef_Coq.micromega.Refl.make_conj_$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('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Symmetric_$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('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Lists.SetoidList.transpose_restr_$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('$adef_Coq.Init.Wf.Acc_$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('$adef_$_prop_23626_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__23626,V_24X1),V_24X2) = c_24__prop__23626___24a2(V_24X1,V_24X2) ).
fof('$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.Logic.Description.constructive_definite_description_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLogic_2eDescription_2econstructive__definite__description,V_24X1),V_24X2),V_24X3) = cCoq_2eLogic_2eDescription_2econstructive__definite__description___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Relations_1.Order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eOrder,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(V_24X1,V_24X2) ) ).
fof('$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.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.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_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$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.Relations.Relation_Operators.clos_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_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.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.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_15966_15969_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__15966__15969,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__15966__15969___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
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('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
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('$adef_Coq.Relations.Relation_Operators.transp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___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('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_163950_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__163950,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__163950___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$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.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Sets.Ensembles.Full_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eFull__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Quotients.equiv_class_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuotients_2eequiv__class,V_24X1),V_24X2),V_24X3) = cQuotients_2eequiv__class___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_925_$a1',axiom,
! [V_24X1] : happ(c_24__lam__925,V_24X1) = c_24__lam__925___24a1(V_24X1) ).
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('$adef_$_prop_23412_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__23412,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__23412___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Ensembles.Triple_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eTriple,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eSets_2eEnsembles_2eTriple___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
fof('$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_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_$_case_Coq.Init.Datatypes.prod$21728_$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_2421728,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_2421728___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
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('$adef_Coq.ZArith.BinInt.Z.lt_$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('$adef_Coq.Sets.Cpo.Definition_of_cpo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eDefinition__of__cpo,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Cpo_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eCpo_2eCpo,V_24X1) = cCoq_2eSets_2eCpo_2eCpo___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___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('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_$_lam_925_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__925,V_24X1),V_24X2) = c_24__lam__925___24a2(V_24X1,V_24X2) ).
fof('$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.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$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.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.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.Logic.ChoiceFacts.FunctionalChoice_on_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.NArith.BinNat.N.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Lists.SetoidList.eqlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eeqlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_lam_117_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__117,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__117___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_23416_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__23416,V_24X1),V_24X2),V_24X3) = c_24__prop__23416___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_31844_$a1',axiom,
! [V_24X1] : happ(c_24__prop__31844,V_24X1) = c_24__prop__31844___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('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
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('$adef_Coq.Sets.Ensembles.Union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eUnion,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.Sorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eSorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eSorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
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('$adef_Coq.Init.Specif.exist_$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('$adef_Coq.Init.Specif.projT1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_163950_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__163950,V_24X1),V_24X2) = c_24__lam__163950___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_40254_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__40254,V_24X1),V_24X2),V_24X3) = c_24__prop__40254___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$10151_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2410151,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2410151___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___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('$adef_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___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('$adef_Coq.Sets.Ensembles.Disjoint_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eDisjoint,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V_24X1) ).
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('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$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('$adef_Coq.micromega.EnvRing.Pc_$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('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.clause_$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('$adef_Coq.ZArith.BinInt.Z.divide_$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('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___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('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
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('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___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('$adef_Coq.ZArith.Znat.neq_$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('$adef_Coq.Init.Nat.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.N$824_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eN_24824,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_24824___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_178372_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__178372,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__178372___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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_$_lam_159864_$a1',axiom,
! [V_24X1] : happ(c_24__lam__159864,V_24X1) = c_24__lam__159864___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_105_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__105,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__105___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_163830_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__163830,V_24X1),V_24X2) = c_24__lam__163830___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___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('$adef_Coq.NArith.BinNat.N.le_$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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$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('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___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('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_let_4_P\'_810_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__P_27__810,V_24X1),V_24X2) = c_24__let__4__P_27__810___24a2(V_24X1,V_24X2) ).
fof('$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.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_lam_163945_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__163945,V_24X1),V_24X2) = c_24__lam__163945___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
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('$adef_Coq.Reals.Rfunctions.ZintPos_$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('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.Tauto.Cj_$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('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_178456_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__178456,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__178456___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_5_f\'_811_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__5__f_27__811,V_24X1),V_24X2),V_24X3) = c_24__let__5__f_27__811___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___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('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on___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('$adef_Coq.Init.Datatypes.app_$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('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Operators.transp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Quotients.InducedFunction2.projf_$a1',axiom,
! [V_24X1] : happ(cQuotients_2eInducedFunction2_2eprojf,V_24X1) = cQuotients_2eInducedFunction2_2eprojf___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl___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('$adef_Coq.Sets.Ensembles.Couple_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eCouple,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eCouple___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Cpo.Definition_of_chain_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eDefinition__of__chain,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$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('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
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('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
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('$adef_$_lam_159864_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__159864,V_24X1),V_24X2) = c_24__lam__159864___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_178456_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__178456,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__178456___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.hd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___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('$adef_Coq.setoid_ring.Ring_polynom.Peq_$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('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eidentity___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('$adef_Coq.Init.Nat.eqb_$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('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$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('$adef_Coq.Logic.EqdepFacts.Streicher_K_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_87237_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__87237,V_24X1),V_24X2) = c_24__prop__87237___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$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_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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.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.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.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.same_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.equiv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequiv,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Cpo.Complete_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eCpo_2eComplete,V_24X1),V_24X2))
<=> cCoq_2eSets_2eCpo_2eComplete___24a2(V_24X1,V_24X2) ) ).
fof('$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_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_$_prop_40255_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__40255,V_24X1),V_24X2),V_24X3) = c_24__prop__40255___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_S_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cS,V_24X1),V_24X2))
<=> cS___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
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('$adef_Coq.Init.Nat.add_$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('$adef_Coq.NArith.BinNat.N.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Cpo.Chain_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eCpo_2eChain,V_24X1) = cCoq_2eSets_2eCpo_2eChain___24a1(V_24X1) ).
