TPTP Problem File: SEV638+1.p
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%------------------------------------------------------------------------------
% File : SEV638+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - InteriorsClosures interior closure idempotent
% 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 : InteriorsClosures.interior.closure.idempotent.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2790 (1122 unt; 0 def)
% Number of atoms : 9394 (2325 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6716 ( 112 ~; 665 |;1530 &)
% (1049 <=>;3360 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 591 ( 590 usr; 0 prp; 1-23 aty)
% Number of functors : 1581 (1581 usr;1052 con; 0-22 aty)
% Number of variables : 9256 (8660 !; 596 ?)
% SPC : FOF_UNK_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.list$28356',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2428443___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428356___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__28360] :
( t(Vvar__1___24Anonymous__28360,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__28361] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__28361)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428443___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28360,Vvar__2___24Anonymous__28361)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428356___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28360,c_24__fix__28488__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__28361,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$28443',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428443___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__28447] :
( t(Vvar__1___24Anonymous__28447,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__28448] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__28448)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28447,Vvar__2___24Anonymous__28448)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2428443___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28447,c_24__fix__28488__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__28448,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$2680',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& ( c_24__case__Coq_2eInit_2eDatatypes_2enat_242680___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__1 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0) ) )
| ? [Vvar__0___24Anonymous__2681] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2681)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2681)
& ( c_24__case__Coq_2eInit_2eDatatypes_2enat_242680___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$28607',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428607___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__28608] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28608)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28608)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428607___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__28608)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$28629',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__28630] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28630)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28630)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__28630)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$36138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__36151___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__36143] :
( t(Vvar__2___24Anonymous__36143,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__36144] :
( t(Vvar__3___24Anonymous__36144,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__36143,Vvar__3___24Anonymous__36144)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2436138___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__36143)),Vvar__3___24Anonymous__36144)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$28624',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428624___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__28625] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28625)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28625)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428624___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28625) )
| ? [Vvar__0___24Anonymous__28626] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28626)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__28626)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428624___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__28626) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$37513',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__37514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37514)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37514)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2437513___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__37529__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__37514)) )
| ? [Vvar__0___24Anonymous__37521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37521)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37521)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2437513___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37521) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2437513___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_5_subF_4822',axiom,
! [V0__A,V1__B,V2__T,V3__f,V4__F,V5__a] : c_24__let__5__subF__4822___24a6(V0__A,V1__B,V2__T,V3__f,V4__F,V5__a) = happ(V4__F,happ(V3__f,V5__a)) ).
fof('$_def_$_let_5_subF_4825',axiom,
! [V0__A,V1__B,V2__T,V3__f,V4__F,V5__a] : c_24__let__5__subF__4825___24a6(V0__A,V1__B,V2__T,V3__f,V4__F,V5__a) = happ(V4__F,happ(V3__f,V5__a)) ).
fof('$_def_$_let_var_6_p_34167_34170',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34166] : c_24__let__var__6__p__34167__34170___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34166) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34166) ).
fof('$_def_$_let_var_6_p_34169_34171',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34168] : c_24__let__var__6__p__34169__34171___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34168) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34168) ).
fof('$_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__24172] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24172)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24172)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__24173] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24173)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24173)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__24176] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24176)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__24176)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__24173,Vvar__0___24Anonymous__24176) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Arith.PeanoNat.Nat.le',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2ele = cCoq_2eInit_2ePeano_2ele ).
fof('$_def_Coq.Arith.PeanoNat.Nat.lt',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2elt = cCoq_2eInit_2ePeano_2elt ).
fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__37398___24a1(V0__A)) ).
fof('$_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__27585] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27585)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27585)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__27585,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.ltof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2eltof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> cCoq_2eInit_2ePeano_2elt___24a2(happ(V1__f,V2__a),happ(V1__f,V3__b)) ) ).
fof('$_def_Coq.Bool.Bool.Is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24True) ) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
<=> p(c_24False) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.eqb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).
fof('$_def_Coq.Bool.Bool.ifb',axiom,
! [V0__b1,V1__b2,V2__b3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eBool_2eBool_2eifb___24a3(V0__b1,V1__b2,V2__b3) = V2__b3 ) ) ) ).
fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__22899] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__22899)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__22899) ) ).
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('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__22918] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__22918)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__22918) ) ).
fof('$_def_Coq.Init.Byte.byte_of_byte',axiom,
! [V0__b] : cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V0__b) = V0__b ).
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__23904] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__23904)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__23904,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('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__4428] :
( t(Vvar__1___24Anonymous__4428,V0__A)
& ? [Vvar__2___24Anonymous__4429] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4429)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4428,Vvar__2___24Anonymous__4429)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4428,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__4429,V3__m)) ) ) ) ) ) ).
fof('$_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__4373] :
( t(Vvar__2___24Anonymous__4373,V0__A)
& ? [Vvar__3___24Anonymous__4374] :
( t(Vvar__3___24Anonymous__4374,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__4373,Vvar__3___24Anonymous__4374)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__4373 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.id',axiom,
! [V0__A,V1__x] : cCoq_2eInit_2eDatatypes_2eid___24a2(V0__A,V1__x) = V1__x ).
fof('$_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('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_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('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__4385] :
( t(Vvar__2___24Anonymous__4385,V0__A)
& ? [Vvar__3___24Anonymous__4386] :
( t(Vvar__3___24Anonymous__4386,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__4385,Vvar__3___24Anonymous__4386)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__4386 ) ) ) ) ) ).
fof('$_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.Decimal.nzhead',axiom,
! [V1__d] :
( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
=> ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23939] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23939)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__23939)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__23939) )
| ? [Vvar__0___24Anonymous__23940] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23940)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__23940)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23941] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23941)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__23941)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23942] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23942)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__23942)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23943] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23943)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__23943)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23944] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23944)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__23944)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23945] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23945)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__23945)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23946] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23946)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__23946)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23947] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23947)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__23947)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__23948] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23948)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__23948)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d ) ) ) ).
fof('$_def_Coq.Init.Decimal.uint_of_uint',axiom,
! [V0__i] : cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V0__i) = V0__i ).
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__5094] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5094)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5094)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__5094,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__26774] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26774)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26774)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__26775] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26775)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26775)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__26778] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26778)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26778)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__26775,Vvar__0___24Anonymous__26778) ) ) ) ) ) ) ) ).
fof('$_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__26812] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26812)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26812)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26812)
& ( ( Vvar__0___24Anonymous__26812 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__26815] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26815)
& Vvar__0___24Anonymous__26812 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26815)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__26815)) ) ) ) ) ) ) ) ).
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__26759] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26759)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26759)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__26760] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26760)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26760)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26763] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26763)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26763)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__26760,Vvar__0___24Anonymous__26763) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__26789] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26789)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26789)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26789)
& ( ( Vvar__0___24Anonymous__26789 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26792] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26792)
& Vvar__0___24Anonymous__26789 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26792)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__26792) ) ) ) ) ) ) ) ).
fof('$_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__26768] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26768)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26768)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26771] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26771)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26771)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__26768,Vvar__0___24Anonymous__26771) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__26799] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26799)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26799)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__26799,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__26802] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26802)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26802)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__26799,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__26802) ) ) ) ) ) ) ) ).
fof('$_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__26783] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26783)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26783)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__26786] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26786)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26786)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__26783,Vvar__0___24Anonymous__26786)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__5102] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5102)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5102)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__5105] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5105)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5105)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__5102,Vvar__0___24Anonymous__5105)) ) ) ) ) ) ) ) ).
fof('$_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__5099] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5099)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5099)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__5099,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__5108] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5108)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5108)
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__5108)) ) ) ) ).
fof('$_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__1134] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1134)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1134)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__1134 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__26753] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26753)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26753)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__26756] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26756)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26756)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__26753,Vvar__0___24Anonymous__26756) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__26751] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__26751)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__26751) ) ).
fof('$_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__26796] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26796)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26796)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__26796,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__27582] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27582)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27582)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
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('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__12571___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__12565] :
( t(Vvar__2__x__12565,V0__A)
& p(happ(V1__P,Vvar__2__x__12565))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__12565)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__12565 ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__4836] :
( t(Vvar__1___24Anonymous__4836,V0__A)
& ? [Vvar__2___24Anonymous__4837] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4837)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4836,Vvar__2___24Anonymous__4837)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__4836 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__4837) ) ) ) ) ) ) ) ).
fof('$_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__26665] :
( t(Vvar__1___24Anonymous__26665,V1__B)
& ? [Vvar__2___24Anonymous__26666] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__26666)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__26665,Vvar__2___24Anonymous__26666)
& 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__26666,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__26665)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__4899] :
( t(Vvar__1___24Anonymous__4899,V1__B)
& ? [Vvar__2___24Anonymous__4900] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__4900)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__4899,Vvar__2___24Anonymous__4900)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__4899),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__4900)) ) ) ) ) ) ) ).
fof('$_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__26653] :
( t(Vvar__1___24Anonymous__26653,V0__A)
& ? [Vvar__2___24Anonymous__26654] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__26654)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__26653,Vvar__2___24Anonymous__26654)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__26653 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__4848] :
( t(Vvar__1___24Anonymous__4848,V0__A)
& ? [Vvar__2___24Anonymous__4849] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4849)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4848,Vvar__2___24Anonymous__4849)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__4848 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__4851] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__4851)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4851)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__4858] :
( t(Vvar__1___24Anonymous__4858,V0__A)
& ? [Vvar__2___24Anonymous__4859] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__4859)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__4858,Vvar__2___24Anonymous__4859)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__4851,Vvar__2___24Anonymous__4859,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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.ConstructiveIndefiniteDescription_on',axiom,
! [V0__A] : cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on___24a1(V0__A) = c_24__type__23684___24a1(V0__A) ).
fof('$_def_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__23589___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,happ(V1__B,V3__x))
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__23596___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle)
<=> ! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__3519___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__398___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_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__398___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('$_def_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__23606___24t(V0__A,V1__R)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__n),V3__y)) ) )
=> ? [V3__f] :
( c_24__type__23611___24t(V0__A,V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(happ(V1__R,V4__n),happ(V3__f,V4__n))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__1189___24t(V0__A,V2__R)
=> ! [V3__S] :
( c_24__type__12338___24t(V0__A,V1__B,V3__S)
=> ! [V4__T] :
( c_24__type__3519___24t(V0__A,V1__B,V4__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V1__B,V3__S)
=> ( ! [V7__x] :
( t(V7__x,V0__A)
=> ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ! [V9__y] :
( t(V9__y,V1__B)
=> ! [V10__y_27] :
( t(V10__y_27,V1__B)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> ( p(happ(happ(V3__S,V9__y),V10__y_27))
=> ( p(happ(happ(V4__T,V7__x),V9__y))
=> p(happ(happ(V4__T,V8__x_27),V10__y_27)) ) ) ) ) ) ) )
=> ( ! [V8__x] :
( t(V8__x,V0__A)
=> ? [V9__y] :
( t(V9__y,V1__B)
& p(happ(happ(V4__T,V8__x),V9__y)) ) )
=> ? [V9__f] :
( c_24__type__398___24t(V0__A,V1__B,V9__f)
& ! [V10__x] :
( t(V10__x,V0__A)
=> ( p(happ(happ(V4__T,V10__x),happ(V9__f,V10__x)))
& ! [V11__x_27] :
( t(V11__x_27,V0__A)
=> ( p(happ(happ(V2__R,V10__x),V11__x_27))
=> p(happ(happ(V3__S,happ(V9__f,V10__x)),happ(V9__f,V11__x_27))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1189___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R)
=> ? [V3__f] :
( c_24__type__4737___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('$_def_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__1189___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__3519___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__x_27] :
( t(V6__x_27,V0__A)
=> ! [V7__y] :
( t(V7__y,V1__B)
=> ( p(happ(happ(V2__R,V5__x),V6__x_27))
=> ( p(happ(happ(V3__T,V5__x),V7__y))
=> p(happ(happ(V3__T,V6__x_27),V7__y)) ) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ? [V7__y] :
( t(V7__y,V1__B)
& p(happ(happ(V3__T,V6__x),V7__y)) ) )
=> ? [V7__f] :
( c_24__type__398___24t(V0__A,V1__B,V7__f)
& ! [V8__x] :
( t(V8__x,V0__A)
=> ( p(happ(happ(V3__T,V8__x),happ(V7__f,V8__x)))
& ! [V9__x_27] :
( t(V9__x_27,V0__A)
=> ( p(happ(happ(V2__R,V8__x),V9__x_27))
=> happ(V7__f,V8__x) = happ(V7__f,V9__x_27) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__1189___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__3519___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__398___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('$_def_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(V1__B) )
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_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('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__22313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22313)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22313)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__22316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22316)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22316)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__22313,Vvar__0___24Anonymous__22316)) ) ) ) ) ) ) ) ).
fof('$_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__37375] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37375)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37375)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37375)
& ( ? [Vvar__0___24Anonymous__37379] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37379)
& Vvar__0___24Anonymous__37375 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37379)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37379) )
| ? [Vvar__0___24Anonymous__37380] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37380)
& Vvar__0___24Anonymous__37375 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37380)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37380) )
| ( Vvar__0___24Anonymous__37375 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__37381] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37381)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37381)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37381)
& ( ? [Vvar__0___24Anonymous__37385] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37385)
& Vvar__0___24Anonymous__37381 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37385)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37386] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37386)
& Vvar__0___24Anonymous__37381 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37386)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__37381 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_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__22320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22320)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22320)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__22323] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22323)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22323)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__22320,Vvar__0___24Anonymous__22323)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__37372] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37372)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__37372)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__37372) ) ) ) ).
fof('$_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__22312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22312)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22312)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__22312)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__37371] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__37371)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__37371) ) ).
fof('$_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__22416] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22416)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22416)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__22416,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__22418] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22418)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22418)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__22418) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNArith_2eBinNatDef_2eN_2ezero = cCoq_2eNumbers_2eBinNums_2eN0 ).
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('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__37439] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37439)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37439)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__37439 )
| ? [Vvar__0___24Anonymous__37440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37440)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37440)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__37440 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__37442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37442)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37442)
& ( ? [Vvar__0___24Anonymous__37446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37446)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37446)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__37442,Vvar__0___24Anonymous__37446) )
| ? [Vvar__0___24Anonymous__37447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37447)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37447)
& 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__37448] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37448)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37448)
& ( ? [Vvar__0___24Anonymous__37452] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37452)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37452)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37453)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37453)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__37448,Vvar__0___24Anonymous__37453) )
| ( 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__37454] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37454)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37454)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__37455] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37455)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37455)
& 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__37427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37427)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37427)
& 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__37427),Vvar__0___24Anonymous__37427)) )
| ? [Vvar__0___24Anonymous__37428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37428)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37428)
& 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__37428),Vvar__0___24Anonymous__37428) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__37458] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37458)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37458)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__37458,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__37459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37459)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37459)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__37459,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_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.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__22436] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22436)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22436)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__22436)) )
| ? [Vvar__0___24Anonymous__22437] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22437)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22437)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22437) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__37425] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__37425)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__37425) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__27602] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__27602)
& ? [Vvar__1__Qden__27603] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__27603)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__27602,Vvar__1__Qden__27603)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__27603 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__27597] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__27597)
& ? [Vvar__1__Qden__27598] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__27598)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__27597,Vvar__1__Qden__27598)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__27597 ) ) ) ).
fof('$_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('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_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('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1189___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Ensembles.Add',axiom,
! [V0__U,V1__B,V2__x] : cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__B,V2__x) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x)) ).
fof('$_def_Coq.Sets.Ensembles.Complement',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eComplement___24a3(V0__U,V1__A,V2__x)
<=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x) ) ).
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.Ensembles.Same_set',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__B,V2__C)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__C,V1__B) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Setminus',axiom,
! [V0__U,V1__B,V2__C,V3__x] :
( cCoq_2eSets_2eEnsembles_2eSetminus___24a4(V0__U,V1__B,V2__C,V3__x)
<=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Strict_Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__B,V2__C)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
& V1__B != V2__C ) ) ).
fof('$_def_Coq.Sets.Ensembles.Subtract',axiom,
! [V0__U,V1__B,V2__x] : cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__B,V2__x) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V1__B,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x)) ).
fof('$_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('$_def_Coq.Sets.Partial_Order.Carrier',axiom,
! [V0__U] : cCoq_2eSets_2ePartial__Order_2eCarrier___24a1(V0__U) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U) ).
fof('$_def_Coq.Sets.Partial_Order.Carrier_of',axiom,
! [V0__U,V1__p] :
( cType___24t(V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ? [Vvar__1__Carrier__of__1154] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,Vvar__1__Carrier__of__1154)
& ? [Vvar__2__Rel__of__1155] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,Vvar__2__Rel__of__1155)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,Vvar__1__Carrier__of__1154)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,Vvar__2__Rel__of__1155)
& V1__p = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V0__U,Vvar__1__Carrier__of__1154,Vvar__2__Rel__of__1155)
& cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__p) = Vvar__1__Carrier__of__1154 ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Rel_of',axiom,
! [V0__U,V1__p] :
( cType___24t(V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ? [Vvar__1__Carrier__of__1169] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,Vvar__1__Carrier__of__1169)
& ? [Vvar__2__Rel__of__1170] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,Vvar__2__Rel__of__1170)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,Vvar__1__Carrier__of__1169)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,Vvar__2__Rel__of__1170)
& V1__p = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V0__U,Vvar__1__Carrier__of__1169,Vvar__2__Rel__of__1170)
& cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__p) = Vvar__2__Rel__of__1170 ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Strict_Rel_of',axiom,
! [V0__U,V1__p,V2__x,V3__y] :
( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V2__x,V3__y)
<=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__p,V2__x,V3__y)
& V2__x != V3__y ) ) ).
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.Reflexive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__1189___24a1(V0__U) ).
fof('$_def_Coq.Sets.Relations_1.Transitive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( 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('$_def_Coq.Sets.Relations_1.contains',axiom,
! [V0__U,V1__R,V2__R_27] :
( cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V1__R,V2__R_27)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__y] :
( t(V4__y,V0__U)
=> ( p(happ(happ(V2__R_27,V3__x),V4__y))
=> p(happ(happ(V1__R,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.same_relation',axiom,
! [V0__U,V1__R,V2__R_27] :
( cCoq_2eSets_2eRelations__1_2esame__relation___24a3(V0__U,V1__R,V2__R_27)
<=> ( cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V1__R,V2__R_27)
& cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V2__R_27,V1__R) ) ) ).
fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__26543___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__26543___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__37394] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__37394)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__37394) ) ).
fof('$_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__37422] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__37422)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__37422) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__37308] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37308)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37308)
& ( ? [Vvar__0___24Anonymous__37312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37312)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37312)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__37308,Vvar__0___24Anonymous__37312) ) )
| ? [Vvar__0___24Anonymous__37313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37313)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37313)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__37314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37314)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37314)
& ( ? [Vvar__0___24Anonymous__37318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37318)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37318)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__37319] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37319)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37319)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__37314,Vvar__0___24Anonymous__37319) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__37320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37320)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37320)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__37321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37321)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37321)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) )
| ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24False) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt = cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__37306] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__37306)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__37306) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__37550] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__37550)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__37550) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__37554] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__37554)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__37554) ) ).
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)
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__37575] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__37575)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__37575) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv = cCoq_2eZArith_2eBinIntDef_2eZ_2equot ).
fof('$_def_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo = cCoq_2eZArith_2eBinIntDef_2eZ_2erem ).
fof('$_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('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( 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__23089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23089)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23089)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23089) )
| ? [Vvar__0___24Anonymous__23090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23090)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23090)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23090) ) ) ) ).
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__23035] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23035)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23035)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__23039] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23039)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23039)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23035,Vvar__0___24Anonymous__23039)) )
| ? [Vvar__0___24Anonymous__23040] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23040)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23040)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__23035,Vvar__0___24Anonymous__23040) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23041)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23041)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__23045] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23045)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23045)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__23045,Vvar__0___24Anonymous__23041) )
| ? [Vvar__0___24Anonymous__23046] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23046)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23046)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__23041,Vvar__0___24Anonymous__23046)) ) ) ) ) ) ) ) ).
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__23191] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__23191)
& ? [Vvar__3___24Anonymous__23192] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__23192)
& 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__23191,Vvar__3___24Anonymous__23192)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__23191 ) ) ) ) ).
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__23269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23269)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23269)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23269)
& ( ? [Vvar__0___24Anonymous__23273] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23273)
& Vvar__0___24Anonymous__23269 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23273)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23274)
& Vvar__0___24Anonymous__23269 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23274)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__23269 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__23275] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23275)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23275)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23275)
& ( ? [Vvar__0___24Anonymous__23279] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23279)
& Vvar__0___24Anonymous__23275 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23279)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__23280] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23280)
& Vvar__0___24Anonymous__23275 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23280)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__23275 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = 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__23199] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__23199)
& ? [Vvar__3___24Anonymous__23200] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__23200)
& 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__23199,Vvar__3___24Anonymous__23200)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__23200 ) ) ) ) ).
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__23053] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23053)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23053)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__23057] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23057)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23057)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__23053,Vvar__0___24Anonymous__23057)) )
| ? [Vvar__0___24Anonymous__23058] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23058)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23058)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__23053,Vvar__0___24Anonymous__23058)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__23059] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23059)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23059)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__23063] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23063)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23063)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__23059,Vvar__0___24Anonymous__23063)) )
| ? [Vvar__0___24Anonymous__23064] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23064)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23064)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__23059,Vvar__0___24Anonymous__23064)) ) ) ) ) ) ) ) ).
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__23283] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23283)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23283)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23283)
& ( ? [Vvar__0___24Anonymous__23287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23287)
& Vvar__0___24Anonymous__23283 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23287)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__23288] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23288)
& Vvar__0___24Anonymous__23283 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23288)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__23283 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__23289] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23289)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23289)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23289)
& ( ? [Vvar__0___24Anonymous__23293] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23293)
& Vvar__0___24Anonymous__23289 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23293)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__23294] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23294)
& Vvar__0___24Anonymous__23289 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23294)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__23289 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__23098] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23098)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23098)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23098) ) ) ) ).
fof('$_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__23048] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23048)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23048)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23048) )
| ? [Vvar__0___24Anonymous__23049] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23049)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23049)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23049) ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__37569] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__37569)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__37569) ) ).
fof('$_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__23091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23091)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23091)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23091) )
| ? [Vvar__0___24Anonymous__23092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23092)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23092)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__23101] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23101)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__23101)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__23101 )
| ? [Vvar__0___24Anonymous__23102] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23102)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__23102)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).
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.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__22259] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22259)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22259)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22259)
& ( ? [Vvar__0___24Anonymous__22263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22263)
& Vvar__0___24Anonymous__22259 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22263)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__22264] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22264)
& Vvar__0___24Anonymous__22259 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22264)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__22259 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__22265] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22265)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22265)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22265)
& ( ? [Vvar__0___24Anonymous__22269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22269)
& Vvar__0___24Anonymous__22265 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22269)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__22270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22270)
& Vvar__0___24Anonymous__22265 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22270)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__22265 = 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__22271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22271)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22271)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22271)
& ( ? [Vvar__0___24Anonymous__22275] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22275)
& Vvar__0___24Anonymous__22271 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22275)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__22276] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22276)
& Vvar__0___24Anonymous__22271 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22276)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__22271 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__22277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22277)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22277)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22277)
& ( ? [Vvar__0___24Anonymous__22281] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22281)
& Vvar__0___24Anonymous__22277 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22281)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__22282] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22282)
& Vvar__0___24Anonymous__22277 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22282)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__22277 = 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__37190] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37190)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37190)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__37191] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37191)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37191)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__37191) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__4710___24a1(V0__D) ).
fof('$_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__27829] :
( t(Vvar__1___24Anonymous__27829,V1__A)
& ? [Vvar__2___24Anonymous__27830] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__27830)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__27830)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__27829,Vvar__2___24Anonymous__27830)
& ( ( Vvar__2___24Anonymous__27830 = 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__27829)) ) )
| ? [Vvar__1___24Anonymous__27841] :
( t(Vvar__1___24Anonymous__27841,V1__A)
& ? [Vvar__2___24Anonymous__27842] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__27842)
& Vvar__2___24Anonymous__27830 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__27841,Vvar__2___24Anonymous__27842)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__27829))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__27830) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__27810] :
( t(Vvar__1___24Anonymous__27810,V1__A)
& ? [Vvar__2___24Anonymous__27811] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__27811)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__27810,Vvar__2___24Anonymous__27811)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__27810))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__27811,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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.ZMicromega.coneMember',axiom,
! [Vvar__37188] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__37188)
<=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__37188) ) ).
fof('$_def_Coq.omega.PreOmega.Z_of_N\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__N_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N ).
fof('$_def_Coq.omega.PreOmega.Z_of_nat\'',axiom,
cCoq_2eomega_2ePreOmega_2eZ__of__nat_27 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat ).
fof('$_def_Coq.omega.PreOmega.Zneg\'',axiom,
cCoq_2eomega_2ePreOmega_2eZneg_27 = cCoq_2eNumbers_2eBinNums_2eZneg ).
fof('$_def_Coq.omega.PreOmega.Zpos\'',axiom,
cCoq_2eomega_2ePreOmega_2eZpos_27 = cCoq_2eNumbers_2eBinNums_2eZpos ).
fof('$_def_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNotConstant = cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__26639] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__26639)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__26639) ) ).
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__26605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26605)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26605)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26605)
& ( ? [Vvar__0___24Anonymous__26609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26609)
& Vvar__0___24Anonymous__26605 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26609)
& 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__26605))) )
| ? [Vvar__0___24Anonymous__26610] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26610)
& Vvar__0___24Anonymous__26605 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26610)
& 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__26605))) )
| ( Vvar__0___24Anonymous__26605 = 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__26611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26611)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26611)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26611)
& ( ? [Vvar__0___24Anonymous__26615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26615)
& Vvar__0___24Anonymous__26611 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26615)
& 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__26611)) )
| ? [Vvar__0___24Anonymous__26616] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26616)
& Vvar__0___24Anonymous__26611 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26616)
& 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__26611)) )
| ( Vvar__0___24Anonymous__26611 = 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__26572] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26572)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26572)
& 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__26572))) )
| ? [Vvar__0___24Anonymous__26573] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26573)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26573)
& 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__26573)) )
| ( 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('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__34145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34145)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34145)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,happ(happ(V1__rmul,V3__r),V4__x),V4__x,Vvar__0___24Anonymous__34145),V4__x,Vvar__0___24Anonymous__34145) )
| ? [Vvar__0___24Anonymous__34146] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34146)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34146)
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,Vvar__0___24Anonymous__34146),V4__x,Vvar__0___24Anonymous__34146) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_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__34186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34186)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34186)
& 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__34186) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__34166] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34166)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34166)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__34167__34170___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34166)),c_24__let__var__6__p__34167__34170___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34166))) )
| ? [Vvar__0___24Anonymous__34168] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34168)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34168)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__34169__34171___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34168)),c_24__let__var__6__p__34169__34171___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__34168)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_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_InteriorsClosures.closure',axiom,
! [V0__X,V1__S] : cInteriorsClosures_2eclosure___24a2(V0__X,V1__S) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__150748___24a2(V0__X,V1__S))) ).
fof('$_def_InteriorsClosures.interior',axiom,
! [V0__X,V1__S] : cInteriorsClosures_2einterior___24a2(V0__X,V1__S) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),c_24__lam__150754___24a2(V0__X,V1__S))) ).
fof('$_def_InteriorsClosures.interior_closure_relations.idempotent',axiom,
! [V0__T,V1__f] :
( cInteriorsClosures_2einterior__closure__relations_2eidempotent___24a2(V0__T,V1__f)
<=> ! [V2__x] :
( t(V2__x,V0__T)
=> happ(V1__f,happ(V1__f,V2__x)) = happ(V1__f,V2__x) ) ) ).
fof('$_def_Topology.TopologicalSpaces.closed',axiom,
! [V0__X,V1__F] :
( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
<=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ).
fof('$_def_Topology.TopologicalSpaces.open',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ? [Vvar__0__point__set__236] :
( cType___24t(Vvar__0__point__set__236)
& ? [Vvar__1__open__237] :
( c_24__type__147___24t(Vvar__0__point__set__236,Vvar__1__open__237)
& ! [Vvar__var__2__F__241__245] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__236,Vvar__var__2__F__241__245)
=> ( ! [Vvar__var__3__S__242__246] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__236,Vvar__var__3__S__242__246)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__236),Vvar__var__2__F__241__245,Vvar__var__3__S__242__246)
=> p(happ(Vvar__1__open__237,Vvar__var__3__S__242__246)) ) )
=> p(happ(Vvar__1__open__237,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__236,Vvar__var__2__F__241__245))) ) )
& ! [Vvar__var__3__U__250__254] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__236,Vvar__var__3__U__250__254)
=> ! [Vvar__var__4__V__251__255] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__236,Vvar__var__4__V__251__255)
=> ( p(happ(Vvar__1__open__237,Vvar__var__3__U__250__254))
=> ( p(happ(Vvar__1__open__237,Vvar__var__4__V__251__255))
=> p(happ(Vvar__1__open__237,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__236,Vvar__var__3__U__250__254,Vvar__var__4__V__251__255))) ) ) ) )
& p(happ(Vvar__1__open__237,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__236)))
& V0__t = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__236,Vvar__1__open__237)
& cTopology_2eTopologicalSpaces_2eopen___24a1(V0__t) = Vvar__1__open__237 ) ) ) ).
fof('$_def_Topology.TopologicalSpaces.point_set',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ? [Vvar__0__point__set__169] :
( cType___24t(Vvar__0__point__set__169)
& ? [Vvar__1__open__170] :
( c_24__type__147___24t(Vvar__0__point__set__169,Vvar__1__open__170)
& ! [Vvar__var__2__F__174__178] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__169,Vvar__var__2__F__174__178)
=> ( ! [Vvar__var__3__S__175__179] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__169,Vvar__var__3__S__175__179)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__169),Vvar__var__2__F__174__178,Vvar__var__3__S__175__179)
=> p(happ(Vvar__1__open__170,Vvar__var__3__S__175__179)) ) )
=> p(happ(Vvar__1__open__170,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__169,Vvar__var__2__F__174__178))) ) )
& ! [Vvar__var__3__U__183__187] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__169,Vvar__var__3__U__183__187)
=> ! [Vvar__var__4__V__184__188] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__169,Vvar__var__4__V__184__188)
=> ( p(happ(Vvar__1__open__170,Vvar__var__3__U__183__187))
=> ( p(happ(Vvar__1__open__170,Vvar__var__4__V__184__188))
=> p(happ(Vvar__1__open__170,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__169,Vvar__var__3__U__183__187,Vvar__var__4__V__184__188))) ) ) ) )
& p(happ(Vvar__1__open__170,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__169)))
& V0__t = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__169,Vvar__1__open__170)
& cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t) = Vvar__0__point__set__169 ) ) ) ).
fof('$_def_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
! [V0__X,V1__P] : cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,V1__P) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P) ).
fof('$_def_ZornsLemma.Families.Family',axiom,
! [V0__T] : cZornsLemma_2eFamilies_2eFamily___24a1(V0__T) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T)) ).
fof('$_def_ZornsLemma.FunctionProperties.injective',axiom,
! [V0__X,V1__Y,V2__f] :
( cZornsLemma_2eFunctionProperties_2einjective___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__x1] :
( t(V3__x1,V0__X)
=> ! [V4__x2] :
( t(V4__x2,V0__X)
=> ( happ(V2__f,V3__x1) = happ(V2__f,V4__x2)
=> V3__x1 = V4__x2 ) ) ) ) ).
fof('$_def_ZornsLemma.FunctionProperties.surjective',axiom,
! [V0__X,V1__Y,V2__f] :
( cZornsLemma_2eFunctionProperties_2esurjective___24a3(V0__X,V1__Y,V2__f)
<=> ! [V3__y] :
( t(V3__y,V1__Y)
=> ? [V4__x] :
( t(V4__x,V0__X)
& happ(V2__f,V4__x) = V3__y ) ) ) ).
fof('$_def_ZornsLemma.IndexedFamilies.ImageFamily',axiom,
! [V0__T,V1__A,V2__F] : cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V0__T,V1__A,V2__F) = cCoq_2eSets_2eImage_2eIm___24a4(V1__A,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V1__A),V2__F) ).