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('$adef_Coq.Classes.Morphisms.Proper_$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('$adef_Coq.Init.Logic.unique_$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('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Logic.ClassicalFacts.retract_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eClassicalFacts_2eretract,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_117_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__117,V_24X1),V_24X2),V_24X3) = c_24__lam__117___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.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_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_$_lam_163945_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__163945,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__163945___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Relations.Relation_Definitions.inclusion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___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('$adef_Coq.Lists.SetoidList.InA_$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('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$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('$adef_Coq.Sets.Ensembles.Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$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('$adef_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on___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('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on,V_24X1))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V_24X1) ) ).
fof('$adef_$_lam_163830_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__163830,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__163830___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$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.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.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.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$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_Quotients.induced_function_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuotients_2einduced__function,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuotients_2einduced__function___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_lam_178387_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__178387,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__178387___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
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('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$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('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_23414_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__23414,V_24X1),V_24X2),V_24X3) = c_24__prop__23414___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_4325_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__4325,V_24X1),V_24X2),V_24X3) = c_24__lam__4325___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_178387_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__178387,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__178387___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$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.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
fof('$adef_f_$a1',axiom,
! [V_24X1] : happ(cf,V_24X1) = cf___24a1(V_24X1) ).
fof('$adef_Quotients.equiv_class_in_quotient_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cQuotients_2eequiv__class__in__quotient,V_24X1),V_24X2),V_24X3) = cQuotients_2eequiv__class__in__quotient___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Zdiv.eqm_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZdiv_2eeqm,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZdiv_2eeqm___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_Coq.Sets.Partial_Order.Strict_Rel_of_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
<=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).
fof('$adef_$_lam_159857_$a1',axiom,
! [V_24X1] : happ(c_24__lam__159857,V_24X1) = c_24__lam__159857___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_4329_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__4329,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__4329___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$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.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.Sets.Partial_Order.Definition_of_PO_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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.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.PArith.BinPos.Pos.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$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.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.Sets.Image.Im_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eImage_2eIm,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eImage_2eIm___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).
fof('$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_$_fix_23532_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__23532__v__CANONICAL__0,V_24X1) = c_24__fix__23532__v__CANONICAL__0___24a1(V_24X1) ).
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('$adef_$_prop_5913_$a1',axiom,
! [V_24X1] : happ(c_24__prop__5913,V_24X1) = c_24__prop__5913___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_4329_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__4329,V_24X1),V_24X2),V_24X3) = c_24__lam__4329___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___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('$adef_Coq.Init.Peano.ge_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
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('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_R_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cR,V_24X1),V_24X2))
<=> cR___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('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$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('$adef_Coq.PArith.BinPosDef.Pos.mul_$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('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_Coq.Sets.Ensembles.Same_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSame__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Quotients.description_of_fbar_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cQuotients_2edescription__of__fbar,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cQuotients_2edescription__of__fbar___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_23413_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__23413,V_24X1),V_24X2),V_24X3) = c_24__prop__23413___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_6_p_15968_15970_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__15968__15970,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__15968__15970___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_23418_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__23418,V_24X1),V_24X2) = c_24__prop__23418___24a2(V_24X1,V_24X2) ).
fof('$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.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_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_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.PArith.BinPosDef.Pos.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$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.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$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.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).
fof('$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.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_5_f\'_811_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__5__f_27__811,V_24X1),V_24X2) = c_24__let__5__f_27__811___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('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___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('$adef_Coq.Logic.ClassicalFacts.has_fixpoint_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint,V_24X1))
<=> cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(V_24X1) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Sets.Partial_Order.Rel_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePartial__Order_2eRel,V_24X1) = cCoq_2eSets_2ePartial__Order_2eRel___24a1(V_24X1) ).
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('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
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('$adef_Coq.Lists.List.fold_right_$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('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Init.Specif.left_$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('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Image.injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eImage_2einjective,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eImage_2einjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Sets.Image.Im_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eSets_2eImage_2eIm,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eSets_2eImage_2eIm___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Sets.Partial_Order.PO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePartial__Order_2ePO,V_24X1) = cCoq_2eSets_2ePartial__Order_2ePO___24a1(V_24X1) ).
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('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Ensembles.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eIn,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Ensemble_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEnsemble,V_24X1) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.add_$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('$adef_$_lam_159857_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__159857,V_24X1),V_24X2) = c_24__lam__159857___24a2(V_24X1,V_24X2) ).
fof('$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_$_type_8189',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8189___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8189___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).
fof('$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_3874',axiom,
! [V_24Y] :
( c_24__type__3874___24t(V_24Y)
<=> t(V_24Y,c_24__type__3874) ) ).
fof('$tdef_$_type_163663',axiom,
! [V_24Y] :
( c_24__type__163663___24t(V_24Y)
<=> t(V_24Y,c_24__type__163663) ) ).
fof('$tdef_$_type_159721',axiom,
! [V_24Y] :
( c_24__type__159721___24t(V_24Y)
<=> t(V_24Y,c_24__type__159721) ) ).
fof('$tdef_$_type_9063',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__9063___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__9063___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_16252',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__16252___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__16252___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_87031',axiom,
! [V_24Y] :
( c_24__type__87031___24t(V_24Y)
<=> t(V_24Y,c_24__type__87031) ) ).
fof('$tdef_$_type_20292',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__20292___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__20292___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_180',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__180___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__180___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22534',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22534___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22534___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4083',axiom,
! [V_24Y] :
( c_24__type__4083___24t(V_24Y)
<=> t(V_24Y,c_24__type__4083) ) ).
fof('$tdef_$_type_163839',axiom,
! [V_24Y] :
( c_24__type__163839___24t(V_24Y)
<=> t(V_24Y,c_24__type__163839) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_9914',axiom,
! [V_24Y] :
( c_24__type__9914___24t(V_24Y)
<=> t(V_24Y,c_24__type__9914) ) ).
fof('$tdef_$_type_10075',axiom,
! [V_24Y] :
( c_24__type__10075___24t(V_24Y)
<=> t(V_24Y,c_24__type__10075) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).
fof('$tdef_$_type_23610',axiom,
! [V_24Y] :
( c_24__type__23610___24t(V_24Y)
<=> t(V_24Y,c_24__type__23610) ) ).
fof('$tdef_$_type_22556',axiom,
! [V_24Y] :
( c_24__type__22556___24t(V_24Y)
<=> t(V_24Y,c_24__type__22556) ) ).
fof('$tdef_$_type_378',axiom,
! [V_24Y] :
( c_24__type__378___24t(V_24Y)
<=> t(V_24Y,c_24__type__378) ) ).