fof('$_def_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
! [V0__A,V1__T] : cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V0__A,V1__T) = c_24__type__101___24a2(V0__A,V1__T) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__23550,Vvar__1___24Anonymous__23551,Vvar__0__P__23552,Vvar__1___24Anonymous__23553] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__23550) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__23552) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__22904,Vvar__1___24Anonymous__22905,Vvar__2___24Anonymous__22906] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22904,Vvar__1___24Anonymous__22905,Vvar__2___24Anonymous__22906) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__23866,Vvar__1__Plt__23867,Vvar__2__Pgt__23868,Vvar__3___24Anonymous__23869,Vvar__0__Peq__23870,Vvar__1__Plt__23871,Vvar__2__Pgt__23872,Vvar__3___24Anonymous__23873] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23866,Vvar__1__Plt__23867,Vvar__2__Pgt__23868) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23870,Vvar__1__Plt__23871,Vvar__2__Pgt__23872) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1033] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1033) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__314,Vvar__1___24Anonymous__315,Vvar__0__A__316] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__314,Vvar__1___24Anonymous__315) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__316) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__23805,Vvar__1__B__23806,Vvar__2___24Anonymous__23807,Vvar__0__A__23808,Vvar__1__B__23809,Vvar__2___24Anonymous__23810] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23805,Vvar__1__B__23806,Vvar__2___24Anonymous__23807) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23808,Vvar__1__B__23809,Vvar__2___24Anonymous__23810) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__4399,Vvar__0__A__4400,Vvar__1___24Anonymous__4401,Vvar__2___24Anonymous__4402] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4399) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4400,Vvar__1___24Anonymous__4401,Vvar__2___24Anonymous__4402) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__23923,Vvar__1__f__23924,Vvar__0__i__23925,Vvar__1__f__23926,Vvar__2__e__23927] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__23923,Vvar__1__f__23924) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__23925,Vvar__1__f__23926,Vvar__2__e__23927) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__4572] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__4572) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__23911,Vvar__0__d__23912] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__23911) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__23912) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__36967,Vvar__1__B__36968,Vvar__2___24Anonymous__36969,Vvar__0__A__36970,Vvar__1__B__36971,Vvar__2___24Anonymous__36972] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__36967,Vvar__1__B__36968,Vvar__2___24Anonymous__36969) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__36970,Vvar__1__B__36971) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__20120,Vvar__1__B__20121,Vvar__2___24Anonymous__20122,Vvar__0__A__20123,Vvar__1__B__20124,Vvar__2___24Anonymous__20125] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__20120,Vvar__1__B__20121) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__20123,Vvar__1__B__20124) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__2839] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2839) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__2850] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2850) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__2823,Vvar__0___24Anonymous__2824] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2823) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2824) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__37534,Vvar__1___24Anonymous__37535] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__37534,Vvar__1___24Anonymous__37535) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__22508] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__22508) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__28649,Vvar__1___24Anonymous__28650,Vvar__0__x__28651,Vvar__1__n__28652,Vvar__2___24Anonymous__28653] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28649) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28651,Vvar__1__n__28652) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__20157,Vvar__1___24Anonymous__20158] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__20157,Vvar__1___24Anonymous__20158) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__27534,Vvar__1__lt__27535,Vvar__2__eq__27536,Vvar__3__x__27537,Vvar__4__y__27538,Vvar__5___24Anonymous__27539,Vvar__0__X__27540,Vvar__1__lt__27541,Vvar__2__eq__27542,Vvar__3__x__27543,Vvar__4__y__27544,Vvar__5___24Anonymous__27545] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__27534,Vvar__1__lt__27535,Vvar__2__eq__27536,Vvar__3__x__27537,Vvar__4__y__27538) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__27540,Vvar__1__lt__27541,Vvar__2__eq__27542,Vvar__3__x__27543,Vvar__4__y__27544) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__26473,Vvar__0__n__26474,Vvar__1___24Anonymous__26475] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26473) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26474,Vvar__1___24Anonymous__26475) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__21707,Vvar__0__A__21708,Vvar__1__h__21709,Vvar__2__n__21710,Vvar__3___24Anonymous__21711] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21707) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21708,Vvar__1__h__21709,Vvar__2__n__21710,Vvar__3___24Anonymous__21711) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__24078,Vvar__1___24Anonymous__24079,Vvar__0__C__24080,Vvar__1___24Anonymous__24081] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24078,Vvar__1___24Anonymous__24079) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24080,Vvar__1___24Anonymous__24081) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__24145,Vvar__1___24Anonymous__24146,Vvar__0__C__24147,Vvar__1___24Anonymous__24148,Vvar__2___24Anonymous__24149] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__24145,Vvar__1___24Anonymous__24146) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__24147,Vvar__1___24Anonymous__24148,Vvar__2___24Anonymous__24149) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__4757,Vvar__1___24Anonymous__4758] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__4757,Vvar__1___24Anonymous__4758) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__34073,Vvar__1___24Anonymous__34074,Vvar__0__C__34075,Vvar__1___24Anonymous__34076] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__34073,Vvar__1___24Anonymous__34074) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__34075,Vvar__1___24Anonymous__34076) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__20606,Vvar__1__TX__20607,Vvar__2__AA__20608,Vvar__3__AF__20609,Vvar__0__TA__20610,Vvar__1__TX__20611,Vvar__2__AA__20612,Vvar__3__AF__20613] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__20606,Vvar__1__TX__20607,Vvar__2__AA__20608,Vvar__3__AF__20609) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__20610,Vvar__1__TX__20611,Vvar__2__AA__20612,Vvar__3__AF__20613) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__37009,Vvar__0__A__37010,Vvar__1___24Anonymous__37011] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37009) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37010,Vvar__1___24Anonymous__37011) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__22198,Vvar__1___24Anonymous__22199] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__22198,Vvar__1___24Anonymous__22199) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__25249,Vvar__0__C__25250] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__25249) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__25250) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__6879,Vvar__0__C__6880] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__6879) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__6880) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__6478,Vvar__1___24Anonymous__6479,Vvar__0__C__6480,Vvar__1___24Anonymous__6481,Vvar__2___24Anonymous__6482] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__6478,Vvar__1___24Anonymous__6479) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__6480,Vvar__1___24Anonymous__6481,Vvar__2___24Anonymous__6482) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__6646,Vvar__1___24Anonymous__6647] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__6646,Vvar__1___24Anonymous__6647) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__36549,Vvar__1__req__36550,Vvar__2__reqb__36551,Vvar__3___24Anonymous__36552] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__36549,Vvar__1__req__36550,Vvar__2__reqb__36551) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_fix_28488_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__28488__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__28492] :
( t(Vvar__1___24Anonymous__28492,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__28493] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__28493)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28492,Vvar__2___24Anonymous__28493)
& c_24__fix__28488__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__28492,c_24__fix__28488__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__28493,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_37529_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__37530] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37530)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37530)
& c_24__fix__37529__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__37529__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__37530)) )
| ? [Vvar__0___24Anonymous__37531] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37531)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__37531)
& c_24__fix__37529__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__37531) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__37529__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__23558,Vvar__0__P__23559,Vvar__1___24Anonymous__23560,Vvar__1___24Anonymous__23561] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__23558) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__23559)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__23558 = Vvar__0__P__23559 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__23554,Vvar__0__P__23555,Vvar__1___24Anonymous__23556,Vvar__1___24Anonymous__23557] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__23554) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__23555)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__23554 = Vvar__0__P__23555 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__22907,Vvar__0___24Anonymous__22908,Vvar__1___24Anonymous__22909,Vvar__1___24Anonymous__22910,Vvar__2___24Anonymous__22911,Vvar__2___24Anonymous__22912] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22907,Vvar__1___24Anonymous__22909,Vvar__2___24Anonymous__22911) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22908,Vvar__1___24Anonymous__22910,Vvar__2___24Anonymous__22912)
=> ( Vvar__2___24Anonymous__22911 = Vvar__2___24Anonymous__22912
& Vvar__1___24Anonymous__22909 = Vvar__1___24Anonymous__22910
& Vvar__0___24Anonymous__22907 = Vvar__0___24Anonymous__22908 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__23874,Vvar__0__Peq__23875,Vvar__1__Plt__23876,Vvar__1__Plt__23877,Vvar__2__Pgt__23878,Vvar__2__Pgt__23879,Vvar__3___24Anonymous__23880,Vvar__3___24Anonymous__23881] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23874,Vvar__1__Plt__23876,Vvar__2__Pgt__23878) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23875,Vvar__1__Plt__23877,Vvar__2__Pgt__23879)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__23878 = Vvar__2__Pgt__23879
& Vvar__1__Plt__23876 = Vvar__1__Plt__23877
& Vvar__0__Peq__23874 = Vvar__0__Peq__23875 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__23890,Vvar__0__Peq__23891,Vvar__1__Plt__23892,Vvar__1__Plt__23893,Vvar__2__Pgt__23894,Vvar__2__Pgt__23895,Vvar__3___24Anonymous__23896,Vvar__3___24Anonymous__23897] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23890,Vvar__1__Plt__23892,Vvar__2__Pgt__23894) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23891,Vvar__1__Plt__23893,Vvar__2__Pgt__23895)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__23894 = Vvar__2__Pgt__23895
& Vvar__1__Plt__23892 = Vvar__1__Plt__23893
& Vvar__0__Peq__23890 = Vvar__0__Peq__23891 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__23882,Vvar__0__Peq__23883,Vvar__1__Plt__23884,Vvar__1__Plt__23885,Vvar__2__Pgt__23886,Vvar__2__Pgt__23887,Vvar__3___24Anonymous__23888,Vvar__3___24Anonymous__23889] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23882,Vvar__1__Plt__23884,Vvar__2__Pgt__23886) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23883,Vvar__1__Plt__23885,Vvar__2__Pgt__23887)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__23886 = Vvar__2__Pgt__23887
& Vvar__1__Plt__23884 = Vvar__1__Plt__23885
& Vvar__0__Peq__23882 = Vvar__0__Peq__23883 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__321,Vvar__0__A__322] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__321) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__322)
=> Vvar__0__A__321 = Vvar__0__A__322 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1034,Vvar__0___24Anonymous__1035] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1034) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1035)
=> Vvar__0___24Anonymous__1034 = Vvar__0___24Anonymous__1035 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__317,Vvar__0__A__318,Vvar__1___24Anonymous__319,Vvar__1___24Anonymous__320] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__317,Vvar__1___24Anonymous__319) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__318,Vvar__1___24Anonymous__320)
=> ( Vvar__1___24Anonymous__319 = Vvar__1___24Anonymous__320
& Vvar__0__A__317 = Vvar__0__A__318 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__4405,Vvar__0__A__4406,Vvar__1___24Anonymous__4407,Vvar__1___24Anonymous__4408,Vvar__2___24Anonymous__4409,Vvar__2___24Anonymous__4410] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4405,Vvar__1___24Anonymous__4407,Vvar__2___24Anonymous__4409) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4406,Vvar__1___24Anonymous__4408,Vvar__2___24Anonymous__4410)
=> ( Vvar__2___24Anonymous__4409 = Vvar__2___24Anonymous__4410
& Vvar__1___24Anonymous__4407 = Vvar__1___24Anonymous__4408
& Vvar__0__A__4405 = Vvar__0__A__4406 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__23811,Vvar__0__A__23812,Vvar__1__B__23813,Vvar__1__B__23814,Vvar__2___24Anonymous__23815,Vvar__2___24Anonymous__23816] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23811,Vvar__1__B__23813,Vvar__2___24Anonymous__23815) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23812,Vvar__1__B__23814,Vvar__2___24Anonymous__23816)
=> ( Vvar__2___24Anonymous__23815 = Vvar__2___24Anonymous__23816
& Vvar__1__B__23813 = Vvar__1__B__23814
& Vvar__0__A__23811 = Vvar__0__A__23812 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__23817,Vvar__0__A__23818,Vvar__1__B__23819,Vvar__1__B__23820,Vvar__2___24Anonymous__23821,Vvar__2___24Anonymous__23822] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23817,Vvar__1__B__23819,Vvar__2___24Anonymous__23821) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23818,Vvar__1__B__23820,Vvar__2___24Anonymous__23822)
=> ( Vvar__2___24Anonymous__23821 = Vvar__2___24Anonymous__23822
& Vvar__1__B__23819 = Vvar__1__B__23820
& Vvar__0__A__23817 = Vvar__0__A__23818 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__4403,Vvar__0__A__4404] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4403) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4404)
=> Vvar__0__A__4403 = Vvar__0__A__4404 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__4353,Vvar__0__A__4354,Vvar__1__B__4355,Vvar__1__B__4356,Vvar__2___24Anonymous__4357,Vvar__2___24Anonymous__4358,Vvar__3___24Anonymous__4359,Vvar__3___24Anonymous__4360] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__4353,Vvar__1__B__4355,Vvar__2___24Anonymous__4357,Vvar__3___24Anonymous__4359) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__4354,Vvar__1__B__4356,Vvar__2___24Anonymous__4358,Vvar__3___24Anonymous__4360)
=> ( Vvar__3___24Anonymous__4359 = Vvar__3___24Anonymous__4360
& Vvar__2___24Anonymous__4357 = Vvar__2___24Anonymous__4358
& Vvar__1__B__4355 = Vvar__1__B__4356
& Vvar__0__A__4353 = Vvar__0__A__4354 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__4573,Vvar__0___24Anonymous__4574] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__4573) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__4574)
=> Vvar__0___24Anonymous__4573 = Vvar__0___24Anonymous__4574 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__4575,Vvar__0___24Anonymous__4576] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__4575) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__4576)
=> Vvar__0___24Anonymous__4575 = Vvar__0___24Anonymous__4576 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__4577,Vvar__0___24Anonymous__4578] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__4577) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__4578)
=> Vvar__0___24Anonymous__4577 = Vvar__0___24Anonymous__4578 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__4579,Vvar__0___24Anonymous__4580] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__4579) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__4580)
=> Vvar__0___24Anonymous__4579 = Vvar__0___24Anonymous__4580 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__4581,Vvar__0___24Anonymous__4582] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__4581) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__4582)
=> Vvar__0___24Anonymous__4581 = Vvar__0___24Anonymous__4582 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__4583,Vvar__0___24Anonymous__4584] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__4583) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__4584)
=> Vvar__0___24Anonymous__4583 = Vvar__0___24Anonymous__4584 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__4585,Vvar__0___24Anonymous__4586] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__4585) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__4586)
=> Vvar__0___24Anonymous__4585 = Vvar__0___24Anonymous__4586 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__4587,Vvar__0___24Anonymous__4588] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__4587) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__4588)
=> Vvar__0___24Anonymous__4587 = Vvar__0___24Anonymous__4588 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__4589,Vvar__0___24Anonymous__4590] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__4589) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__4590)
=> Vvar__0___24Anonymous__4589 = Vvar__0___24Anonymous__4590 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__4591,Vvar__0___24Anonymous__4592] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__4591) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__4592)
=> Vvar__0___24Anonymous__4591 = Vvar__0___24Anonymous__4592 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__23928,Vvar__0__i__23929,Vvar__1__f__23930,Vvar__1__f__23931] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__23928,Vvar__1__f__23930) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__23929,Vvar__1__f__23931)
=> ( Vvar__1__f__23930 = Vvar__1__f__23931
& Vvar__0__i__23928 = Vvar__0__i__23929 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__23932,Vvar__0__i__23933,Vvar__1__f__23934,Vvar__1__f__23935,Vvar__2__e__23936,Vvar__2__e__23937] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__23932,Vvar__1__f__23934,Vvar__2__e__23936) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__23933,Vvar__1__f__23935,Vvar__2__e__23937)
=> ( Vvar__2__e__23936 = Vvar__2__e__23937
& Vvar__1__f__23934 = Vvar__1__f__23935
& Vvar__0__i__23932 = Vvar__0__i__23933 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__23915,Vvar__0__d__23916] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__23915) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__23916)
=> Vvar__0__d__23915 = Vvar__0__d__23916 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__23913,Vvar__0__d__23914] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__23913) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__23914)
=> Vvar__0__d__23913 = Vvar__0__d__23914 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__12452,Vvar__0__A__12453,Vvar__1__P__12454,Vvar__1__P__12455,Vvar__2__x__12456,Vvar__2__x__12457,Vvar__3___24Anonymous__12458,Vvar__3___24Anonymous__12459] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__12452,Vvar__1__P__12454,Vvar__2__x__12456) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__12453,Vvar__1__P__12455,Vvar__2__x__12457)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__12456 = Vvar__2__x__12457
& Vvar__1__P__12454 = Vvar__1__P__12455
& Vvar__0__A__12452 = Vvar__0__A__12453 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__12514,Vvar__0__A__12515,Vvar__1__P__12516,Vvar__1__P__12517,Vvar__2__Q__12518,Vvar__2__Q__12519,Vvar__3__x__12520,Vvar__3__x__12521,Vvar__4___24Anonymous__12522,Vvar__4___24Anonymous__12523,Vvar__5___24Anonymous__12524,Vvar__5___24Anonymous__12525] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__12514,Vvar__1__P__12516,Vvar__2__Q__12518,Vvar__3__x__12520) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__12515,Vvar__1__P__12517,Vvar__2__Q__12519,Vvar__3__x__12521)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__12520 = Vvar__3__x__12521
& Vvar__2__Q__12518 = Vvar__2__Q__12519
& Vvar__1__P__12516 = Vvar__1__P__12517
& Vvar__0__A__12514 = Vvar__0__A__12515 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__12549,Vvar__0__A__12550,Vvar__1__P__12551,Vvar__1__P__12552,Vvar__2__x__12553,Vvar__2__x__12554,Vvar__3___24Anonymous__12555,Vvar__3___24Anonymous__12556] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__12549,Vvar__1__P__12551,Vvar__2__x__12553,Vvar__3___24Anonymous__12555) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__12550,Vvar__1__P__12552,Vvar__2__x__12554,Vvar__3___24Anonymous__12556)
=> ( Vvar__3___24Anonymous__12555 = Vvar__3___24Anonymous__12556
& Vvar__2__x__12553 = Vvar__2__x__12554
& Vvar__1__P__12551 = Vvar__1__P__12552
& Vvar__0__A__12549 = Vvar__0__A__12550 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__36943,Vvar__0__A__36944,Vvar__1__P__36945,Vvar__1__P__36946,Vvar__2__Q__36947,Vvar__2__Q__36948,Vvar__3__x__36949,Vvar__3__x__36950,Vvar__4___24Anonymous__36951,Vvar__4___24Anonymous__36952,Vvar__5___24Anonymous__36953,Vvar__5___24Anonymous__36954] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__36943,Vvar__1__P__36945,Vvar__2__Q__36947,Vvar__3__x__36949,Vvar__4___24Anonymous__36951,Vvar__5___24Anonymous__36953) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__36944,Vvar__1__P__36946,Vvar__2__Q__36948,Vvar__3__x__36950,Vvar__4___24Anonymous__36952,Vvar__5___24Anonymous__36954)
=> ( Vvar__5___24Anonymous__36953 = Vvar__5___24Anonymous__36954
& Vvar__4___24Anonymous__36951 = Vvar__4___24Anonymous__36952
& Vvar__3__x__36949 = Vvar__3__x__36950
& Vvar__2__Q__36947 = Vvar__2__Q__36948
& Vvar__1__P__36945 = Vvar__1__P__36946
& Vvar__0__A__36943 = Vvar__0__A__36944 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__36973,Vvar__0__A__36974,Vvar__1__B__36975,Vvar__1__B__36976,Vvar__2___24Anonymous__36977,Vvar__2___24Anonymous__36978] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__36973,Vvar__1__B__36975,Vvar__2___24Anonymous__36977) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__36974,Vvar__1__B__36976,Vvar__2___24Anonymous__36978)
=> ( Vvar__2___24Anonymous__36977 = Vvar__2___24Anonymous__36978
& Vvar__1__B__36975 = Vvar__1__B__36976
& Vvar__0__A__36973 = Vvar__0__A__36974 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__36979,Vvar__0__A__36980,Vvar__1__B__36981,Vvar__1__B__36982,Vvar__2___24Anonymous__36983,Vvar__2___24Anonymous__36984] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__36979,Vvar__1__B__36981) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__36980,Vvar__1__B__36982)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__36981 = Vvar__1__B__36982
& Vvar__0__A__36979 = Vvar__0__A__36980 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__20126,Vvar__0__A__20127,Vvar__1__B__20128,Vvar__1__B__20129,Vvar__2___24Anonymous__20130,Vvar__2___24Anonymous__20131] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__20126,Vvar__1__B__20128) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__20127,Vvar__1__B__20129)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__20128 = Vvar__1__B__20129
& Vvar__0__A__20126 = Vvar__0__A__20127 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__20132,Vvar__0__A__20133,Vvar__1__B__20134,Vvar__1__B__20135,Vvar__2___24Anonymous__20136,Vvar__2___24Anonymous__20137] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__20132,Vvar__1__B__20134) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__20133,Vvar__1__B__20135)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__20134 = Vvar__1__B__20135
& Vvar__0__A__20132 = Vvar__0__A__20133 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__2840,Vvar__0___24Anonymous__2841] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2840) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2841)
=> Vvar__0___24Anonymous__2840 = Vvar__0___24Anonymous__2841 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__2853,Vvar__0___24Anonymous__2854] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2853) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2854)
=> Vvar__0___24Anonymous__2853 = Vvar__0___24Anonymous__2854 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__2851,Vvar__0___24Anonymous__2852] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2851) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2852)
=> Vvar__0___24Anonymous__2851 = Vvar__0___24Anonymous__2852 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__2825,Vvar__0___24Anonymous__2826] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2825) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2826)
=> Vvar__0___24Anonymous__2825 = Vvar__0___24Anonymous__2826 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__2827,Vvar__0___24Anonymous__2828] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2827) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2828)
=> Vvar__0___24Anonymous__2827 = Vvar__0___24Anonymous__2828 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__37536,Vvar__0__p__37537,Vvar__1___24Anonymous__37538,Vvar__1___24Anonymous__37539] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__37536,Vvar__1___24Anonymous__37538) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__37537,Vvar__1___24Anonymous__37539)
=> ( Vvar__1___24Anonymous__37538 = Vvar__1___24Anonymous__37539
& Vvar__0__p__37536 = Vvar__0__p__37537 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__22509,Vvar__0___24Anonymous__22510] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__22509) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__22510)
=> Vvar__0___24Anonymous__22509 = Vvar__0___24Anonymous__22510 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__27590,Vvar__0__Qnum__27591,Vvar__1__Qden__27592,Vvar__1__Qden__27593] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__27590,Vvar__1__Qden__27592) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__27591,Vvar__1__Qden__27593)
=> ( Vvar__1__Qden__27592 = Vvar__1__Qden__27593
& Vvar__0__Qnum__27590 = Vvar__0__Qnum__27591 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__27633,Vvar__0__neg__27634,Vvar__1__cond__neg__27635,Vvar__1__cond__neg__27636] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__27633) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__27634)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__27633 = Vvar__0__neg__27634 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__27612,Vvar__0__nonneg__27613,Vvar__1__cond__nonneg__27614,Vvar__1__cond__nonneg__27615] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__27612) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__27613)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__27612 = Vvar__0__nonneg__27613 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__27626,Vvar__0__nonpos__27627,Vvar__1__cond__nonpos__27628,Vvar__1__cond__nonpos__27629] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__27626) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__27627)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__27626 = Vvar__0__nonpos__27627 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__27640,Vvar__0__nonzero__27641,Vvar__1__cond__nonzero__27642,Vvar__1__cond__nonzero__27643] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__27640) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__27641)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__27640 = Vvar__0__nonzero__27641 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__27619,Vvar__0__pos__27620,Vvar__1__cond__pos__27621,Vvar__1__cond__pos__27622] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__27619) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__27620)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__27619 = Vvar__0__pos__27620 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__28664,Vvar__0__x__28665,Vvar__1__n__28666,Vvar__1__n__28667,Vvar__2___24Anonymous__28668,Vvar__2___24Anonymous__28669] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__28664,Vvar__1__n__28666) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__28665,Vvar__1__n__28667)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__28666 = Vvar__1__n__28667
& Vvar__0__x__28664 = Vvar__0__x__28665 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__28654,Vvar__0__x__28655,Vvar__1___24Anonymous__28656,Vvar__1___24Anonymous__28657] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28654) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28655)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__28654 = Vvar__0__x__28655 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__28658,Vvar__0__x__28659,Vvar__1__n__28660,Vvar__1__n__28661,Vvar__2___24Anonymous__28662,Vvar__2___24Anonymous__28663] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28658,Vvar__1__n__28660) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28659,Vvar__1__n__28661)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__28660 = Vvar__1__n__28661
& Vvar__0__x__28658 = Vvar__0__x__28659 ) ) ).