fof('$tdef_$_type_1259',axiom,
! [V_24Y] :
( c_24__type__1259___24t(V_24Y)
<=> t(V_24Y,c_24__type__1259) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24065',axiom,
! [V_24Y] :
( c_24__type__24065___24t(V_24Y)
<=> t(V_24Y,c_24__type__24065) ) ).
fof('$tdef_$_type_15948',axiom,
! [V_24Y] :
( c_24__type__15948___24t(V_24Y)
<=> t(V_24Y,c_24__type__15948) ) ).
fof('$tdef_$_type_18840',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_24Y] :
( c_24__type__18840___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_24Y)
<=> t(V_24Y,c_24__type__18840___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('$tdef_$_type_7839',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__7839___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__7839___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9456',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__9456___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__9456___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4202',axiom,
! [V_24Y] :
( c_24__type__4202___24t(V_24Y)
<=> t(V_24Y,c_24__type__4202) ) ).
fof('$tdef_$_type_16519',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16519___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__16519___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_9904',axiom,
! [V_24Y] :
( c_24__type__9904___24t(V_24Y)
<=> t(V_24Y,c_24__type__9904) ) ).
fof('$tdef_$_type_8293',axiom,
! [V_24Y] :
( c_24__type__8293___24t(V_24Y)
<=> t(V_24Y,c_24__type__8293) ) ).
fof('$tdef_$_type_23106',axiom,
! [V_24Y] :
( c_24__type__23106___24t(V_24Y)
<=> t(V_24Y,c_24__type__23106) ) ).
fof('$tdef_$_type_5763',axiom,
! [V_24Y] :
( c_24__type__5763___24t(V_24Y)
<=> t(V_24Y,c_24__type__5763) ) ).
fof('$tdef_$_type_9821',axiom,
! [V_24Y] :
( c_24__type__9821___24t(V_24Y)
<=> t(V_24Y,c_24__type__9821) ) ).
fof('$tdef_$_type_5992',axiom,
! [V_24Y] :
( c_24__type__5992___24t(V_24Y)
<=> t(V_24Y,c_24__type__5992) ) ).
fof('$tdef_$_type_15953',axiom,
! [V_24Y] :
( c_24__type__15953___24t(V_24Y)
<=> t(V_24Y,c_24__type__15953) ) ).
fof('$tdef_$_type_18229',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_24Y] :
( c_24__type__18229___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_24Y)
<=> t(V_24Y,c_24__type__18229___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('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_$_type_52652',axiom,
! [V_24Y] :
( c_24__type__52652___24t(V_24Y)
<=> t(V_24Y,c_24__type__52652) ) ).
fof('$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_14144',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__14144___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__14144___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('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5846',axiom,
! [V_24Y] :
( c_24__type__5846___24t(V_24Y)
<=> t(V_24Y,c_24__type__5846) ) ).
fof('$tdef_$_type_19245',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19245___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19245___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Decimal.decimal',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2edecimal) ) ).
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_$_type_788',axiom,
! [V_24Y] :
( c_24__type__788___24t(V_24Y)
<=> t(V_24Y,c_24__type__788) ) ).
fof('$tdef_$_type_900',axiom,
! [V_24X1,V_24Y] :
( c_24__type__900___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__900___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37126',axiom,
! [V_24Y] :
( c_24__type__37126___24t(V_24Y)
<=> t(V_24Y,c_24__type__37126) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
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_8419',axiom,
! [V_24Y] :
( c_24__type__8419___24t(V_24Y)
<=> t(V_24Y,c_24__type__8419) ) ).
fof('$tdef_$_type_34448',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34448___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34448___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_876',axiom,
! [V_24X1,V_24Y] :
( c_24__type__876___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__876___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8450',axiom,
! [V_24Y] :
( c_24__type__8450___24t(V_24Y)
<=> t(V_24Y,c_24__type__8450) ) ).
fof('$tdef_$_type_21665',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21665___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21665___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.t',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2et) ) ).
fof('$tdef_$_type_942',axiom,
! [V_24X1,V_24Y] :
( c_24__type__942___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__942___24a1(V_24X1)) ) ).
fof('$tdef_$_type_852',axiom,
! [V_24X1,V_24Y] :
( c_24__type__852___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__852___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5720',axiom,
! [V_24Y] :
( c_24__type__5720___24t(V_24Y)
<=> t(V_24Y,c_24__type__5720) ) ).
fof('$tdef_$_type_4523',axiom,
! [V_24Y] :
( c_24__type__4523___24t(V_24Y)
<=> t(V_24Y,c_24__type__4523) ) ).
fof('$tdef_$_type_23629',axiom,
! [V_24Y] :
( c_24__type__23629___24t(V_24Y)
<=> t(V_24Y,c_24__type__23629) ) ).
fof('$tdef_$_type_4901',axiom,
! [V_24Y] :
( c_24__type__4901___24t(V_24Y)
<=> t(V_24Y,c_24__type__4901) ) ).
fof('$tdef_$_type_16582',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16582___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__16582___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23584',axiom,
! [V_24Y] :
( c_24__type__23584___24t(V_24Y)
<=> t(V_24Y,c_24__type__23584) ) ).
fof('$tdef_$_type_8551',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__8551___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__8551___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_4',axiom,
! [V_24Y] :
( c_24__type__4___24t(V_24Y)
<=> t(V_24Y,c_24__type__4) ) ).
fof('$tdef_$_type_13129',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__13129___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__13129___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_53',axiom,
! [V_24Y] :
( c_24__type__53___24t(V_24Y)
<=> t(V_24Y,c_24__type__53) ) ).
fof('$tdef_$_type_17162',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17162___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__17162___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_14490',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__14490___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__14490___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('$tdef_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ) ).
fof('$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_966',axiom,
! [V_24X1,V_24Y] :
( c_24__type__966___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__966___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32808',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32808___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32808___24a1(V_24X1)) ) ).
fof('$tdef_$_type_38969',axiom,
! [V_24Y] :
( c_24__type__38969___24t(V_24Y)
<=> t(V_24Y,c_24__type__38969) ) ).
fof('$tdef_$_type_31972',axiom,
! [V_24Y] :
( c_24__type__31972___24t(V_24Y)
<=> t(V_24Y,c_24__type__31972) ) ).