fof('$_inj_Coq.Sets.Cpo.Definition_of_chain',axiom,
! [Vvar__0__U__23783,Vvar__0__U__23784,Vvar__1__PO__of__chain__23785,Vvar__1__PO__of__chain__23786,Vvar__2__Chain__cond__23787,Vvar__2__Chain__cond__23788] :
( cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(Vvar__0__U__23783,Vvar__1__PO__of__chain__23785) = cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(Vvar__0__U__23784,Vvar__1__PO__of__chain__23786)
=> ( c_24Proof = c_24Proof
& Vvar__1__PO__of__chain__23785 = Vvar__1__PO__of__chain__23786
& Vvar__0__U__23783 = Vvar__0__U__23784 ) ) ).
fof('$_inj_Coq.Sets.Cpo.Definition_of_cpo',axiom,
! [Vvar__0__U__23772,Vvar__0__U__23773,Vvar__1__PO__of__cpo__23774,Vvar__1__PO__of__cpo__23775,Vvar__2__Cpo__cond__23776,Vvar__2__Cpo__cond__23777] :
( cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(Vvar__0__U__23772,Vvar__1__PO__of__cpo__23774) = cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(Vvar__0__U__23773,Vvar__1__PO__of__cpo__23775)
=> ( c_24Proof = c_24Proof
& Vvar__1__PO__of__cpo__23774 = Vvar__1__PO__of__cpo__23775
& Vvar__0__U__23772 = Vvar__0__U__23773 ) ) ).
fof('$_inj_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
! [Vvar__0__U__1142,Vvar__0__U__1143,Vvar__1__Carrier__of__1144,Vvar__1__Carrier__of__1145,Vvar__2__Rel__of__1146,Vvar__2__Rel__of__1147,Vvar__3__PO__cond1__1148,Vvar__3__PO__cond1__1149,Vvar__4__PO__cond2__1150,Vvar__4__PO__cond2__1151] :
( cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__1142,Vvar__1__Carrier__of__1144,Vvar__2__Rel__of__1146) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__1143,Vvar__1__Carrier__of__1145,Vvar__2__Rel__of__1147)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__Rel__of__1146 = Vvar__2__Rel__of__1147
& Vvar__1__Carrier__of__1144 = Vvar__1__Carrier__of__1145
& Vvar__0__U__1142 = Vvar__0__U__1143 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__2802,Vvar__0___24Anonymous__2803,Vvar__1___24Anonymous__2804,Vvar__1___24Anonymous__2805,Vvar__2___24Anonymous__2806,Vvar__2___24Anonymous__2807,Vvar__3___24Anonymous__2808,Vvar__3___24Anonymous__2809,Vvar__4___24Anonymous__2810,Vvar__4___24Anonymous__2811,Vvar__5___24Anonymous__2812,Vvar__5___24Anonymous__2813,Vvar__6___24Anonymous__2814,Vvar__6___24Anonymous__2815,Vvar__7___24Anonymous__2816,Vvar__7___24Anonymous__2817] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2802,Vvar__1___24Anonymous__2804,Vvar__2___24Anonymous__2806,Vvar__3___24Anonymous__2808,Vvar__4___24Anonymous__2810,Vvar__5___24Anonymous__2812,Vvar__6___24Anonymous__2814,Vvar__7___24Anonymous__2816) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2803,Vvar__1___24Anonymous__2805,Vvar__2___24Anonymous__2807,Vvar__3___24Anonymous__2809,Vvar__4___24Anonymous__2811,Vvar__5___24Anonymous__2813,Vvar__6___24Anonymous__2815,Vvar__7___24Anonymous__2817)
=> ( Vvar__7___24Anonymous__2816 = Vvar__7___24Anonymous__2817
& Vvar__6___24Anonymous__2814 = Vvar__6___24Anonymous__2815
& Vvar__5___24Anonymous__2812 = Vvar__5___24Anonymous__2813
& Vvar__4___24Anonymous__2810 = Vvar__4___24Anonymous__2811
& Vvar__3___24Anonymous__2808 = Vvar__3___24Anonymous__2809
& Vvar__2___24Anonymous__2806 = Vvar__2___24Anonymous__2807
& Vvar__1___24Anonymous__2804 = Vvar__1___24Anonymous__2805
& Vvar__0___24Anonymous__2802 = Vvar__0___24Anonymous__2803 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__20159,Vvar__0___24Anonymous__20160,Vvar__1___24Anonymous__20161,Vvar__1___24Anonymous__20162] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__20159,Vvar__1___24Anonymous__20161) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__20160,Vvar__1___24Anonymous__20162)
=> ( Vvar__1___24Anonymous__20161 = Vvar__1___24Anonymous__20162
& Vvar__0___24Anonymous__20159 = Vvar__0___24Anonymous__20160 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__27558,Vvar__0__X__27559,Vvar__1__lt__27560,Vvar__1__lt__27561,Vvar__2__eq__27562,Vvar__2__eq__27563,Vvar__3__x__27564,Vvar__3__x__27565,Vvar__4__y__27566,Vvar__4__y__27567,Vvar__5___24Anonymous__27568,Vvar__5___24Anonymous__27569] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__27558,Vvar__1__lt__27560,Vvar__2__eq__27562,Vvar__3__x__27564,Vvar__4__y__27566) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__27559,Vvar__1__lt__27561,Vvar__2__eq__27563,Vvar__3__x__27565,Vvar__4__y__27567)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__27566 = Vvar__4__y__27567
& Vvar__3__x__27564 = Vvar__3__x__27565
& Vvar__2__eq__27562 = Vvar__2__eq__27563
& Vvar__1__lt__27560 = Vvar__1__lt__27561
& Vvar__0__X__27558 = Vvar__0__X__27559 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__27570,Vvar__0__X__27571,Vvar__1__lt__27572,Vvar__1__lt__27573,Vvar__2__eq__27574,Vvar__2__eq__27575,Vvar__3__x__27576,Vvar__3__x__27577,Vvar__4__y__27578,Vvar__4__y__27579,Vvar__5___24Anonymous__27580,Vvar__5___24Anonymous__27581] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__27570,Vvar__1__lt__27572,Vvar__2__eq__27574,Vvar__3__x__27576,Vvar__4__y__27578) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__27571,Vvar__1__lt__27573,Vvar__2__eq__27575,Vvar__3__x__27577,Vvar__4__y__27579)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__27578 = Vvar__4__y__27579
& Vvar__3__x__27576 = Vvar__3__x__27577
& Vvar__2__eq__27574 = Vvar__2__eq__27575
& Vvar__1__lt__27572 = Vvar__1__lt__27573
& Vvar__0__X__27570 = Vvar__0__X__27571 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__27546,Vvar__0__X__27547,Vvar__1__lt__27548,Vvar__1__lt__27549,Vvar__2__eq__27550,Vvar__2__eq__27551,Vvar__3__x__27552,Vvar__3__x__27553,Vvar__4__y__27554,Vvar__4__y__27555,Vvar__5___24Anonymous__27556,Vvar__5___24Anonymous__27557] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__27546,Vvar__1__lt__27548,Vvar__2__eq__27550,Vvar__3__x__27552,Vvar__4__y__27554) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__27547,Vvar__1__lt__27549,Vvar__2__eq__27551,Vvar__3__x__27553,Vvar__4__y__27555)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__27554 = Vvar__4__y__27555
& Vvar__3__x__27552 = Vvar__3__x__27553
& Vvar__2__eq__27550 = Vvar__2__eq__27551
& Vvar__1__lt__27548 = Vvar__1__lt__27549
& Vvar__0__X__27546 = Vvar__0__X__27547 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__26476,Vvar__0__n__26477] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26476) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26477)
=> Vvar__0__n__26476 = Vvar__0__n__26477 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__26478,Vvar__0__n__26479,Vvar__1___24Anonymous__26480,Vvar__1___24Anonymous__26481] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26478,Vvar__1___24Anonymous__26480) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26479,Vvar__1___24Anonymous__26481)
=> ( Vvar__1___24Anonymous__26480 = Vvar__1___24Anonymous__26481
& Vvar__0__n__26478 = Vvar__0__n__26479 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__21714,Vvar__0__A__21715,Vvar__1__h__21716,Vvar__1__h__21717,Vvar__2__n__21718,Vvar__2__n__21719,Vvar__3___24Anonymous__21720,Vvar__3___24Anonymous__21721] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21714,Vvar__1__h__21716,Vvar__2__n__21718,Vvar__3___24Anonymous__21720) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21715,Vvar__1__h__21717,Vvar__2__n__21719,Vvar__3___24Anonymous__21721)
=> ( Vvar__3___24Anonymous__21720 = Vvar__3___24Anonymous__21721
& Vvar__2__n__21718 = Vvar__2__n__21719
& Vvar__1__h__21716 = Vvar__1__h__21717
& Vvar__0__A__21714 = Vvar__0__A__21715 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__21712,Vvar__0__A__21713] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21712) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21713)
=> Vvar__0__A__21712 = Vvar__0__A__21713 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__37231,Vvar__0__a__37232,Vvar__1__b__37233,Vvar__1__b__37234,Vvar__2__u__37235,Vvar__2__u__37236,Vvar__3__v__37237,Vvar__3__v__37238,Vvar__4__d__37239,Vvar__4__d__37240,Vvar__5___24Anonymous__37241,Vvar__5___24Anonymous__37242,Vvar__6___24Anonymous__37243,Vvar__6___24Anonymous__37244] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__37231,Vvar__1__b__37233,Vvar__2__u__37235,Vvar__3__v__37237,Vvar__4__d__37239) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__37232,Vvar__1__b__37234,Vvar__2__u__37236,Vvar__3__v__37238,Vvar__4__d__37240)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__37239 = Vvar__4__d__37240
& Vvar__3__v__37237 = Vvar__3__v__37238
& Vvar__2__u__37235 = Vvar__2__u__37236
& Vvar__1__b__37233 = Vvar__1__b__37234
& Vvar__0__a__37231 = Vvar__0__a__37232 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__37292,Vvar__0__x__37293,Vvar__1__p__37294,Vvar__1__p__37295,Vvar__2__q__37296,Vvar__2__q__37297,Vvar__3__r__37298,Vvar__3__r__37299,Vvar__4___24Anonymous__37300,Vvar__4___24Anonymous__37301,Vvar__5___24Anonymous__37302,Vvar__5___24Anonymous__37303,Vvar__6___24Anonymous__37304,Vvar__6___24Anonymous__37305] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__37292,Vvar__1__p__37294,Vvar__2__q__37296,Vvar__3__r__37298) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__37293,Vvar__1__p__37295,Vvar__2__q__37297,Vvar__3__r__37299)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__37298 = Vvar__3__r__37299
& Vvar__2__q__37296 = Vvar__2__q__37297
& Vvar__1__p__37294 = Vvar__1__p__37295
& Vvar__0__x__37292 = Vvar__0__x__37293 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__24086,Vvar__0__C__24087,Vvar__1___24Anonymous__24088,Vvar__1___24Anonymous__24089] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24086,Vvar__1___24Anonymous__24088) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24087,Vvar__1___24Anonymous__24089)
=> ( Vvar__1___24Anonymous__24088 = Vvar__1___24Anonymous__24089
& Vvar__0__C__24086 = Vvar__0__C__24087 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__24090,Vvar__0__C__24091,Vvar__1___24Anonymous__24092,Vvar__1___24Anonymous__24093,Vvar__2___24Anonymous__24094,Vvar__2___24Anonymous__24095] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__24090,Vvar__1___24Anonymous__24092,Vvar__2___24Anonymous__24094) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__24091,Vvar__1___24Anonymous__24093,Vvar__2___24Anonymous__24095)
=> ( Vvar__2___24Anonymous__24094 = Vvar__2___24Anonymous__24095
& Vvar__1___24Anonymous__24092 = Vvar__1___24Anonymous__24093
& Vvar__0__C__24090 = Vvar__0__C__24091 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__24082,Vvar__0__C__24083,Vvar__1___24Anonymous__24084,Vvar__1___24Anonymous__24085] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24082,Vvar__1___24Anonymous__24084) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24083,Vvar__1___24Anonymous__24085)
=> ( Vvar__1___24Anonymous__24084 = Vvar__1___24Anonymous__24085
& Vvar__0__C__24082 = Vvar__0__C__24083 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__24102,Vvar__0__C__24103,Vvar__1___24Anonymous__24104,Vvar__1___24Anonymous__24105,Vvar__2___24Anonymous__24106,Vvar__2___24Anonymous__24107] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__24102,Vvar__1___24Anonymous__24104,Vvar__2___24Anonymous__24106) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__24103,Vvar__1___24Anonymous__24105,Vvar__2___24Anonymous__24107)
=> ( Vvar__2___24Anonymous__24106 = Vvar__2___24Anonymous__24107
& Vvar__1___24Anonymous__24104 = Vvar__1___24Anonymous__24105
& Vvar__0__C__24102 = Vvar__0__C__24103 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__24108,Vvar__0__C__24109,Vvar__1___24Anonymous__24110,Vvar__1___24Anonymous__24111] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__24108,Vvar__1___24Anonymous__24110) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__24109,Vvar__1___24Anonymous__24111)
=> ( Vvar__1___24Anonymous__24110 = Vvar__1___24Anonymous__24111
& Vvar__0__C__24108 = Vvar__0__C__24109 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__24112,Vvar__0__C__24113,Vvar__1___24Anonymous__24114,Vvar__1___24Anonymous__24115,Vvar__2___24Anonymous__24116,Vvar__2___24Anonymous__24117] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__24112,Vvar__1___24Anonymous__24114,Vvar__2___24Anonymous__24116) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__24113,Vvar__1___24Anonymous__24115,Vvar__2___24Anonymous__24117)
=> ( Vvar__2___24Anonymous__24116 = Vvar__2___24Anonymous__24117
& Vvar__1___24Anonymous__24114 = Vvar__1___24Anonymous__24115
& Vvar__0__C__24112 = Vvar__0__C__24113 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__24096,Vvar__0__C__24097,Vvar__1___24Anonymous__24098,Vvar__1___24Anonymous__24099,Vvar__2___24Anonymous__24100,Vvar__2___24Anonymous__24101] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__24096,Vvar__1___24Anonymous__24098,Vvar__2___24Anonymous__24100) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__24097,Vvar__1___24Anonymous__24099,Vvar__2___24Anonymous__24101)
=> ( Vvar__2___24Anonymous__24100 = Vvar__2___24Anonymous__24101
& Vvar__1___24Anonymous__24098 = Vvar__1___24Anonymous__24099
& Vvar__0__C__24096 = Vvar__0__C__24097 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__24160,Vvar__0__C__24161,Vvar__1___24Anonymous__24162,Vvar__1___24Anonymous__24163,Vvar__2___24Anonymous__24164,Vvar__2___24Anonymous__24165,Vvar__3___24Anonymous__24166,Vvar__3___24Anonymous__24167] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__24160,Vvar__1___24Anonymous__24162,Vvar__2___24Anonymous__24164,Vvar__3___24Anonymous__24166) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__24161,Vvar__1___24Anonymous__24163,Vvar__2___24Anonymous__24165,Vvar__3___24Anonymous__24167)
=> ( Vvar__3___24Anonymous__24166 = Vvar__3___24Anonymous__24167
& Vvar__2___24Anonymous__24164 = Vvar__2___24Anonymous__24165
& Vvar__1___24Anonymous__24162 = Vvar__1___24Anonymous__24163
& Vvar__0__C__24160 = Vvar__0__C__24161 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__24150,Vvar__0__C__24151,Vvar__1___24Anonymous__24152,Vvar__1___24Anonymous__24153] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__24150,Vvar__1___24Anonymous__24152) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__24151,Vvar__1___24Anonymous__24153)
=> ( Vvar__1___24Anonymous__24152 = Vvar__1___24Anonymous__24153
& Vvar__0__C__24150 = Vvar__0__C__24151 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__24154,Vvar__0__C__24155,Vvar__1___24Anonymous__24156,Vvar__1___24Anonymous__24157,Vvar__2___24Anonymous__24158,Vvar__2___24Anonymous__24159] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__24154,Vvar__1___24Anonymous__24156,Vvar__2___24Anonymous__24158) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__24155,Vvar__1___24Anonymous__24157,Vvar__2___24Anonymous__24159)
=> ( Vvar__2___24Anonymous__24158 = Vvar__2___24Anonymous__24159
& Vvar__1___24Anonymous__24156 = Vvar__1___24Anonymous__24157
& Vvar__0__C__24154 = Vvar__0__C__24155 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__4763,Vvar__0___24Anonymous__4764,Vvar__1___24Anonymous__4765,Vvar__1___24Anonymous__4766] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__4763,Vvar__1___24Anonymous__4765) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__4764,Vvar__1___24Anonymous__4766)
=> ( Vvar__1___24Anonymous__4765 = Vvar__1___24Anonymous__4766
& Vvar__0___24Anonymous__4763 = Vvar__0___24Anonymous__4764 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__4759,Vvar__0___24Anonymous__4760,Vvar__1___24Anonymous__4761,Vvar__1___24Anonymous__4762] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__4759,Vvar__1___24Anonymous__4761) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__4760,Vvar__1___24Anonymous__4762)
=> ( Vvar__1___24Anonymous__4761 = Vvar__1___24Anonymous__4762
& Vvar__0___24Anonymous__4759 = Vvar__0___24Anonymous__4760 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__27785,Vvar__0__r__27786] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__27785) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__27786)
=> Vvar__0__r__27785 = Vvar__0__r__27786 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__27773,Vvar__0__r1__27774,Vvar__1__r2__27775,Vvar__1__r2__27776] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__27773,Vvar__1__r2__27775) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__27774,Vvar__1__r2__27776)