fof('$tdef_$_type_23588',axiom,
! [V_24Y] :
( c_24__type__23588___24t(V_24Y)
<=> t(V_24Y,c_24__type__23588) ) ).
fof('$tdef_$_type_8457',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8457___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8457___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31853',axiom,
! [V_24Y] :
( c_24__type__31853___24t(V_24Y)
<=> t(V_24Y,c_24__type__31853) ) ).
fof('$tdef_$_type_20913',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__20913___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__20913___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_9',axiom,
! [V_24Y] :
( c_24__type__9___24t(V_24Y)
<=> t(V_24Y,c_24__type__9) ) ).
fof('$tdef_$_type_6084',axiom,
! [V_24Y] :
( c_24__type__6084___24t(V_24Y)
<=> t(V_24Y,c_24__type__6084) ) ).
fof('$tdef_$_type_163842',axiom,
! [V_24Y] :
( c_24__type__163842___24t(V_24Y)
<=> t(V_24Y,c_24__type__163842) ) ).
fof('$tdef_$_type_10077',axiom,
! [V_24Y] :
( c_24__type__10077___24t(V_24Y)
<=> t(V_24Y,c_24__type__10077) ) ).
fof('$tdef_$_type_8014',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__8014___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__8014___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_22708',axiom,
! [V_24Y] :
( c_24__type__22708___24t(V_24Y)
<=> t(V_24Y,c_24__type__22708) ) ).
fof('$tdef_$_type_21321',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__21321___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__21321___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('$tdef_Coq.Sets.Cpo.Chain',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eCpo_2eChain___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eCpo_2eChain___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21573',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21573___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21573___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_$_type_159874',axiom,
! [V_24Y] :
( c_24__type__159874___24t(V_24Y)
<=> t(V_24Y,c_24__type__159874) ) ).
fof('$tdef_$_type_17710',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17710___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17710___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22443',axiom,
! [V_24Y] :
( c_24__type__22443___24t(V_24Y)
<=> t(V_24Y,c_24__type__22443) ) ).
fof('$tdef_$_type_8395',axiom,
! [V_24Y] :
( c_24__type__8395___24t(V_24Y)
<=> t(V_24Y,c_24__type__8395) ) ).
fof('$tdef_$_type_18354',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__18354___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__18354___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_159732',axiom,
! [V_24Y] :
( c_24__type__159732___24t(V_24Y)
<=> t(V_24Y,c_24__type__159732) ) ).
fof('$tdef_Coq.Sets.Ensembles.Ensemble',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5835',axiom,
! [V_24Y] :
( c_24__type__5835___24t(V_24Y)
<=> t(V_24Y,c_24__type__5835) ) ).
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_159727',axiom,
! [V_24Y] :
( c_24__type__159727___24t(V_24Y)
<=> t(V_24Y,c_24__type__159727) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22063',axiom,
! [V_24X1,V_24Y] :
( c_24__type__22063___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__22063___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1234',axiom,
! [V_24Y] :
( c_24__type__1234___24t(V_24Y)
<=> t(V_24Y,c_24__type__1234) ) ).
fof('$tdef_$_type_17216',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17216___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__17216___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_6443',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__6443___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__6443___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$tdef_$_type_955',axiom,
! [V_24X1,V_24Y] :
( c_24__type__955___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__955___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32803',axiom,
! [V_24Y] :
( c_24__type__32803___24t(V_24Y)
<=> t(V_24Y,c_24__type__32803) ) ).
fof('$tdef_$_type_19866',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__19866___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__19866___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_17036',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17036___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__17036___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4579',axiom,
! [V_24Y] :
( c_24__type__4579___24t(V_24Y)
<=> t(V_24Y,c_24__type__4579) ) ).
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_$_type_6391',axiom,
! [V_24Y] :
( c_24__type__6391___24t(V_24Y)
<=> t(V_24Y,c_24__type__6391) ) ).
fof('$tdef_$_type_19671',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__19671___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__19671___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_21853',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21853___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21853___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_17764',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17764___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17764___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_8383',axiom,
! [V_24Y] :
( c_24__type__8383___24t(V_24Y)
<=> t(V_24Y,c_24__type__8383) ) ).
fof('$tdef_$_type_380',axiom,
! [V_24Y] :
( c_24__type__380___24t(V_24Y)
<=> t(V_24Y,c_24__type__380) ) ).
fof('$tdef_$_type_14',axiom,
! [V_24Y] :
( c_24__type__14___24t(V_24Y)
<=> t(V_24Y,c_24__type__14) ) ).
fof('$tdef_$_type_15482',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__15482___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__15482___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_24324',axiom,
! [V_24Y] :
( c_24__type__24324___24t(V_24Y)
<=> t(V_24Y,c_24__type__24324) ) ).
fof('$tdef_$_type_10105',axiom,
! [V_24Y] :
( c_24__type__10105___24t(V_24Y)
<=> t(V_24Y,c_24__type__10105) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_8426',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8426___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8426___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23158',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23158___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23158___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_8329',axiom,
! [V_24Y] :
( c_24__type__8329___24t(V_24Y)
<=> t(V_24Y,c_24__type__8329) ) ).
fof('$tdef_$_type_17454',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17454___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17454___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_13798',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__13798___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__13798___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_9265',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9265___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9265___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4013',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4013___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4013___24a1(V_24X1)) ) ).
fof('$tdef_$_type_159752',axiom,
! [V_24Y] :
( c_24__type__159752___24t(V_24Y)
<=> t(V_24Y,c_24__type__159752) ) ).
fof('$tdef_$_type_22439',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22439___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22439___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6126',axiom,
! [V_24Y] :
( c_24__type__6126___24t(V_24Y)
<=> t(V_24Y,c_24__type__6126) ) ).
fof('$tdef_$_type_1246',axiom,
! [V_24Y] :
( c_24__type__1246___24t(V_24Y)
<=> t(V_24Y,c_24__type__1246) ) ).
fof('$tdef_$_type_11076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__11076___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__11076___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_3847',axiom,
! [V_24Y] :
( c_24__type__3847___24t(V_24Y)
<=> t(V_24Y,c_24__type__3847) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_17099',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17099___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__17099___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_11422',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__11422___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__11422___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_1206',axiom,
! [V_24Y] :
( c_24__type__1206___24t(V_24Y)
<=> t(V_24Y,c_24__type__1206) ) ).