=> ( Vvar__1__r2__27775 = Vvar__1__r2__27776
& Vvar__0__r1__27773 = Vvar__0__r1__27774 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__27777,Vvar__0__r1__27778,Vvar__1__r2__27779,Vvar__1__r2__27780] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__27777,Vvar__1__r2__27779) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__27778,Vvar__1__r2__27780)
=> ( Vvar__1__r2__27779 = Vvar__1__r2__27780
& Vvar__0__r1__27777 = Vvar__0__r1__27778 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__27787,Vvar__0__r__27788] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__27787) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__27788)
=> Vvar__0__r__27787 = Vvar__0__r__27788 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__27769,Vvar__0__r1__27770,Vvar__1__r2__27771,Vvar__1__r2__27772] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__27769,Vvar__1__r2__27771) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__27770,Vvar__1__r2__27772)
=> ( Vvar__1__r2__27771 = Vvar__1__r2__27772
& Vvar__0__r1__27769 = Vvar__0__r1__27770 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__27781,Vvar__0__r1__27782,Vvar__1__z__27783,Vvar__1__z__27784] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__27781,Vvar__1__z__27783) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__27782,Vvar__1__z__27784)
=> ( Vvar__1__z__27783 = Vvar__1__z__27784
& Vvar__0__r1__27781 = Vvar__0__r1__27782 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__27765,Vvar__0__r__27766] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__27765) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__27766)
=> Vvar__0__r__27765 = Vvar__0__r__27766 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__27767,Vvar__0__r__27768] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__27767) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__27768)
=> Vvar__0__r__27767 = Vvar__0__r__27768 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__34116,Vvar__0__T__34117,Vvar__1__Flhs__34118,Vvar__1__Flhs__34119,Vvar__2__Fop__34120,Vvar__2__Fop__34121,Vvar__3__Frhs__34122,Vvar__3__Frhs__34123] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__34116,Vvar__1__Flhs__34118,Vvar__2__Fop__34120,Vvar__3__Frhs__34122) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__34117,Vvar__1__Flhs__34119,Vvar__2__Fop__34121,Vvar__3__Frhs__34123)
=> ( Vvar__3__Frhs__34122 = Vvar__3__Frhs__34123
& Vvar__2__Fop__34120 = Vvar__2__Fop__34121
& Vvar__1__Flhs__34118 = Vvar__1__Flhs__34119
& Vvar__0__T__34116 = Vvar__0__T__34117 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__34097,Vvar__0__C__34098,Vvar__1___24Anonymous__34099,Vvar__1___24Anonymous__34100,Vvar__2___24Anonymous__34101,Vvar__2___24Anonymous__34102] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__34097,Vvar__1___24Anonymous__34099,Vvar__2___24Anonymous__34101) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__34098,Vvar__1___24Anonymous__34100,Vvar__2___24Anonymous__34102)
=> ( Vvar__2___24Anonymous__34101 = Vvar__2___24Anonymous__34102
& Vvar__1___24Anonymous__34099 = Vvar__1___24Anonymous__34100
& Vvar__0__C__34097 = Vvar__0__C__34098 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__34103,Vvar__0__C__34104,Vvar__1___24Anonymous__34105,Vvar__1___24Anonymous__34106] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__34103,Vvar__1___24Anonymous__34105) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__34104,Vvar__1___24Anonymous__34106)
=> ( Vvar__1___24Anonymous__34105 = Vvar__1___24Anonymous__34106
& Vvar__0__C__34103 = Vvar__0__C__34104 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__34077,Vvar__0__C__34078,Vvar__1___24Anonymous__34079,Vvar__1___24Anonymous__34080] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__34077,Vvar__1___24Anonymous__34079) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__34078,Vvar__1___24Anonymous__34080)
=> ( Vvar__1___24Anonymous__34079 = Vvar__1___24Anonymous__34080
& Vvar__0__C__34077 = Vvar__0__C__34078 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__34085,Vvar__0__C__34086,Vvar__1___24Anonymous__34087,Vvar__1___24Anonymous__34088,Vvar__2___24Anonymous__34089,Vvar__2___24Anonymous__34090] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__34085,Vvar__1___24Anonymous__34087,Vvar__2___24Anonymous__34089) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__34086,Vvar__1___24Anonymous__34088,Vvar__2___24Anonymous__34090)
=> ( Vvar__2___24Anonymous__34089 = Vvar__2___24Anonymous__34090
& Vvar__1___24Anonymous__34087 = Vvar__1___24Anonymous__34088
& Vvar__0__C__34085 = Vvar__0__C__34086 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__34091,Vvar__0__C__34092,Vvar__1___24Anonymous__34093,Vvar__1___24Anonymous__34094,Vvar__2___24Anonymous__34095,Vvar__2___24Anonymous__34096] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__34091,Vvar__1___24Anonymous__34093,Vvar__2___24Anonymous__34095) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__34092,Vvar__1___24Anonymous__34094,Vvar__2___24Anonymous__34096)
=> ( Vvar__2___24Anonymous__34095 = Vvar__2___24Anonymous__34096
& Vvar__1___24Anonymous__34093 = Vvar__1___24Anonymous__34094
& Vvar__0__C__34091 = Vvar__0__C__34092 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__34081,Vvar__0__C__34082,Vvar__1___24Anonymous__34083,Vvar__1___24Anonymous__34084] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__34081,Vvar__1___24Anonymous__34083) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__34082,Vvar__1___24Anonymous__34084)
=> ( Vvar__1___24Anonymous__34083 = Vvar__1___24Anonymous__34084
& Vvar__0__C__34081 = Vvar__0__C__34082 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__34107,Vvar__0__C__34108] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__34107) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__34108)
=> Vvar__0__C__34107 = Vvar__0__C__34108 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__20640,Vvar__0__TA__20641,Vvar__1__TX__20642,Vvar__1__TX__20643,Vvar__2__AA__20644,Vvar__2__AA__20645,Vvar__3__AF__20646,Vvar__3__AF__20647,Vvar__4___24Anonymous__20648,Vvar__4___24Anonymous__20649,Vvar__5___24Anonymous__20650,Vvar__5___24Anonymous__20651] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__20640,Vvar__1__TX__20642,Vvar__2__AA__20644,Vvar__3__AF__20646,Vvar__4___24Anonymous__20648,Vvar__5___24Anonymous__20650) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__20641,Vvar__1__TX__20643,Vvar__2__AA__20645,Vvar__3__AF__20647,Vvar__4___24Anonymous__20649,Vvar__5___24Anonymous__20651)
=> ( Vvar__5___24Anonymous__20650 = Vvar__5___24Anonymous__20651
& Vvar__4___24Anonymous__20648 = Vvar__4___24Anonymous__20649
& Vvar__3__AF__20646 = Vvar__3__AF__20647
& Vvar__2__AA__20644 = Vvar__2__AA__20645
& Vvar__1__TX__20642 = Vvar__1__TX__20643
& Vvar__0__TA__20640 = Vvar__0__TA__20641 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__20652,Vvar__0__TA__20653,Vvar__1__TX__20654,Vvar__1__TX__20655,Vvar__2__AA__20656,Vvar__2__AA__20657,Vvar__3__AF__20658,Vvar__3__AF__20659,Vvar__4___24Anonymous__20660,Vvar__4___24Anonymous__20661,Vvar__5___24Anonymous__20662,Vvar__5___24Anonymous__20663] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__20652,Vvar__1__TX__20654,Vvar__2__AA__20656,Vvar__3__AF__20658,Vvar__4___24Anonymous__20660,Vvar__5___24Anonymous__20662) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__20653,Vvar__1__TX__20655,Vvar__2__AA__20657,Vvar__3__AF__20659,Vvar__4___24Anonymous__20661,Vvar__5___24Anonymous__20663)
=> ( Vvar__5___24Anonymous__20662 = Vvar__5___24Anonymous__20663
& Vvar__4___24Anonymous__20660 = Vvar__4___24Anonymous__20661
& Vvar__3__AF__20658 = Vvar__3__AF__20659
& Vvar__2__AA__20656 = Vvar__2__AA__20657
& Vvar__1__TX__20654 = Vvar__1__TX__20655
& Vvar__0__TA__20652 = Vvar__0__TA__20653 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__20664,Vvar__0__TA__20665,Vvar__1__TX__20666,Vvar__1__TX__20667,Vvar__2__AA__20668,Vvar__2__AA__20669,Vvar__3__AF__20670,Vvar__3__AF__20671,Vvar__4___24Anonymous__20672,Vvar__4___24Anonymous__20673,Vvar__5___24Anonymous__20674,Vvar__5___24Anonymous__20675] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__20664,Vvar__1__TX__20666,Vvar__2__AA__20668,Vvar__3__AF__20670,Vvar__4___24Anonymous__20672,Vvar__5___24Anonymous__20674) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__20665,Vvar__1__TX__20667,Vvar__2__AA__20669,Vvar__3__AF__20671,Vvar__4___24Anonymous__20673,Vvar__5___24Anonymous__20675)
=> ( Vvar__5___24Anonymous__20674 = Vvar__5___24Anonymous__20675
& Vvar__4___24Anonymous__20672 = Vvar__4___24Anonymous__20673
& Vvar__3__AF__20670 = Vvar__3__AF__20671
& Vvar__2__AA__20668 = Vvar__2__AA__20669
& Vvar__1__TX__20666 = Vvar__1__TX__20667
& Vvar__0__TA__20664 = Vvar__0__TA__20665 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__20622,Vvar__0__TA__20623,Vvar__1__TX__20624,Vvar__1__TX__20625,Vvar__2__AA__20626,Vvar__2__AA__20627,Vvar__3__AF__20628,Vvar__3__AF__20629] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__20622,Vvar__1__TX__20624,Vvar__2__AA__20626,Vvar__3__AF__20628) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__20623,Vvar__1__TX__20625,Vvar__2__AA__20627,Vvar__3__AF__20629)
=> ( Vvar__3__AF__20628 = Vvar__3__AF__20629
& Vvar__2__AA__20626 = Vvar__2__AA__20627
& Vvar__1__TX__20624 = Vvar__1__TX__20625
& Vvar__0__TA__20622 = Vvar__0__TA__20623 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__20686,Vvar__0__TA__20687,Vvar__1__TX__20688,Vvar__1__TX__20689,Vvar__2__AA__20690,Vvar__2__AA__20691,Vvar__3__AF__20692,Vvar__3__AF__20693,Vvar__4___24Anonymous__20694,Vvar__4___24Anonymous__20695,Vvar__5___24Anonymous__20696,Vvar__5___24Anonymous__20697,Vvar__6___24Anonymous__20698,Vvar__6___24Anonymous__20699] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__20686,Vvar__1__TX__20688,Vvar__2__AA__20690,Vvar__3__AF__20692,Vvar__4___24Anonymous__20694,Vvar__5___24Anonymous__20696,Vvar__6___24Anonymous__20698) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__20687,Vvar__1__TX__20689,Vvar__2__AA__20691,Vvar__3__AF__20693,Vvar__4___24Anonymous__20695,Vvar__5___24Anonymous__20697,Vvar__6___24Anonymous__20699)
=> ( Vvar__6___24Anonymous__20698 = Vvar__6___24Anonymous__20699
& Vvar__5___24Anonymous__20696 = Vvar__5___24Anonymous__20697
& Vvar__4___24Anonymous__20694 = Vvar__4___24Anonymous__20695
& Vvar__3__AF__20692 = Vvar__3__AF__20693
& Vvar__2__AA__20690 = Vvar__2__AA__20691
& Vvar__1__TX__20688 = Vvar__1__TX__20689
& Vvar__0__TA__20686 = Vvar__0__TA__20687 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__20676,Vvar__0__TA__20677,Vvar__1__TX__20678,Vvar__1__TX__20679,Vvar__2__AA__20680,Vvar__2__AA__20681,Vvar__3__AF__20682,Vvar__3__AF__20683,Vvar__4___24Anonymous__20684,Vvar__4___24Anonymous__20685] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__20676,Vvar__1__TX__20678,Vvar__2__AA__20680,Vvar__3__AF__20682,Vvar__4___24Anonymous__20684) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__20677,Vvar__1__TX__20679,Vvar__2__AA__20681,Vvar__3__AF__20683,Vvar__4___24Anonymous__20685)
=> ( Vvar__4___24Anonymous__20684 = Vvar__4___24Anonymous__20685
& Vvar__3__AF__20682 = Vvar__3__AF__20683
& Vvar__2__AA__20680 = Vvar__2__AA__20681
& Vvar__1__TX__20678 = Vvar__1__TX__20679
& Vvar__0__TA__20676 = Vvar__0__TA__20677 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__20614,Vvar__0__TA__20615,Vvar__1__TX__20616,Vvar__1__TX__20617,Vvar__2__AA__20618,Vvar__2__AA__20619,Vvar__3__AF__20620,Vvar__3__AF__20621] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__20614,Vvar__1__TX__20616,Vvar__2__AA__20618,Vvar__3__AF__20620) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__20615,Vvar__1__TX__20617,Vvar__2__AA__20619,Vvar__3__AF__20621)
=> ( Vvar__3__AF__20620 = Vvar__3__AF__20621
& Vvar__2__AA__20618 = Vvar__2__AA__20619
& Vvar__1__TX__20616 = Vvar__1__TX__20617
& Vvar__0__TA__20614 = Vvar__0__TA__20615 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__20630,Vvar__0__TA__20631,Vvar__1__TX__20632,Vvar__1__TX__20633,Vvar__2__AA__20634,Vvar__2__AA__20635,Vvar__3__AF__20636,Vvar__3__AF__20637,Vvar__4___24Anonymous__20638,Vvar__4___24Anonymous__20639] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__20630,Vvar__1__TX__20632,Vvar__2__AA__20634,Vvar__3__AF__20636,Vvar__4___24Anonymous__20638) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__20631,Vvar__1__TX__20633,Vvar__2__AA__20635,Vvar__3__AF__20637,Vvar__4___24Anonymous__20639)
=> ( Vvar__4___24Anonymous__20638 = Vvar__4___24Anonymous__20639
& Vvar__3__AF__20636 = Vvar__3__AF__20637
& Vvar__2__AA__20634 = Vvar__2__AA__20635
& Vvar__1__TX__20632 = Vvar__1__TX__20633
& Vvar__0__TA__20630 = Vvar__0__TA__20631 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__37018,Vvar__0__A__37019,Vvar__1___24Anonymous__37020,Vvar__1___24Anonymous__37021,Vvar__2___24Anonymous__37022,Vvar__2___24Anonymous__37023,Vvar__3___24Anonymous__37024,Vvar__3___24Anonymous__37025] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__37018,Vvar__1___24Anonymous__37020,Vvar__2___24Anonymous__37022,Vvar__3___24Anonymous__37024) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__37019,Vvar__1___24Anonymous__37021,Vvar__2___24Anonymous__37023,Vvar__3___24Anonymous__37025)
=> ( Vvar__3___24Anonymous__37024 = Vvar__3___24Anonymous__37025
& Vvar__2___24Anonymous__37022 = Vvar__2___24Anonymous__37023
& Vvar__1___24Anonymous__37020 = Vvar__1___24Anonymous__37021
& Vvar__0__A__37018 = Vvar__0__A__37019 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__37014,Vvar__0__A__37015,Vvar__1___24Anonymous__37016,Vvar__1___24Anonymous__37017] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37014,Vvar__1___24Anonymous__37016) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__37015,Vvar__1___24Anonymous__37017)
=> ( Vvar__1___24Anonymous__37016 = Vvar__1___24Anonymous__37017
& Vvar__0__A__37014 = Vvar__0__A__37015 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__37012,Vvar__0__A__37013] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37012) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__37013)
=> Vvar__0__A__37012 = Vvar__0__A__37013 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__22204,Vvar__0___24Anonymous__22205,Vvar__1___24Anonymous__22206,Vvar__1___24Anonymous__22207] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__22204,Vvar__1___24Anonymous__22206) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__22205,Vvar__1___24Anonymous__22207)
=> ( Vvar__1___24Anonymous__22206 = Vvar__1___24Anonymous__22207
& Vvar__0___24Anonymous__22204 = Vvar__0___24Anonymous__22205 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__22208,Vvar__0___24Anonymous__22209,Vvar__1___24Anonymous__22210,Vvar__1___24Anonymous__22211,Vvar__2___24Anonymous__22212,Vvar__2___24Anonymous__22213] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__22208,Vvar__1___24Anonymous__22210,Vvar__2___24Anonymous__22212) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__22209,Vvar__1___24Anonymous__22211,Vvar__2___24Anonymous__22213)
=> ( Vvar__2___24Anonymous__22212 = Vvar__2___24Anonymous__22213
& Vvar__1___24Anonymous__22210 = Vvar__1___24Anonymous__22211
& Vvar__0___24Anonymous__22208 = Vvar__0___24Anonymous__22209 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__22200,Vvar__0___24Anonymous__22201,Vvar__1___24Anonymous__22202,Vvar__1___24Anonymous__22203] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__22200,Vvar__1___24Anonymous__22202) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__22201,Vvar__1___24Anonymous__22203)
=> ( Vvar__1___24Anonymous__22202 = Vvar__1___24Anonymous__22203
& Vvar__0___24Anonymous__22200 = Vvar__0___24Anonymous__22201 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__25253,Vvar__0__C__25254] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__25253) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__25254)
=> Vvar__0__C__25253 = Vvar__0__C__25254 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__25251,Vvar__0__C__25252] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__25251) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__25252)
=> Vvar__0__C__25251 = Vvar__0__C__25252 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__25259,Vvar__0__C__25260,Vvar__1___24Anonymous__25261,Vvar__1___24Anonymous__25262] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__25259,Vvar__1___24Anonymous__25261) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__25260,Vvar__1___24Anonymous__25262)
=> ( Vvar__1___24Anonymous__25261 = Vvar__1___24Anonymous__25262
& Vvar__0__C__25259 = Vvar__0__C__25260 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__25263,Vvar__0__C__25264,Vvar__1___24Anonymous__25265,Vvar__1___24Anonymous__25266,Vvar__2___24Anonymous__25267,Vvar__2___24Anonymous__25268] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__25263,Vvar__1___24Anonymous__25265,Vvar__2___24Anonymous__25267) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__25264,Vvar__1___24Anonymous__25266,Vvar__2___24Anonymous__25268)
=> ( Vvar__2___24Anonymous__25267 = Vvar__2___24Anonymous__25268
& Vvar__1___24Anonymous__25265 = Vvar__1___24Anonymous__25266
& Vvar__0__C__25263 = Vvar__0__C__25264 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__25255,Vvar__0__C__25256,Vvar__1___24Anonymous__25257,Vvar__1___24Anonymous__25258] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__25255,Vvar__1___24Anonymous__25257) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__25256,Vvar__1___24Anonymous__25258)
=> ( Vvar__1___24Anonymous__25257 = Vvar__1___24Anonymous__25258
& Vvar__0__C__25255 = Vvar__0__C__25256 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__25289,Vvar__0__C__25290,Vvar__1___24Anonymous__25291,Vvar__1___24Anonymous__25292,Vvar__2___24Anonymous__25293,Vvar__2___24Anonymous__25294] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__25289,Vvar__1___24Anonymous__25291,Vvar__2___24Anonymous__25293) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__25290,Vvar__1___24Anonymous__25292,Vvar__2___24Anonymous__25294)
=> ( Vvar__2___24Anonymous__25293 = Vvar__2___24Anonymous__25294
& Vvar__1___24Anonymous__25291 = Vvar__1___24Anonymous__25292
& Vvar__0__C__25289 = Vvar__0__C__25290 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__25285,Vvar__0__C__25286,Vvar__1___24Anonymous__25287,Vvar__1___24Anonymous__25288] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__25285,Vvar__1___24Anonymous__25287) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__25286,Vvar__1___24Anonymous__25288)
=> ( Vvar__1___24Anonymous__25287 = Vvar__1___24Anonymous__25288
& Vvar__0__C__25285 = Vvar__0__C__25286 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__25275,Vvar__0__C__25276,Vvar__1___24Anonymous__25277,Vvar__1___24Anonymous__25278,Vvar__2___24Anonymous__25279,Vvar__2___24Anonymous__25280] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__25275,Vvar__1___24Anonymous__25277,Vvar__2___24Anonymous__25279) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__25276,Vvar__1___24Anonymous__25278,Vvar__2___24Anonymous__25280)
=> ( Vvar__2___24Anonymous__25279 = Vvar__2___24Anonymous__25280
& Vvar__1___24Anonymous__25277 = Vvar__1___24Anonymous__25278
& Vvar__0__C__25275 = Vvar__0__C__25276 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__25281,Vvar__0__C__25282,Vvar__1___24Anonymous__25283,Vvar__1___24Anonymous__25284] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__25281,Vvar__1___24Anonymous__25283) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__25282,Vvar__1___24Anonymous__25284)
=> ( Vvar__1___24Anonymous__25283 = Vvar__1___24Anonymous__25284
& Vvar__0__C__25281 = Vvar__0__C__25282 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__25295,Vvar__0__C__25296,Vvar__1___24Anonymous__25297,Vvar__1___24Anonymous__25298,Vvar__2___24Anonymous__25299,Vvar__2___24Anonymous__25300] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__25295,Vvar__1___24Anonymous__25297,Vvar__2___24Anonymous__25299) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__25296,Vvar__1___24Anonymous__25298,Vvar__2___24Anonymous__25300)
=> ( Vvar__2___24Anonymous__25299 = Vvar__2___24Anonymous__25300
& Vvar__1___24Anonymous__25297 = Vvar__1___24Anonymous__25298
& Vvar__0__C__25295 = Vvar__0__C__25296 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__25269,Vvar__0__C__25270,Vvar__1___24Anonymous__25271,Vvar__1___24Anonymous__25272,Vvar__2___24Anonymous__25273,Vvar__2___24Anonymous__25274] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__25269,Vvar__1___24Anonymous__25271,Vvar__2___24Anonymous__25273) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__25270,Vvar__1___24Anonymous__25272,Vvar__2___24Anonymous__25274)
=> ( Vvar__2___24Anonymous__25273 = Vvar__2___24Anonymous__25274
& Vvar__1___24Anonymous__25271 = Vvar__1___24Anonymous__25272
& Vvar__0__C__25269 = Vvar__0__C__25270 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__25313,Vvar__0__C__25314,Vvar__1__num__25315,Vvar__1__num__25316,Vvar__2__denum__25317,Vvar__2__denum__25318,Vvar__3__condition__25319,Vvar__3__condition__25320] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__25313,Vvar__1__num__25315,Vvar__2__denum__25317,Vvar__3__condition__25319) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__25314,Vvar__1__num__25316,Vvar__2__denum__25318,Vvar__3__condition__25320)
=> ( Vvar__3__condition__25319 = Vvar__3__condition__25320
& Vvar__2__denum__25317 = Vvar__2__denum__25318
& Vvar__1__num__25315 = Vvar__1__num__25316
& Vvar__0__C__25313 = Vvar__0__C__25314 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__25327,Vvar__0__C__25328,Vvar__1__rsplit__left__25329,Vvar__1__rsplit__left__25330,Vvar__2__rsplit__common__25331,Vvar__2__rsplit__common__25332,Vvar__3__rsplit__right__25333,Vvar__3__rsplit__right__25334] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__25327,Vvar__1__rsplit__left__25329,Vvar__2__rsplit__common__25331,Vvar__3__rsplit__right__25333) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__25328,Vvar__1__rsplit__left__25330,Vvar__2__rsplit__common__25332,Vvar__3__rsplit__right__25334)
=> ( Vvar__3__rsplit__right__25333 = Vvar__3__rsplit__right__25334
& Vvar__2__rsplit__common__25331 = Vvar__2__rsplit__common__25332
& Vvar__1__rsplit__left__25329 = Vvar__1__rsplit__left__25330
& Vvar__0__C__25327 = Vvar__0__C__25328 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__26643,Vvar__0__hypo__type__26644,Vvar__1__hypo__proof__26645,Vvar__1__hypo__proof__26646] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__26643,Vvar__1__hypo__proof__26645) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__26644,Vvar__1__hypo__proof__26646)
=> ( Vvar__1__hypo__proof__26645 = Vvar__1__hypo__proof__26646
& Vvar__0__hypo__type__26643 = Vvar__0__hypo__type__26644 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__6883,Vvar__0__C__6884] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__6883) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__6884)
=> Vvar__0__C__6883 = Vvar__0__C__6884 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__6881,Vvar__0__C__6882] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__6881) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__6882)
=> Vvar__0__C__6881 = Vvar__0__C__6882 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__6889,Vvar__0__C__6890,Vvar__1___24Anonymous__6891,Vvar__1___24Anonymous__6892] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__6889,Vvar__1___24Anonymous__6891) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__6890,Vvar__1___24Anonymous__6892)
=> ( Vvar__1___24Anonymous__6891 = Vvar__1___24Anonymous__6892
& Vvar__0__C__6889 = Vvar__0__C__6890 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__6893,Vvar__0__C__6894,Vvar__1___24Anonymous__6895,Vvar__1___24Anonymous__6896,Vvar__2___24Anonymous__6897,Vvar__2___24Anonymous__6898] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__6893,Vvar__1___24Anonymous__6895,Vvar__2___24Anonymous__6897) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__6894,Vvar__1___24Anonymous__6896,Vvar__2___24Anonymous__6898)
=> ( Vvar__2___24Anonymous__6897 = Vvar__2___24Anonymous__6898
& Vvar__1___24Anonymous__6895 = Vvar__1___24Anonymous__6896
& Vvar__0__C__6893 = Vvar__0__C__6894 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__6885,Vvar__0__C__6886,Vvar__1___24Anonymous__6887,Vvar__1___24Anonymous__6888] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__6885,Vvar__1___24Anonymous__6887) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__6886,Vvar__1___24Anonymous__6888)
=> ( Vvar__1___24Anonymous__6887 = Vvar__1___24Anonymous__6888
& Vvar__0__C__6885 = Vvar__0__C__6886 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__6905,Vvar__0__C__6906,Vvar__1___24Anonymous__6907,Vvar__1___24Anonymous__6908,Vvar__2___24Anonymous__6909,Vvar__2___24Anonymous__6910] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__6905,Vvar__1___24Anonymous__6907,Vvar__2___24Anonymous__6909) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__6906,Vvar__1___24Anonymous__6908,Vvar__2___24Anonymous__6910)
=> ( Vvar__2___24Anonymous__6909 = Vvar__2___24Anonymous__6910
& Vvar__1___24Anonymous__6907 = Vvar__1___24Anonymous__6908
& Vvar__0__C__6905 = Vvar__0__C__6906 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__6911,Vvar__0__C__6912,Vvar__1___24Anonymous__6913,Vvar__1___24Anonymous__6914] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__6911,Vvar__1___24Anonymous__6913) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__6912,Vvar__1___24Anonymous__6914)
=> ( Vvar__1___24Anonymous__6913 = Vvar__1___24Anonymous__6914
& Vvar__0__C__6911 = Vvar__0__C__6912 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__6915,Vvar__0__C__6916,Vvar__1___24Anonymous__6917,Vvar__1___24Anonymous__6918,Vvar__2___24Anonymous__6919,Vvar__2___24Anonymous__6920] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__6915,Vvar__1___24Anonymous__6917,Vvar__2___24Anonymous__6919) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__6916,Vvar__1___24Anonymous__6918,Vvar__2___24Anonymous__6920)
=> ( Vvar__2___24Anonymous__6919 = Vvar__2___24Anonymous__6920
& Vvar__1___24Anonymous__6917 = Vvar__1___24Anonymous__6918
& Vvar__0__C__6915 = Vvar__0__C__6916 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__6899,Vvar__0__C__6900,Vvar__1___24Anonymous__6901,Vvar__1___24Anonymous__6902,Vvar__2___24Anonymous__6903,Vvar__2___24Anonymous__6904] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__6899,Vvar__1___24Anonymous__6901,Vvar__2___24Anonymous__6903) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__6900,Vvar__1___24Anonymous__6902,Vvar__2___24Anonymous__6904)
=> ( Vvar__2___24Anonymous__6903 = Vvar__2___24Anonymous__6904
& Vvar__1___24Anonymous__6901 = Vvar__1___24Anonymous__6902
& Vvar__0__C__6899 = Vvar__0__C__6900 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__6493,Vvar__0__C__6494,Vvar__1___24Anonymous__6495,Vvar__1___24Anonymous__6496,Vvar__2___24Anonymous__6497,Vvar__2___24Anonymous__6498,Vvar__3___24Anonymous__6499,Vvar__3___24Anonymous__6500] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__6493,Vvar__1___24Anonymous__6495,Vvar__2___24Anonymous__6497,Vvar__3___24Anonymous__6499) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__6494,Vvar__1___24Anonymous__6496,Vvar__2___24Anonymous__6498,Vvar__3___24Anonymous__6500)
=> ( Vvar__3___24Anonymous__6499 = Vvar__3___24Anonymous__6500
& Vvar__2___24Anonymous__6497 = Vvar__2___24Anonymous__6498
& Vvar__1___24Anonymous__6495 = Vvar__1___24Anonymous__6496
& Vvar__0__C__6493 = Vvar__0__C__6494 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__6483,Vvar__0__C__6484,Vvar__1___24Anonymous__6485,Vvar__1___24Anonymous__6486] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__6483,Vvar__1___24Anonymous__6485) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__6484,Vvar__1___24Anonymous__6486)
=> ( Vvar__1___24Anonymous__6485 = Vvar__1___24Anonymous__6486
& Vvar__0__C__6483 = Vvar__0__C__6484 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__6487,Vvar__0__C__6488,Vvar__1___24Anonymous__6489,Vvar__1___24Anonymous__6490,Vvar__2___24Anonymous__6491,Vvar__2___24Anonymous__6492] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__6487,Vvar__1___24Anonymous__6489,Vvar__2___24Anonymous__6491) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__6488,Vvar__1___24Anonymous__6490,Vvar__2___24Anonymous__6492)
=> ( Vvar__2___24Anonymous__6491 = Vvar__2___24Anonymous__6492
& Vvar__1___24Anonymous__6489 = Vvar__1___24Anonymous__6490
& Vvar__0__C__6487 = Vvar__0__C__6488 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__6652,Vvar__0___24Anonymous__6653,Vvar__1___24Anonymous__6654,Vvar__1___24Anonymous__6655] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__6652,Vvar__1___24Anonymous__6654) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__6653,Vvar__1___24Anonymous__6655)
=> ( Vvar__1___24Anonymous__6654 = Vvar__1___24Anonymous__6655
& Vvar__0___24Anonymous__6652 = Vvar__0___24Anonymous__6653 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__6648,Vvar__0___24Anonymous__6649,Vvar__1___24Anonymous__6650,Vvar__1___24Anonymous__6651] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__6648,Vvar__1___24Anonymous__6650) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__6649,Vvar__1___24Anonymous__6651)
=> ( Vvar__1___24Anonymous__6650 = Vvar__1___24Anonymous__6651
& Vvar__0___24Anonymous__6648 = Vvar__0___24Anonymous__6649 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__36553,Vvar__0__R__36554,Vvar__1__req__36555,Vvar__1__req__36556,Vvar__2__reqb__36557,Vvar__2__reqb__36558,Vvar__3___24Anonymous__36559,Vvar__3___24Anonymous__36560] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__36553,Vvar__1__req__36555,Vvar__2__reqb__36557) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__36554,Vvar__1__req__36556,Vvar__2__reqb__36558)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__36557 = Vvar__2__reqb__36558
& Vvar__1__req__36555 = Vvar__1__req__36556
& Vvar__0__R__36553 = Vvar__0__R__36554 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__36561,Vvar__0__R__36562,Vvar__1__rO__36563,Vvar__1__rO__36564,Vvar__2__rI__36565,Vvar__2__rI__36566,Vvar__3__radd__36567,Vvar__3__radd__36568,Vvar__4__rmul__36569,Vvar__4__rmul__36570,Vvar__5__rsub__36571,Vvar__5__rsub__36572,Vvar__6__ropp__36573,Vvar__6__ropp__36574,Vvar__7__req__36575,Vvar__7__req__36576,Vvar__8__C__36577,Vvar__8__C__36578,Vvar__9__cO__36579,Vvar__9__cO__36580,Vvar__10__cI__36581,Vvar__10__cI__36582,Vvar__11__cadd__36583,Vvar__11__cadd__36584,Vvar__12__cmul__36585,Vvar__12__cmul__36586,Vvar__13__csub__36587,Vvar__13__csub__36588,Vvar__14__copp__36589,Vvar__14__copp__36590,Vvar__15__ceqb__36591,Vvar__15__ceqb__36592,Vvar__16__phi__36593,Vvar__16__phi__36594,Vvar__17___24Anonymous__36595,Vvar__17___24Anonymous__36596] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__36561,Vvar__1__rO__36563,Vvar__2__rI__36565,Vvar__3__radd__36567,Vvar__4__rmul__36569,Vvar__5__rsub__36571,Vvar__6__ropp__36573,Vvar__7__req__36575,Vvar__8__C__36577,Vvar__9__cO__36579,Vvar__10__cI__36581,Vvar__11__cadd__36583,Vvar__12__cmul__36585,Vvar__13__csub__36587,Vvar__14__copp__36589,Vvar__15__ceqb__36591,Vvar__16__phi__36593) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__36562,Vvar__1__rO__36564,Vvar__2__rI__36566,Vvar__3__radd__36568,Vvar__4__rmul__36570,Vvar__5__rsub__36572,Vvar__6__ropp__36574,Vvar__7__req__36576,Vvar__8__C__36578,Vvar__9__cO__36580,Vvar__10__cI__36582,Vvar__11__cadd__36584,Vvar__12__cmul__36586,Vvar__13__csub__36588,Vvar__14__copp__36590,Vvar__15__ceqb__36592,Vvar__16__phi__36594)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__36593 = Vvar__16__phi__36594
& Vvar__15__ceqb__36591 = Vvar__15__ceqb__36592
& Vvar__14__copp__36589 = Vvar__14__copp__36590
& Vvar__13__csub__36587 = Vvar__13__csub__36588
& Vvar__12__cmul__36585 = Vvar__12__cmul__36586
& Vvar__11__cadd__36583 = Vvar__11__cadd__36584
& Vvar__10__cI__36581 = Vvar__10__cI__36582
& Vvar__9__cO__36579 = Vvar__9__cO__36580
& Vvar__8__C__36577 = Vvar__8__C__36578
& Vvar__7__req__36575 = Vvar__7__req__36576
& Vvar__6__ropp__36573 = Vvar__6__ropp__36574
& Vvar__5__rsub__36571 = Vvar__5__rsub__36572
& Vvar__4__rmul__36569 = Vvar__4__rmul__36570
& Vvar__3__radd__36567 = Vvar__3__radd__36568
& Vvar__2__rI__36565 = Vvar__2__rI__36566
& Vvar__1__rO__36563 = Vvar__1__rO__36564
& Vvar__0__R__36561 = Vvar__0__R__36562 ) ) ).