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_$_type_5724',axiom,
! [V_24Y] :
( c_24__type__5724___24t(V_24Y)
<=> t(V_24Y,c_24__type__5724) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_87045',axiom,
! [V_24Y] :
( c_24__type__87045___24t(V_24Y)
<=> t(V_24Y,c_24__type__87045) ) ).
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_$_type_25117',axiom,
! [V_24Y] :
( c_24__type__25117___24t(V_24Y)
<=> t(V_24Y,c_24__type__25117) ) ).
fof('$tdef_$_type_17472',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17472___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17472___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_5878',axiom,
! [V_24Y] :
( c_24__type__5878___24t(V_24Y)
<=> t(V_24Y,c_24__type__5878) ) ).
fof('$tdef_$_type_8334',axiom,
! [V_24X1,V_24Y] :
( c_24__type__8334___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__8334___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5782',axiom,
! [V_24Y] :
( c_24__type__5782___24t(V_24Y)
<=> t(V_24Y,c_24__type__5782) ) ).
fof('$tdef_$_type_17797',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17797___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17797___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15942',axiom,
! [V_24Y] :
( c_24__type__15942___24t(V_24Y)
<=> t(V_24Y,c_24__type__15942) ) ).
fof('$tdef_$_type_6655',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6655___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6655___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.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_20505',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__20505___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__20505___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_39349',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__39349___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__39349___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_9658',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__9658___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__9658___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Sets.Partial_Order.PO',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2ePartial__Order_2ePO___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4518',axiom,
! [V_24Y] :
( c_24__type__4518___24t(V_24Y)
<=> t(V_24Y,c_24__type__4518) ) ).
fof('$tdef_$_type_178430',axiom,
! [V_24Y] :
( c_24__type__178430___24t(V_24Y)
<=> t(V_24Y,c_24__type__178430) ) ).
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_$_type_772',axiom,
! [V_24Y] :
( c_24__type__772___24t(V_24Y)
<=> t(V_24Y,c_24__type__772) ) ).
fof('$tdef_$_type_50',axiom,
! [V_24X1,V_24Y] :
( c_24__type__50___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__50___24a1(V_24X1)) ) ).
fof('$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_31857',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31857___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31857___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5025',axiom,
! [V_24Y] :
( c_24__type__5025___24t(V_24Y)
<=> t(V_24Y,c_24__type__5025) ) ).
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_$_type_23423',axiom,
! [V_24Y] :
( c_24__type__23423___24t(V_24Y)
<=> t(V_24Y,c_24__type__23423) ) ).
fof('$tdef_$_type_34467',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34467___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34467___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_159835',axiom,
! [V_24Y] :
( c_24__type__159835___24t(V_24Y)
<=> t(V_24Y,c_24__type__159835) ) ).
fof('$tdef_$_type_20079',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20079___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20079___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_5596',axiom,
! [V_24Y] :
( c_24__type__5596___24t(V_24Y)
<=> t(V_24Y,c_24__type__5596) ) ).
fof('$tdef_$_type_23434',axiom,
! [V_24Y] :
( c_24__type__23434___24t(V_24Y)
<=> t(V_24Y,c_24__type__23434) ) ).
fof('$tdef_$_type_163850',axiom,
! [V_24Y] :
( c_24__type__163850___24t(V_24Y)
<=> t(V_24Y,c_24__type__163850) ) ).
fof('$tdef_$_type_847',axiom,
! [V_24X1,V_24Y] :
( c_24__type__847___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__847___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23370',axiom,
! [V_24Y] :
( c_24__type__23370___24t(V_24Y)
<=> t(V_24Y,c_24__type__23370) ) ).
fof('$tdef_$_type_22504',axiom,
! [V_24Y] :
( c_24__type__22504___24t(V_24Y)
<=> t(V_24Y,c_24__type__22504) ) ).
fof('$tdef_$_type_159793',axiom,
! [V_24Y] :
( c_24__type__159793___24t(V_24Y)
<=> t(V_24Y,c_24__type__159793) ) ).
fof('$tdef_$_type_18104',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_24Y] :
( c_24__type__18104___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_24Y)
<=> t(V_24Y,c_24__type__18104___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('$tdef_$_type_21933',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21933___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21933___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_909',axiom,
! [V_24X1,V_24Y] :
( c_24__type__909___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__909___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17385',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17385___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_39286',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__39286___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__39286___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_32790',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32790___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32790___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9909',axiom,
! [V_24Y] :
( c_24__type__9909___24t(V_24Y)
<=> t(V_24Y,c_24__type__9909) ) ).
fof('$tdef_$_type_4435',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4435___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4435___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21977',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21977___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21977___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_871',axiom,
! [V_24Y] :
( c_24__type__871___24t(V_24Y)
<=> t(V_24Y,c_24__type__871) ) ).
fof('$tdef_$_type_842',axiom,
! [V_24Y] :
( c_24__type__842___24t(V_24Y)
<=> t(V_24Y,c_24__type__842) ) ).
fof('$tdef_$_type_40123',axiom,
! [V_24Y] :
( c_24__type__40123___24t(V_24Y)
<=> t(V_24Y,c_24__type__40123) ) ).
fof('$tdef_$_type_159786',axiom,
! [V_24Y] :
( c_24__type__159786___24t(V_24Y)
<=> t(V_24Y,c_24__type__159786) ) ).
fof('$tdef_$_type_11745',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__11745___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__11745___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_31112',axiom,
! [V_24Y] :
( c_24__type__31112___24t(V_24Y)
<=> t(V_24Y,c_24__type__31112) ) ).
fof('$tdef_$_type_5872',axiom,
! [V_24Y] :
( c_24__type__5872___24t(V_24Y)
<=> t(V_24Y,c_24__type__5872) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_17498',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17498___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17498___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_17656',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17656___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17656___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_27879',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27879___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27879___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6060',axiom,
! [V_24Y] :
( c_24__type__6060___24t(V_24Y)
<=> t(V_24Y,c_24__type__6060) ) ).
fof('$tdef_$_type_37109',axiom,
! [V_24Y] :
( c_24__type__37109___24t(V_24Y)
<=> t(V_24Y,c_24__type__37109) ) ).
fof('$tdef_$_type_975',axiom,
! [V_24X1,V_24Y] :
( c_24__type__975___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__975___24a1(V_24X1)) ) ).
fof('$tdef_B',axiom,
! [V_24Y] :
( cB___24t(V_24Y)
<=> t(V_24Y,cB) ) ).
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_$_type_31860',axiom,
! [V_24Y] :
( c_24__type__31860___24t(V_24Y)
<=> t(V_24Y,c_24__type__31860) ) ).
fof('$tdef_$_type_39466',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__39466___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__39466___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_17516',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17516___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17516___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_21741',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21741___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21741___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12437',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__12437___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__12437___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_4943',axiom,
! [V_24Y] :
( c_24__type__4943___24t(V_24Y)
<=> t(V_24Y,c_24__type__4943) ) ).
fof('$tdef_$_type_27862',axiom,
! [V_24Y] :
( c_24__type__27862___24t(V_24Y)
<=> t(V_24Y,c_24__type__27862) ) ).
fof('$tdef_$_type_15945',axiom,
! [V_24Y] :
( c_24__type__15945___24t(V_24Y)
<=> t(V_24Y,c_24__type__15945) ) ).
fof('$tdef_$_type_6923',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6923___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6923___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___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_$_type_31895',axiom,
! [V_24Y] :
( c_24__type__31895___24t(V_24Y)
<=> t(V_24Y,c_24__type__31895) ) ).
fof('$tdef_$_type_10071',axiom,
! [V_24Y] :
( c_24__type__10071___24t(V_24Y)
<=> t(V_24Y,c_24__type__10071) ) ).
fof('$tdef_$_type_38965',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38965___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38965___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4697',axiom,
! [V_24Y] :
( c_24__type__4697___24t(V_24Y)
<=> t(V_24Y,c_24__type__4697) ) ).
fof('$tdef_$_type_159871',axiom,
! [V_24Y] :
( c_24__type__159871___24t(V_24Y)
<=> t(V_24Y,c_24__type__159871) ) ).
fof('$tdef_$_type_38958',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__38958___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__38958___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_87245',axiom,
! [V_24Y] :
( c_24__type__87245___24t(V_24Y)
<=> t(V_24Y,c_24__type__87245) ) ).
fof('$tdef_$_type_5758',axiom,
! [V_24Y] :
( c_24__type__5758___24t(V_24Y)
<=> t(V_24Y,c_24__type__5758) ) ).
fof('$tdef_$_type_22496',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22496___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22496___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24163',axiom,
! [V_24Y] :
( c_24__type__24163___24t(V_24Y)
<=> t(V_24Y,c_24__type__24163) ) ).
fof('$tdef_$_type_7932',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7932___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7932___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_37429',axiom,
! [V_24Y] :
( c_24__type__37429___24t(V_24Y)
<=> t(V_24Y,c_24__type__37429) ) ).
fof('$tdef_$_type_22105',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22105___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22105___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6841',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6841___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6841___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_87080',axiom,
! [V_24Y] :
( c_24__type__87080___24t(V_24Y)
<=> t(V_24Y,c_24__type__87080) ) ).
fof('$tdef_$_type_159789',axiom,
! [V_24Y] :
( c_24__type__159789___24t(V_24Y)
<=> t(V_24Y,c_24__type__159789) ) ).
fof('$tdef_$_type_16645',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16645___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__16645___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_22423',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22423___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22423___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6451',axiom,
! [V_24Y] :
( c_24__type__6451___24t(V_24Y)
<=> t(V_24Y,c_24__type__6451) ) ).
fof('$tdef_$_type_21897',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21897___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21897___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_3869',axiom,
! [V_24Y] :
( c_24__type__3869___24t(V_24Y)
<=> t(V_24Y,c_24__type__3869) ) ).
fof('$tdef_$_type_9355',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__9355___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__9355___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34584',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34584___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34584___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22488',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22488___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22488___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5700',axiom,
! [V_24Y] :
( c_24__type__5700___24t(V_24Y)
<=> t(V_24Y,c_24__type__5700) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_17821',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17821___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17821___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_22538',axiom,
! [V_24Y] :
( c_24__type__22538___24t(V_24Y)
<=> t(V_24Y,c_24__type__22538) ) ).
fof('$tdef_$_type_29399',axiom,
! [V_24Y] :
( c_24__type__29399___24t(V_24Y)
<=> t(V_24Y,c_24__type__29399) ) ).
fof('$tdef_$_type_163939',axiom,
! [V_24Y] :
( c_24__type__163939___24t(V_24Y)
<=> t(V_24Y,c_24__type__163939) ) ).
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_$_type_937',axiom,
! [V_24Y] :
( c_24__type__937___24t(V_24Y)
<=> t(V_24Y,c_24__type__937) ) ).
fof('$tdef_$_type_16001',axiom,
! [V_24Y] :
( c_24__type__16001___24t(V_24Y)
<=> t(V_24Y,c_24__type__16001) ) ).
fof('$tdef_$_type_31648',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31648___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31648___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_159724',axiom,
! [V_24Y] :
( c_24__type__159724___24t(V_24Y)
<=> t(V_24Y,c_24__type__159724) ) ).
fof('$tdef_$_type_22109',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22109___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22109___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21473',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21473___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21473___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_8107',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8107___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8107___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_16762',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16762___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__16762___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_3890',axiom,
! [V_24Y] :
( c_24__type__3890___24t(V_24Y)
<=> t(V_24Y,c_24__type__3890) ) ).
fof('$tdef_$_type_9557',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9557___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9557___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1267',axiom,
! [V_24Y] :
( c_24__type__1267___24t(V_24Y)
<=> t(V_24Y,c_24__type__1267) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_$_type_889',axiom,
! [V_24X1,V_24Y] :
( c_24__type__889___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__889___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21749',axiom,
! [V_24Y] :
( c_24__type__21749___24t(V_24Y)
<=> t(V_24Y,c_24__type__21749) ) ).
fof('$tdef_$_type_38945',axiom,
! [V_24Y] :
( c_24__type__38945___24t(V_24Y)
<=> t(V_24Y,c_24__type__38945) ) ).
fof('$tdef_$_type_8504',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8504___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8504___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_5754',axiom,
! [V_24Y] :
( c_24__type__5754___24t(V_24Y)
<=> t(V_24Y,c_24__type__5754) ) ).