fof('$_inj_Topology.TopologicalSpaces.Build_TopologicalSpace',axiom,
! [Vvar__0__point__set__159,Vvar__0__point__set__160,Vvar__1__open__161,Vvar__1__open__162,Vvar__2__open__family__union__163,Vvar__2__open__family__union__164,Vvar__3__open__intersection2__165,Vvar__3__open__intersection2__166,Vvar__4__open__full__167,Vvar__4__open__full__168] :
( cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__159,Vvar__1__open__161) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__160,Vvar__1__open__162)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__1__open__161 = Vvar__1__open__162
& Vvar__0__point__set__159 = Vvar__0__point__set__160 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__23489,Vvar__1__Q__23491,Vvar__2__init__23494,Vvar__3___24Anonymous__23495,Vvar__4___24Anonymous__23496] :
( c_24__type__23522___24t(Vvar__0__P__23489,Vvar__1__Q__23491,Vvar__2__init__23494,Vvar__3___24Anonymous__23495,Vvar__4___24Anonymous__23496,Vvar__0__P__23489)
=> ( c_24__type__23530___24t(Vvar__0__P__23489,Vvar__1__Q__23491,Vvar__2__init__23494,Vvar__3___24Anonymous__23495,Vvar__4___24Anonymous__23496,Vvar__1__Q__23491)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__23494)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__23495)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__23496)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__23489,Vvar__1__Q__23491,Vvar__2__init__23494,Vvar__3___24Anonymous__23495,Vvar__4___24Anonymous__23496)
=> ( ( Vvar__4___24Anonymous__23496 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__23495 = Vvar__2__init__23494 )
| ? [Vvar__3__k__23510] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__23510)
& ? [Vvar__4__l__23511] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__23511)
& ? [Vvar__5__n__23512] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__23512)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__23489,Vvar__1__Q__23491,Vvar__2__init__23494,Vvar__3__k__23510,Vvar__5__n__23512)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__23489,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__23510),Vvar__4__l__23511)
& p(happ(Vvar__1__Q__23491,Vvar__4__l__23511))
& Vvar__4___24Anonymous__23496 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__23512)
& Vvar__3___24Anonymous__23495 = Vvar__4__l__23511 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__23449,Vvar__1__k__23451,Vvar__2___24Anonymous__23452] :
( c_24__type__23466___24t(Vvar__0__P__23449,Vvar__1__k__23451,Vvar__2___24Anonymous__23452,Vvar__0__P__23449)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__23451)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__23452)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__23449,Vvar__1__k__23451,Vvar__2___24Anonymous__23452)
=> ( Vvar__2___24Anonymous__23452 = Vvar__1__k__23451
| ? [Vvar__2__l__23460] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__23460)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__23449,Vvar__1__k__23451,Vvar__2__l__23460)
& p(happ(Vvar__0__P__23449,Vvar__2__l__23460))
& Vvar__2___24Anonymous__23452 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__23460) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__23468,Vvar__1__k__23470,Vvar__2___24Anonymous__23471] :
( c_24__type__23487___24t(Vvar__0__Q__23468,Vvar__1__k__23470,Vvar__2___24Anonymous__23471,Vvar__0__Q__23468)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__23470)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__23471)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__23468,Vvar__1__k__23470,Vvar__2___24Anonymous__23471)
=> ( ? [Vvar__2__l__23476] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__23476)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__23468,Vvar__1__k__23470,Vvar__2__l__23476)
& Vvar__2___24Anonymous__23471 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__23476) )
| ? [Vvar__2__l__23481] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__23481)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__23470,Vvar__2__l__23481)
& p(happ(Vvar__0__Q__23468,Vvar__2__l__23481))
& Vvar__2___24Anonymous__23471 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__23481) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__24230] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24230)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__24230)
=> ( Vvar__0___24Anonymous__24230 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__24232] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__24232)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__24232)
& Vvar__0___24Anonymous__24230 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__24232) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__24234] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24234)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__24234)
=> ? [Vvar__0__n__24236] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__24236)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__24236)
& Vvar__0___24Anonymous__24234 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__24236) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__23540,Vvar__1___24Anonymous__23541,VX23542] :
( cProp___24t(Vvar__0__P__23540)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__23541)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__23540,Vvar__1___24Anonymous__23541,VX23542)
=> ( ( p(Vvar__0__P__23540)
& Vvar__1___24Anonymous__23541 = cCoq_2eInit_2eDatatypes_2etrue
& VX23542 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__23540) )
| ( ~ p(Vvar__0__P__23540)
& Vvar__1___24Anonymous__23541 = cCoq_2eInit_2eDatatypes_2efalse
& VX23542 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__23540) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__37541,Vvar__1___24Anonymous__37542,Vvar__2___24Anonymous__37543] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__37541)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__37542)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__37543)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__37541,Vvar__1___24Anonymous__37542,Vvar__2___24Anonymous__37543)
=> ( ? [Vvar__0__x__37545] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__37545)
& Vvar__2___24Anonymous__37543 = Vvar__0__x__37545
& Vvar__1___24Anonymous__37542 = Vvar__0__x__37545
& Vvar__0___24Anonymous__37541 = Vvar__0__x__37545 )
| ? [Vvar__0__x__37546] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__37546)
& Vvar__2___24Anonymous__37543 = Vvar__0__x__37546
& Vvar__1___24Anonymous__37542 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__37541 = Vvar__0__x__37546 )
| ? [Vvar__0__x__37547] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__37547)
& Vvar__2___24Anonymous__37543 = Vvar__0__x__37547
& Vvar__1___24Anonymous__37542 = Vvar__0__x__37547
& Vvar__0___24Anonymous__37541 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__37548] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__37548)
& Vvar__2___24Anonymous__37543 = Vvar__0__x__37548
& Vvar__1___24Anonymous__37542 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__37541 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__37549] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__37549)
& Vvar__2___24Anonymous__37543 = Vvar__0__x__37549
& Vvar__1___24Anonymous__37542 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__37541 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX22900] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX22900)
=> ( VX22900 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__22901] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__22901)
& ? [Vvar__1___24Anonymous__22902] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__22902)
& ? [Vvar__2___24Anonymous__22903] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__22903)
& VX22900 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22901,Vvar__1___24Anonymous__22902,Vvar__2___24Anonymous__22903) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX2866] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX2866)
=> ( VX2866 = cCoq_2eInit_2eByte_2ex00
| VX2866 = cCoq_2eInit_2eByte_2ex01
| VX2866 = cCoq_2eInit_2eByte_2ex02
| VX2866 = cCoq_2eInit_2eByte_2ex03
| VX2866 = cCoq_2eInit_2eByte_2ex04
| VX2866 = cCoq_2eInit_2eByte_2ex05
| VX2866 = cCoq_2eInit_2eByte_2ex06
| VX2866 = cCoq_2eInit_2eByte_2ex07
| VX2866 = cCoq_2eInit_2eByte_2ex08
| VX2866 = cCoq_2eInit_2eByte_2ex09
| VX2866 = cCoq_2eInit_2eByte_2ex0a
| VX2866 = cCoq_2eInit_2eByte_2ex0b
| VX2866 = cCoq_2eInit_2eByte_2ex0c
| VX2866 = cCoq_2eInit_2eByte_2ex0d
| VX2866 = cCoq_2eInit_2eByte_2ex0e
| VX2866 = cCoq_2eInit_2eByte_2ex0f
| VX2866 = cCoq_2eInit_2eByte_2ex10
| VX2866 = cCoq_2eInit_2eByte_2ex11
| VX2866 = cCoq_2eInit_2eByte_2ex12
| VX2866 = cCoq_2eInit_2eByte_2ex13
| VX2866 = cCoq_2eInit_2eByte_2ex14
| VX2866 = cCoq_2eInit_2eByte_2ex15
| VX2866 = cCoq_2eInit_2eByte_2ex16
| VX2866 = cCoq_2eInit_2eByte_2ex17
| VX2866 = cCoq_2eInit_2eByte_2ex18
| VX2866 = cCoq_2eInit_2eByte_2ex19
| VX2866 = cCoq_2eInit_2eByte_2ex1a
| VX2866 = cCoq_2eInit_2eByte_2ex1b
| VX2866 = cCoq_2eInit_2eByte_2ex1c
| VX2866 = cCoq_2eInit_2eByte_2ex1d
| VX2866 = cCoq_2eInit_2eByte_2ex1e
| VX2866 = cCoq_2eInit_2eByte_2ex1f
| VX2866 = cCoq_2eInit_2eByte_2ex20
| VX2866 = cCoq_2eInit_2eByte_2ex21
| VX2866 = cCoq_2eInit_2eByte_2ex22
| VX2866 = cCoq_2eInit_2eByte_2ex23
| VX2866 = cCoq_2eInit_2eByte_2ex24
| VX2866 = cCoq_2eInit_2eByte_2ex25
| VX2866 = cCoq_2eInit_2eByte_2ex26
| VX2866 = cCoq_2eInit_2eByte_2ex27
| VX2866 = cCoq_2eInit_2eByte_2ex28
| VX2866 = cCoq_2eInit_2eByte_2ex29
| VX2866 = cCoq_2eInit_2eByte_2ex2a
| VX2866 = cCoq_2eInit_2eByte_2ex2b
| VX2866 = cCoq_2eInit_2eByte_2ex2c
| VX2866 = cCoq_2eInit_2eByte_2ex2d
| VX2866 = cCoq_2eInit_2eByte_2ex2e
| VX2866 = cCoq_2eInit_2eByte_2ex2f
| VX2866 = cCoq_2eInit_2eByte_2ex30
| VX2866 = cCoq_2eInit_2eByte_2ex31
| VX2866 = cCoq_2eInit_2eByte_2ex32
| VX2866 = cCoq_2eInit_2eByte_2ex33
| VX2866 = cCoq_2eInit_2eByte_2ex34
| VX2866 = cCoq_2eInit_2eByte_2ex35
| VX2866 = cCoq_2eInit_2eByte_2ex36
| VX2866 = cCoq_2eInit_2eByte_2ex37
| VX2866 = cCoq_2eInit_2eByte_2ex38
| VX2866 = cCoq_2eInit_2eByte_2ex39
| VX2866 = cCoq_2eInit_2eByte_2ex3a
| VX2866 = cCoq_2eInit_2eByte_2ex3b
| VX2866 = cCoq_2eInit_2eByte_2ex3c
| VX2866 = cCoq_2eInit_2eByte_2ex3d
| VX2866 = cCoq_2eInit_2eByte_2ex3e
| VX2866 = cCoq_2eInit_2eByte_2ex3f
| VX2866 = cCoq_2eInit_2eByte_2ex40
| VX2866 = cCoq_2eInit_2eByte_2ex41
| VX2866 = cCoq_2eInit_2eByte_2ex42
| VX2866 = cCoq_2eInit_2eByte_2ex43
| VX2866 = cCoq_2eInit_2eByte_2ex44
| VX2866 = cCoq_2eInit_2eByte_2ex45
| VX2866 = cCoq_2eInit_2eByte_2ex46
| VX2866 = cCoq_2eInit_2eByte_2ex47
| VX2866 = cCoq_2eInit_2eByte_2ex48
| VX2866 = cCoq_2eInit_2eByte_2ex49
| VX2866 = cCoq_2eInit_2eByte_2ex4a
| VX2866 = cCoq_2eInit_2eByte_2ex4b
| VX2866 = cCoq_2eInit_2eByte_2ex4c
| VX2866 = cCoq_2eInit_2eByte_2ex4d
| VX2866 = cCoq_2eInit_2eByte_2ex4e
| VX2866 = cCoq_2eInit_2eByte_2ex4f
| VX2866 = cCoq_2eInit_2eByte_2ex50
| VX2866 = cCoq_2eInit_2eByte_2ex51
| VX2866 = cCoq_2eInit_2eByte_2ex52
| VX2866 = cCoq_2eInit_2eByte_2ex53
| VX2866 = cCoq_2eInit_2eByte_2ex54
| VX2866 = cCoq_2eInit_2eByte_2ex55
| VX2866 = cCoq_2eInit_2eByte_2ex56
| VX2866 = cCoq_2eInit_2eByte_2ex57
| VX2866 = cCoq_2eInit_2eByte_2ex58
| VX2866 = cCoq_2eInit_2eByte_2ex59
| VX2866 = cCoq_2eInit_2eByte_2ex5a
| VX2866 = cCoq_2eInit_2eByte_2ex5b
| VX2866 = cCoq_2eInit_2eByte_2ex5c
| VX2866 = cCoq_2eInit_2eByte_2ex5d
| VX2866 = cCoq_2eInit_2eByte_2ex5e
| VX2866 = cCoq_2eInit_2eByte_2ex5f
| VX2866 = cCoq_2eInit_2eByte_2ex60
| VX2866 = cCoq_2eInit_2eByte_2ex61
| VX2866 = cCoq_2eInit_2eByte_2ex62
| VX2866 = cCoq_2eInit_2eByte_2ex63
| VX2866 = cCoq_2eInit_2eByte_2ex64
| VX2866 = cCoq_2eInit_2eByte_2ex65
| VX2866 = cCoq_2eInit_2eByte_2ex66
| VX2866 = cCoq_2eInit_2eByte_2ex67
| VX2866 = cCoq_2eInit_2eByte_2ex68
| VX2866 = cCoq_2eInit_2eByte_2ex69
| VX2866 = cCoq_2eInit_2eByte_2ex6a
| VX2866 = cCoq_2eInit_2eByte_2ex6b
| VX2866 = cCoq_2eInit_2eByte_2ex6c
| VX2866 = cCoq_2eInit_2eByte_2ex6d
| VX2866 = cCoq_2eInit_2eByte_2ex6e
| VX2866 = cCoq_2eInit_2eByte_2ex6f
| VX2866 = cCoq_2eInit_2eByte_2ex70
| VX2866 = cCoq_2eInit_2eByte_2ex71
| VX2866 = cCoq_2eInit_2eByte_2ex72
| VX2866 = cCoq_2eInit_2eByte_2ex73
| VX2866 = cCoq_2eInit_2eByte_2ex74
| VX2866 = cCoq_2eInit_2eByte_2ex75
| VX2866 = cCoq_2eInit_2eByte_2ex76
| VX2866 = cCoq_2eInit_2eByte_2ex77
| VX2866 = cCoq_2eInit_2eByte_2ex78
| VX2866 = cCoq_2eInit_2eByte_2ex79
| VX2866 = cCoq_2eInit_2eByte_2ex7a
| VX2866 = cCoq_2eInit_2eByte_2ex7b
| VX2866 = cCoq_2eInit_2eByte_2ex7c
| VX2866 = cCoq_2eInit_2eByte_2ex7d
| VX2866 = cCoq_2eInit_2eByte_2ex7e
| VX2866 = cCoq_2eInit_2eByte_2ex7f
| VX2866 = cCoq_2eInit_2eByte_2ex80
| VX2866 = cCoq_2eInit_2eByte_2ex81
| VX2866 = cCoq_2eInit_2eByte_2ex82
| VX2866 = cCoq_2eInit_2eByte_2ex83
| VX2866 = cCoq_2eInit_2eByte_2ex84
| VX2866 = cCoq_2eInit_2eByte_2ex85
| VX2866 = cCoq_2eInit_2eByte_2ex86
| VX2866 = cCoq_2eInit_2eByte_2ex87
| VX2866 = cCoq_2eInit_2eByte_2ex88
| VX2866 = cCoq_2eInit_2eByte_2ex89
| VX2866 = cCoq_2eInit_2eByte_2ex8a
| VX2866 = cCoq_2eInit_2eByte_2ex8b
| VX2866 = cCoq_2eInit_2eByte_2ex8c
| VX2866 = cCoq_2eInit_2eByte_2ex8d
| VX2866 = cCoq_2eInit_2eByte_2ex8e
| VX2866 = cCoq_2eInit_2eByte_2ex8f
| VX2866 = cCoq_2eInit_2eByte_2ex90
| VX2866 = cCoq_2eInit_2eByte_2ex91
| VX2866 = cCoq_2eInit_2eByte_2ex92
| VX2866 = cCoq_2eInit_2eByte_2ex93
| VX2866 = cCoq_2eInit_2eByte_2ex94
| VX2866 = cCoq_2eInit_2eByte_2ex95
| VX2866 = cCoq_2eInit_2eByte_2ex96
| VX2866 = cCoq_2eInit_2eByte_2ex97
| VX2866 = cCoq_2eInit_2eByte_2ex98
| VX2866 = cCoq_2eInit_2eByte_2ex99
| VX2866 = cCoq_2eInit_2eByte_2ex9a
| VX2866 = cCoq_2eInit_2eByte_2ex9b
| VX2866 = cCoq_2eInit_2eByte_2ex9c
| VX2866 = cCoq_2eInit_2eByte_2ex9d
| VX2866 = cCoq_2eInit_2eByte_2ex9e
| VX2866 = cCoq_2eInit_2eByte_2ex9f
| VX2866 = cCoq_2eInit_2eByte_2exa0
| VX2866 = cCoq_2eInit_2eByte_2exa1
| VX2866 = cCoq_2eInit_2eByte_2exa2
| VX2866 = cCoq_2eInit_2eByte_2exa3
| VX2866 = cCoq_2eInit_2eByte_2exa4
| VX2866 = cCoq_2eInit_2eByte_2exa5
| VX2866 = cCoq_2eInit_2eByte_2exa6
| VX2866 = cCoq_2eInit_2eByte_2exa7
| VX2866 = cCoq_2eInit_2eByte_2exa8
| VX2866 = cCoq_2eInit_2eByte_2exa9
| VX2866 = cCoq_2eInit_2eByte_2exaa
| VX2866 = cCoq_2eInit_2eByte_2exab
| VX2866 = cCoq_2eInit_2eByte_2exac
| VX2866 = cCoq_2eInit_2eByte_2exad
| VX2866 = cCoq_2eInit_2eByte_2exae
| VX2866 = cCoq_2eInit_2eByte_2exaf
| VX2866 = cCoq_2eInit_2eByte_2exb0
| VX2866 = cCoq_2eInit_2eByte_2exb1
| VX2866 = cCoq_2eInit_2eByte_2exb2
| VX2866 = cCoq_2eInit_2eByte_2exb3
| VX2866 = cCoq_2eInit_2eByte_2exb4
| VX2866 = cCoq_2eInit_2eByte_2exb5
| VX2866 = cCoq_2eInit_2eByte_2exb6
| VX2866 = cCoq_2eInit_2eByte_2exb7
| VX2866 = cCoq_2eInit_2eByte_2exb8
| VX2866 = cCoq_2eInit_2eByte_2exb9
| VX2866 = cCoq_2eInit_2eByte_2exba
| VX2866 = cCoq_2eInit_2eByte_2exbb
| VX2866 = cCoq_2eInit_2eByte_2exbc
| VX2866 = cCoq_2eInit_2eByte_2exbd
| VX2866 = cCoq_2eInit_2eByte_2exbe
| VX2866 = cCoq_2eInit_2eByte_2exbf
| VX2866 = cCoq_2eInit_2eByte_2exc0
| VX2866 = cCoq_2eInit_2eByte_2exc1
| VX2866 = cCoq_2eInit_2eByte_2exc2
| VX2866 = cCoq_2eInit_2eByte_2exc3
| VX2866 = cCoq_2eInit_2eByte_2exc4
| VX2866 = cCoq_2eInit_2eByte_2exc5
| VX2866 = cCoq_2eInit_2eByte_2exc6
| VX2866 = cCoq_2eInit_2eByte_2exc7
| VX2866 = cCoq_2eInit_2eByte_2exc8
| VX2866 = cCoq_2eInit_2eByte_2exc9
| VX2866 = cCoq_2eInit_2eByte_2exca
| VX2866 = cCoq_2eInit_2eByte_2excb
| VX2866 = cCoq_2eInit_2eByte_2excc
| VX2866 = cCoq_2eInit_2eByte_2excd
| VX2866 = cCoq_2eInit_2eByte_2exce
| VX2866 = cCoq_2eInit_2eByte_2excf
| VX2866 = cCoq_2eInit_2eByte_2exd0
| VX2866 = cCoq_2eInit_2eByte_2exd1
| VX2866 = cCoq_2eInit_2eByte_2exd2
| VX2866 = cCoq_2eInit_2eByte_2exd3
| VX2866 = cCoq_2eInit_2eByte_2exd4
| VX2866 = cCoq_2eInit_2eByte_2exd5
| VX2866 = cCoq_2eInit_2eByte_2exd6
| VX2866 = cCoq_2eInit_2eByte_2exd7
| VX2866 = cCoq_2eInit_2eByte_2exd8
| VX2866 = cCoq_2eInit_2eByte_2exd9
| VX2866 = cCoq_2eInit_2eByte_2exda
| VX2866 = cCoq_2eInit_2eByte_2exdb
| VX2866 = cCoq_2eInit_2eByte_2exdc
| VX2866 = cCoq_2eInit_2eByte_2exdd
| VX2866 = cCoq_2eInit_2eByte_2exde
| VX2866 = cCoq_2eInit_2eByte_2exdf
| VX2866 = cCoq_2eInit_2eByte_2exe0
| VX2866 = cCoq_2eInit_2eByte_2exe1
| VX2866 = cCoq_2eInit_2eByte_2exe2
| VX2866 = cCoq_2eInit_2eByte_2exe3
| VX2866 = cCoq_2eInit_2eByte_2exe4
| VX2866 = cCoq_2eInit_2eByte_2exe5
| VX2866 = cCoq_2eInit_2eByte_2exe6
| VX2866 = cCoq_2eInit_2eByte_2exe7
| VX2866 = cCoq_2eInit_2eByte_2exe8
| VX2866 = cCoq_2eInit_2eByte_2exe9
| VX2866 = cCoq_2eInit_2eByte_2exea
| VX2866 = cCoq_2eInit_2eByte_2exeb
| VX2866 = cCoq_2eInit_2eByte_2exec
| VX2866 = cCoq_2eInit_2eByte_2exed
| VX2866 = cCoq_2eInit_2eByte_2exee
| VX2866 = cCoq_2eInit_2eByte_2exef
| VX2866 = cCoq_2eInit_2eByte_2exf0
| VX2866 = cCoq_2eInit_2eByte_2exf1
| VX2866 = cCoq_2eInit_2eByte_2exf2
| VX2866 = cCoq_2eInit_2eByte_2exf3
| VX2866 = cCoq_2eInit_2eByte_2exf4
| VX2866 = cCoq_2eInit_2eByte_2exf5
| VX2866 = cCoq_2eInit_2eByte_2exf6
| VX2866 = cCoq_2eInit_2eByte_2exf7
| VX2866 = cCoq_2eInit_2eByte_2exf8
| VX2866 = cCoq_2eInit_2eByte_2exf9
| VX2866 = cCoq_2eInit_2eByte_2exfa
| VX2866 = cCoq_2eInit_2eByte_2exfb
| VX2866 = cCoq_2eInit_2eByte_2exfc
| VX2866 = cCoq_2eInit_2eByte_2exfd
| VX2866 = cCoq_2eInit_2eByte_2exfe
| VX2866 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__4313,Vvar__1__Q__4314,Vvar__2___24Anonymous__4315] :
( cProp___24t(Vvar__0__P__4313)
=> ( cProp___24t(Vvar__1__Q__4314)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__4315)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__4313,Vvar__1__Q__4314,Vvar__2___24Anonymous__4315)
=> ( ( p(Vvar__0__P__4313)
& Vvar__2___24Anonymous__4315 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__4314)