fof('$tdef_$_type_17279',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__17279___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__17279___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_159740',axiom,
! [V_24Y] :
( c_24__type__159740___24t(V_24Y)
<=> t(V_24Y,c_24__type__159740) ) ).
fof('$tdef_$_type_16699',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__16699___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__16699___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4186',axiom,
! [V_24Y] :
( c_24__type__4186___24t(V_24Y)
<=> t(V_24Y,c_24__type__4186) ) ).
fof('$tdef_$_type_4750',axiom,
! [V_24Y] :
( c_24__type__4750___24t(V_24Y)
<=> t(V_24Y,c_24__type__4750) ) ).
fof('$tdef_$_type_27885',axiom,
! [V_24Y] :
( c_24__type__27885___24t(V_24Y)
<=> t(V_24Y,c_24__type__27885) ) ).
fof('$tdef_$_type_912',axiom,
! [V_24X1,V_24Y] :
( c_24__type__912___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__912___24a1(V_24X1)) ) ).
fof('$tdef_$_type_438',axiom,
! [V_24Y] :
( c_24__type__438___24t(V_24Y)
<=> t(V_24Y,c_24__type__438) ) ).
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_$_type_4706',axiom,
! [V_24Y] :
( c_24__type__4706___24t(V_24Y)
<=> t(V_24Y,c_24__type__4706) ) ).
fof('$tdef_$_type_10730',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__10730___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__10730___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_159784',axiom,
! [V_24Y] :
( c_24__type__159784___24t(V_24Y)
<=> t(V_24Y,c_24__type__159784) ) ).
fof('$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_14813',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__14813___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__14813___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_840',axiom,
! [V_24Y] :
( c_24__type__840___24t(V_24Y)
<=> t(V_24Y,c_24__type__840) ) ).
fof('$tdef_$_type_784',axiom,
! [V_24Y] :
( c_24__type__784___24t(V_24Y)
<=> t(V_24Y,c_24__type__784) ) ).
fof('$tdef_$_type_23458',axiom,
! [V_24Y] :
( c_24__type__23458___24t(V_24Y)
<=> t(V_24Y,c_24__type__23458) ) ).
fof('$tdef_$_type_22314',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22314___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22314___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_7098',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__7098___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__7098___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9916',axiom,
! [V_24Y] :
( c_24__type__9916___24t(V_24Y)
<=> t(V_24Y,c_24__type__9916) ) ).
fof('$tdef_$_type_38072',axiom,
! [V_24Y] :
( c_24__type__38072___24t(V_24Y)
<=> t(V_24Y,c_24__type__38072) ) ).
fof('$tdef_$_type_21615',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21615___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21615___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_6748',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__6748___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__6748___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_12091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__12091___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__12091___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_23426',axiom,
! [V_24Y] :
( c_24__type__23426___24t(V_24Y)
<=> t(V_24Y,c_24__type__23426) ) ).
fof('$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_178346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__178346___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__178346___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$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_17408',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17408___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17408___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_13475',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__13475___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__13475___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('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_31846',axiom,
! [V_24Y] :
( c_24__type__31846___24t(V_24Y)
<=> t(V_24Y,c_24__type__31846) ) ).
fof('$tdef_$_type_21523',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__21523___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__21523___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_31721',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__31721___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__31721___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22625',axiom,
! [V_24Y] :
( c_24__type__22625___24t(V_24Y)
<=> t(V_24Y,c_24__type__22625) ) ).
fof('$tdef_$_type_15962',axiom,
! [V_24Y] :
( c_24__type__15962___24t(V_24Y)
<=> t(V_24Y,c_24__type__15962) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_5865',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__5865___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__5865___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9164',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__9164___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__9164___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3893',axiom,
! [V_24Y] :
( c_24__type__3893___24t(V_24Y)
<=> t(V_24Y,c_24__type__3893) ) ).
fof('$tdef_$_type_17680',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17680___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17680___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_8586',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8586___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8586___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4271',axiom,
! [V_24Y] :
( c_24__type__4271___24t(V_24Y)
<=> t(V_24Y,c_24__type__4271) ) ).
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_$_type_7746',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7746___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7746___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_159716',axiom,
! [V_24Y] :
( c_24__type__159716___24t(V_24Y)
<=> t(V_24Y,c_24__type__159716) ) ).
fof('$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_31669',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31669___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31669___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23432',axiom,
! [V_24Y] :
( c_24__type__23432___24t(V_24Y)
<=> t(V_24Y,c_24__type__23432) ) ).
fof('$tdef_$_type_34481',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34481___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34481___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_16213',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__16213___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__16213___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_4209',axiom,
! [V_24Y] :
( c_24__type__4209___24t(V_24Y)
<=> t(V_24Y,c_24__type__4209) ) ).
fof('$tdef_$_type_163834',axiom,
! [V_24Y] :
( c_24__type__163834___24t(V_24Y)
<=> t(V_24Y,c_24__type__163834) ) ).
fof('$tdef_$_type_39403',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__39403___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__39403___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_854',axiom,
! [V_24Y] :
( c_24__type__854___24t(V_24Y)
<=> t(V_24Y,c_24__type__854) ) ).
fof('$tdef_$_type_23557',axiom,
! [V_24Y] :
( c_24__type__23557___24t(V_24Y)
<=> t(V_24Y,c_24__type__23557) ) ).
fof('$tdef_$_type_22388',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22388___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22388___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_22086',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22086___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22086___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12783',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__12783___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__12783___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_8282',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__8282___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__8282___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_22599',axiom,
! [V_24Y] :
( c_24__type__22599___24t(V_24Y)
<=> t(V_24Y,c_24__type__22599) ) ).
fof('$tdef_$_type_6048',axiom,
! [V_24Y] :
( c_24__type__6048___24t(V_24Y)
<=> t(V_24Y,c_24__type__6048) ) ).
fof('$tdef_$_type_34574',axiom,
! [V_24Y] :
( c_24__type__34574___24t(V_24Y)
<=> t(V_24Y,c_24__type__34574) ) ).
fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).
fof('$tdef_$_type_6072',axiom,
! [V_24Y] :
( c_24__type__6072___24t(V_24Y)
<=> t(V_24Y,c_24__type__6072) ) ).
fof('$tdef_$_type_5994',axiom,
! [V_24Y] :
( c_24__type__5994___24t(V_24Y)
<=> t(V_24Y,c_24__type__5994) ) ).
fof('$tdef_$_type_18604',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_24Y] :
( c_24__type__18604___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_24Y)
<=> t(V_24Y,c_24__type__18604___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('$tdef_$_type_4495',axiom,
! [V_24Y] :
( c_24__type__4495___24t(V_24Y)
<=> t(V_24Y,c_24__type__4495) ) ).
fof('$tdef_$_type_15136',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__15136___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__15136___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_7191',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__7191___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__7191___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
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_$_type_22353',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22353___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22353___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18729',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__18729___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__18729___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_21126',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__21126___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__21126___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_22239',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__22239___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__22239___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Sets.Relations_1.Relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_214',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__214___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__214___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22591',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22591___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22591___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31679',axiom,
! [V_24Y] :
( c_24__type__31679___24t(V_24Y)
<=> t(V_24Y,c_24__type__31679) ) ).
fof('$tdef_$_type_4983',axiom,
! [V_24Y] :
( c_24__type__4983___24t(V_24Y)
<=> t(V_24Y,c_24__type__4983) ) ).
fof('$tdef_Quotients.quotient',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cQuotients_2equotient___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cQuotients_2equotient___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9801',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9801___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9801___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_827',axiom,
! [V_24X1,V_24Y] :
( c_24__type__827___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__827___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18479',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__18479___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__18479___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_9782',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9782___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_23454',axiom,
! [V_24Y] :
( c_24__type__23454___24t(V_24Y)
<=> t(V_24Y,c_24__type__23454) ) ).
fof('$tdef_$_type_17740',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17740___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17740___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_17431',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__17431___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__17431___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_23472',axiom,
! [V_24Y] :
( c_24__type__23472___24t(V_24Y)
<=> t(V_24Y,c_24__type__23472) ) ).
fof('$tdef_$_type_92',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__92___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__92___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6006',axiom,
! [V_24Y] :
( c_24__type__6006___24t(V_24Y)
<=> t(V_24Y,c_24__type__6006) ) ).
fof('$tdef_$_type_15980',axiom,
! [V_24Y] :
( c_24__type__15980___24t(V_24Y)
<=> t(V_24Y,c_24__type__15980) ) ).
fof('$tdef_$_type_159747',axiom,
! [V_24Y] :
( c_24__type__159747___24t(V_24Y)
<=> t(V_24Y,c_24__type__159747) ) ).
fof('$tdef_$_type_5703',axiom,
! [V_24Y] :
( c_24__type__5703___24t(V_24Y)
<=> t(V_24Y,c_24__type__5703) ) ).
fof('$tdef_$_type_20718',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__20718___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__20718___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_86187',axiom,
! [V_24Y] :
( c_24__type__86187___24t(V_24Y)
<=> t(V_24Y,c_24__type__86187) ) ).
fof('$tdef_$_type_22583',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22583___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22583___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_27856',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27856___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27856___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_17848',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17848___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17848___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Sets.Cpo.Cpo',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eCpo_2eCpo___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eCpo_2eCpo___24a1(V_24X1)) ) ).
fof('$tdef_$_type_178336',axiom,
! [V_24Y] :
( c_24__type__178336___24t(V_24Y)
<=> t(V_24Y,c_24__type__178336) ) ).
fof('$tdef_$_type_23242',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23242___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23242___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_38751',axiom,
! [V_24Y] :
( c_24__type__38751___24t(V_24Y)
<=> t(V_24Y,c_24__type__38751) ) ).
fof('$tdef_$_type_4000',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__4000___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__4000___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_5833',axiom,
! [V_24Y] :
( c_24__type__5833___24t(V_24Y)
<=> t(V_24Y,c_24__type__5833) ) ).
fof('$tdef_$_type_40221',axiom,
! [V_24Y] :
( c_24__type__40221___24t(V_24Y)
<=> t(V_24Y,c_24__type__40221) ) ).
fof('$tdef_$_type_10163',axiom,
! [V_24Y] :
( c_24__type__10163___24t(V_24Y)
<=> t(V_24Y,c_24__type__10163) ) ).
fof('$tdef_$_type_31891',axiom,
! [V_24Y] :
( c_24__type__31891___24t(V_24Y)
<=> t(V_24Y,c_24__type__31891) ) ).
fof('$tdef_$_type_1208',axiom,
! [V_24Y] :
( c_24__type__1208___24t(V_24Y)
<=> t(V_24Y,c_24__type__1208) ) ).
fof('$tdef_$_type_2',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2___24a1(V_24X1)) ) ).
fof('$tdef_$_type_19458',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__19458___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__19458___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_4409',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4409___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4409___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_16174',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__16174___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__16174___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_23233',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23233___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23233___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22274',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__22274___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__22274___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_17626',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__17626___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__17626___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_1193',axiom,
! [V_24Y] :
( c_24__type__1193___24t(V_24Y)
<=> t(V_24Y,c_24__type__1193) ) ).
fof('$tdef_$_type_4358',axiom,
! [V_24Y] :
( c_24__type__4358___24t(V_24Y)
<=> t(V_24Y,c_24__type__4358) ) ).
fof('$tdef_$_type_39223',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__39223___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__39223___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_38975',axiom,
! [V_24X1,V_24Y] :
( c_24__type__38975___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__38975___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4905',axiom,
! [V_24Y] :
( c_24__type__4905___24t(V_24Y)
<=> t(V_24Y,c_24__type__4905) ) ).
fof('$tdef_$_type_4399',axiom,
! [V_24Y] :
( c_24__type__4399___24t(V_24Y)
<=> t(V_24Y,c_24__type__4399) ) ).
fof('$tdef_$_type_7016',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__7016___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__7016___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_22461',axiom,
! [V_24Y] :
( c_24__type__22461___24t(V_24Y)
<=> t(V_24Y,c_24__type__22461) ) ).
fof('$tdef_$_type_6177',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6177___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6177___24a1(V_24X1)) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__a1] :
( cA___24t(V0__a1)
=> ! [V1__a2] :
( cA___24t(V1__a2)
=> ( cR___24a2(V0__a1,V1__a2)
=> cQuotients_2eInducedFunction2_2eprojf___24a1(V0__a1) = cQuotients_2eInducedFunction2_2eprojf___24a1(V1__a2) ) ) ) ).
%------------------------------------------------------------------------------