& Vvar__2___24Anonymous__4315 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__4437,Vvar__1__Plt__4438,Vvar__2__Pgt__4439,Vvar__3___24Anonymous__4440] :
( cProp___24t(Vvar__0__Peq__4437)
=> ( cProp___24t(Vvar__1__Plt__4438)
=> ( cProp___24t(Vvar__2__Pgt__4439)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__4440)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__4437,Vvar__1__Plt__4438,Vvar__2__Pgt__4439,Vvar__3___24Anonymous__4440)
=> ( ( p(Vvar__0__Peq__4437)
& Vvar__3___24Anonymous__4440 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__4438)
& Vvar__3___24Anonymous__4440 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__4439)
& Vvar__3___24Anonymous__4440 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__23825,Vvar__1__Plt__23826,Vvar__2__Pgt__23827,Vvar__3___24Anonymous__23828,VX23829] :
( cProp___24t(Vvar__0__Peq__23825)
=> ( cProp___24t(Vvar__1__Plt__23826)
=> ( cProp___24t(Vvar__2__Pgt__23827)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__23828)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__23825,Vvar__1__Plt__23826,Vvar__2__Pgt__23827,Vvar__3___24Anonymous__23828,VX23829)
=> ( ( p(Vvar__0__Peq__23825)
& Vvar__3___24Anonymous__23828 = cCoq_2eInit_2eDatatypes_2eEq
& VX23829 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23825,Vvar__1__Plt__23826,Vvar__2__Pgt__23827) )
| ( p(Vvar__1__Plt__23826)
& Vvar__3___24Anonymous__23828 = cCoq_2eInit_2eDatatypes_2eLt
& VX23829 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23825,Vvar__1__Plt__23826,Vvar__2__Pgt__23827) )
| ( p(Vvar__2__Pgt__23827)
& Vvar__3___24Anonymous__23828 = cCoq_2eInit_2eDatatypes_2eGt
& VX23829 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23825,Vvar__1__Plt__23826,Vvar__2__Pgt__23827) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX4309] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX4309)
=> ( VX4309 = cCoq_2eInit_2eDatatypes_2etrue
| VX4309 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX4436] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX4436)
=> ( VX4436 = cCoq_2eInit_2eDatatypes_2eEq
| VX4436 = cCoq_2eInit_2eDatatypes_2eLt
| VX4436 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__23793] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__23793)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__23793)
=> Vvar__0___24Anonymous__23793 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__23898,Vvar__1__a__23899,Vvar__2___24Anonymous__23900] :
( cType___24t(Vvar__0__A__23898)
=> ( t(Vvar__1__a__23899,Vvar__0__A__23898)
=> ( t(Vvar__2___24Anonymous__23900,Vvar__0__A__23898)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__23898,Vvar__1__a__23899,Vvar__2___24Anonymous__23900)
=> Vvar__2___24Anonymous__23900 = Vvar__1__a__23899 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__4393,VX4394] :
( cType___24t(Vvar__0__A__4393)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4393,VX4394)
=> ( VX4394 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__4393)
| ? [Vvar__1___24Anonymous__4397] :
( t(Vvar__1___24Anonymous__4397,Vvar__0__A__4393)
& ? [Vvar__2___24Anonymous__4398] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4393,Vvar__2___24Anonymous__4398)
& VX4394 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4393,Vvar__1___24Anonymous__4397,Vvar__2___24Anonymous__4398) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1031] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1031)
=> ( VX1031 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__1032] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1032)
& VX1031 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1032) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__309,VX310] :
( cType___24t(Vvar__0__A__309)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__309,VX310)
=> ( ? [Vvar__1___24Anonymous__312] :
( t(Vvar__1___24Anonymous__312,Vvar__0__A__309)
& VX310 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__309,Vvar__1___24Anonymous__312) )
| VX310 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__309) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__4345,Vvar__1__B__4346,VX4347] :
( cType___24t(Vvar__0__A__4345)
=> ( cType___24t(Vvar__1__B__4346)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__4345,Vvar__1__B__4346,VX4347)
=> ? [Vvar__2___24Anonymous__4350] :
( t(Vvar__2___24Anonymous__4350,Vvar__0__A__4345)
& ? [Vvar__3___24Anonymous__4351] :
( t(Vvar__3___24Anonymous__4351,Vvar__1__B__4346)
& VX4347 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__4345,Vvar__1__B__4346,Vvar__2___24Anonymous__4350,Vvar__3___24Anonymous__4351) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__23795,Vvar__1__B__23796,VX23797] :
( cType___24t(Vvar__0__A__23795)
=> ( cType___24t(Vvar__1__B__23796)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__23795,Vvar__1__B__23796,VX23797)
=> ( ? [Vvar__2___24Anonymous__23800] :
( t(Vvar__2___24Anonymous__23800,Vvar__0__A__23795)
& VX23797 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23795,Vvar__1__B__23796,Vvar__2___24Anonymous__23800) )
| ? [Vvar__2___24Anonymous__23803] :
( t(Vvar__2___24Anonymous__23803,Vvar__1__B__23796)
& VX23797 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23795,Vvar__1__B__23796,Vvar__2___24Anonymous__23803) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX4308] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX4308)
=> VX4308 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX23917] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX23917)
=> ( ? [Vvar__0__i__23918] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__23918)
& ? [Vvar__1__f__23919] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__23919)
& VX23917 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__23918,Vvar__1__f__23919) ) )
| ? [Vvar__0__i__23920] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__23920)
& ? [Vvar__1__f__23921] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__23921)
& ? [Vvar__2__e__23922] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__23922)
& VX23917 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__23920,Vvar__1__f__23921,Vvar__2__e__23922) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX23908] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX23908)
=> ( ? [Vvar__0__d__23909] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__23909)
& VX23908 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__23909) )
| ? [Vvar__0__d__23910] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__23910)
& VX23908 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__23910) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX4462] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX4462)
=> ( VX4462 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__4463] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4463)
& VX4462 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__4463) )
| ? [Vvar__0___24Anonymous__4464] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4464)
& VX4462 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__4464) )
| ? [Vvar__0___24Anonymous__4465] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4465)
& VX4462 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__4465) )
| ? [Vvar__0___24Anonymous__4466] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4466)
& VX4462 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__4466) )
| ? [Vvar__0___24Anonymous__4467] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4467)
& VX4462 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__4467) )
| ? [Vvar__0___24Anonymous__4468] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4468)
& VX4462 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__4468) )
| ? [Vvar__0___24Anonymous__4469] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4469)
& VX4462 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__4469) )
| ? [Vvar__0___24Anonymous__4470] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4470)
& VX4462 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__4470) )
| ? [Vvar__0___24Anonymous__4471] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4471)
& VX4462 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__4471) )
| ? [Vvar__0___24Anonymous__4472] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__4472)
& VX4462 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__4472) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__2760,Vvar__1___24Anonymous__2761] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2760)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2761)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2760,Vvar__1___24Anonymous__2761)
=> ( Vvar__1___24Anonymous__2761 = Vvar__0__n__2760
| ? [Vvar__1__m__2765] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__2765)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__2760,Vvar__1__m__2765)
& Vvar__1___24Anonymous__2761 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__2765) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__12431,Vvar__1__P__12432,VX12435] :
( cType___24t(Vvar__0__A__12431)
=> ( c_24__type__12445___24t(Vvar__0__A__12431,Vvar__1__P__12432,Vvar__1__P__12432)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__12431,Vvar__1__P__12432,VX12435)
=> ? [Vvar__2__x__12440] :
( t(Vvar__2__x__12440,Vvar__0__A__12431)
& p(happ(Vvar__1__P__12432,Vvar__2__x__12440))
& VX12435 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__12431,Vvar__1__P__12432,Vvar__2__x__12440) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__12470,Vvar__1__P__12471,Vvar__2__Q__12474,VX12477] :
( cType___24t(Vvar__0__A__12470)
=> ( c_24__type__12494___24t(Vvar__0__A__12470,Vvar__1__P__12471,Vvar__2__Q__12474,Vvar__1__P__12471)
=> ( c_24__type__12502___24t(Vvar__0__A__12470,Vvar__1__P__12471,Vvar__2__Q__12474,Vvar__2__Q__12474)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__12470,Vvar__1__P__12471,Vvar__2__Q__12474,VX12477)
=> ? [Vvar__3__x__12485] :
( t(Vvar__3__x__12485,Vvar__0__A__12470)
& p(happ(Vvar__1__P__12471,Vvar__3__x__12485))
& p(happ(Vvar__2__Q__12474,Vvar__3__x__12485))
& VX12477 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__12470,Vvar__1__P__12471,Vvar__2__Q__12474,Vvar__3__x__12485) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__12526,Vvar__1__P__12527,VX12530] :
( cType___24t(Vvar__0__A__12526)
=> ( c_24__type__12540___24t(Vvar__0__A__12526,Vvar__1__P__12527,Vvar__1__P__12527)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__12526,Vvar__1__P__12527,VX12530)
=> ? [Vvar__2__x__12535] :
( t(Vvar__2__x__12535,Vvar__0__A__12526)
& ? [Vvar__3___24Anonymous__12536] :
( t(Vvar__3___24Anonymous__12536,happ(Vvar__1__P__12527,Vvar__2__x__12535))
& VX12530 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__12526,Vvar__1__P__12527,Vvar__2__x__12535,Vvar__3___24Anonymous__12536) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__36899,Vvar__1__P__36900,Vvar__2__Q__36903,VX36906] :
( cType___24t(Vvar__0__A__36899)
=> ( c_24__type__36923___24t(Vvar__0__A__36899,Vvar__1__P__36900,Vvar__2__Q__36903,Vvar__1__P__36900)
=> ( c_24__type__36931___24t(Vvar__0__A__36899,Vvar__1__P__36900,Vvar__2__Q__36903,Vvar__2__Q__36903)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__36899,Vvar__1__P__36900,Vvar__2__Q__36903,VX36906)
=> ? [Vvar__3__x__36914] :
( t(Vvar__3__x__36914,Vvar__0__A__36899)
& ? [Vvar__4___24Anonymous__36915] :
( t(Vvar__4___24Anonymous__36915,happ(Vvar__1__P__36900,Vvar__3__x__36914))
& ? [Vvar__5___24Anonymous__36916] :
( t(Vvar__5___24Anonymous__36916,happ(Vvar__2__Q__36903,Vvar__3__x__36914))
& VX36906 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__36899,Vvar__1__P__36900,Vvar__2__Q__36903,Vvar__3__x__36914,Vvar__4___24Anonymous__36915,Vvar__5___24Anonymous__36916) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__20108,Vvar__1__B__20109,VX20110] :
( cProp___24t(Vvar__0__A__20108)
=> ( cProp___24t(Vvar__1__B__20109)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__20108,Vvar__1__B__20109,VX20110)
=> ( ( p(Vvar__0__A__20108)
& VX20110 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__20108,Vvar__1__B__20109) )
| ( p(Vvar__1__B__20109)
& VX20110 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__20108,Vvar__1__B__20109) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__36955,Vvar__1__B__36956,VX36957] :
( cType___24t(Vvar__0__A__36955)
=> ( cProp___24t(Vvar__1__B__36956)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__36955,Vvar__1__B__36956,VX36957)
=> ( ? [Vvar__2___24Anonymous__36960] :
( t(Vvar__2___24Anonymous__36960,Vvar__0__A__36955)
& VX36957 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__36955,Vvar__1__B__36956,Vvar__2___24Anonymous__36960) )
| ( p(Vvar__1__B__36956)
& VX36957 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__36955,Vvar__1__B__36956) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__37026,Vvar__1__R__37027,Vvar__2__x__37032] :
( cType___24t(Vvar__0__A__37026)
=> ( c_24__type__37061___24t(Vvar__0__A__37026,Vvar__1__R__37027,Vvar__2__x__37032,Vvar__1__R__37027)
=> ( t(Vvar__2__x__37032,Vvar__0__A__37026)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__37026,Vvar__1__R__37027,Vvar__2__x__37032)
=> ( ! [Vvar__var__var__var__var__3__y__37042__37044__37046__37048__37050] :
( t(Vvar__var__var__var__var__3__y__37042__37044__37046__37048__37050,Vvar__0__A__37026)
=> ( p(happ(happ(Vvar__1__R__37027,Vvar__var__var__var__var__3__y__37042__37044__37046__37048__37050),Vvar__2__x__37032))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__37026,Vvar__1__R__37027,Vvar__var__var__var__var__3__y__37042__37044__37046__37048__37050) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__4986,Vvar__1__a__4987,Vvar__2___24Anonymous__4988,Vvar__3___24Anonymous__4989] :
( cType___24t(Vvar__0__A__4986)
=> ( t(Vvar__1__a__4987,Vvar__0__A__4986)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4986,Vvar__2___24Anonymous__4988)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4986,Vvar__3___24Anonymous__4989)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__4986,Vvar__1__a__4987,Vvar__2___24Anonymous__4988,Vvar__3___24Anonymous__4989)
=> ( ? [Vvar__2__l__4993] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4986,Vvar__2__l__4993)
& Vvar__3___24Anonymous__4989 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4986,Vvar__1__a__4987,Vvar__2__l__4993)
& Vvar__2___24Anonymous__4988 = Vvar__2__l__4993 )
| ? [Vvar__2__x__4996] :
( t(Vvar__2__x__4996,Vvar__0__A__4986)
& ? [Vvar__3__l__4997] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4986,Vvar__3__l__4997)
& ? [Vvar__4__l_27__4998] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__4986,Vvar__4__l_27__4998)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__4986,Vvar__1__a__4987,Vvar__3__l__4997,Vvar__4__l_27__4998)
& Vvar__3___24Anonymous__4989 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4986,Vvar__2__x__4996,Vvar__4__l_27__4998)
& Vvar__2___24Anonymous__4988 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__4986,Vvar__2__x__4996,Vvar__3__l__4997) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__5014,Vvar__1__P__5015,Vvar__2___24Anonymous__5018] :
( cType___24t(Vvar__0__A__5014)
=> ( c_24__type__5038___24t(Vvar__0__A__5014,Vvar__1__P__5015,Vvar__2___24Anonymous__5018,Vvar__1__P__5015)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5014,Vvar__2___24Anonymous__5018)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__5014,Vvar__1__P__5015,Vvar__2___24Anonymous__5018)
=> ( ? [Vvar__2__x__5024] :
( t(Vvar__2__x__5024,Vvar__0__A__5014)
& ? [Vvar__3__l__5025] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5014,Vvar__3__l__5025)
& p(happ(Vvar__1__P__5015,Vvar__2__x__5024))
& Vvar__2___24Anonymous__5018 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__5014,Vvar__2__x__5024,Vvar__3__l__5025) ) )
| ? [Vvar__2__x__5031] :
( t(Vvar__2__x__5031,Vvar__0__A__5014)
& ? [Vvar__3__l__5032] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5014,Vvar__3__l__5032)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__5014,Vvar__1__P__5015,Vvar__3__l__5032)
& Vvar__2___24Anonymous__5018 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__5014,Vvar__2__x__5031,Vvar__3__l__5032) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__26692,Vvar__1__P__26693,Vvar__2___24Anonymous__26696] :
( cType___24t(Vvar__0__A__26692)
=> ( c_24__type__26714___24t(Vvar__0__A__26692,Vvar__1__P__26693,Vvar__2___24Anonymous__26696,Vvar__1__P__26693)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26692,Vvar__2___24Anonymous__26696)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__26692,Vvar__1__P__26693,Vvar__2___24Anonymous__26696)
=> ( Vvar__2___24Anonymous__26696 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26692)
| ? [Vvar__2__x__26706] :
( t(Vvar__2__x__26706,Vvar__0__A__26692)
& ? [Vvar__3__l__26707] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26692,Vvar__3__l__26707)
& p(happ(Vvar__1__P__26693,Vvar__2__x__26706))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__26692,Vvar__1__P__26693,Vvar__3__l__26707)
& Vvar__2___24Anonymous__26696 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26692,Vvar__2__x__26706,Vvar__3__l__26707) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__5041,Vvar__1__B__5042,Vvar__2__R__5043,Vvar__3___24Anonymous__5048,Vvar__4___24Anonymous__5049] :
( cType___24t(Vvar__0__A__5041)
=> ( cType___24t(Vvar__1__B__5042)
=> ( c_24__type__5086___24t(Vvar__0__A__5041,Vvar__1__B__5042,Vvar__2__R__5043,Vvar__3___24Anonymous__5048,Vvar__4___24Anonymous__5049,Vvar__2__R__5043)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5041,Vvar__3___24Anonymous__5048)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__5042,Vvar__4___24Anonymous__5049)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__5041,Vvar__1__B__5042,Vvar__2__R__5043,Vvar__3___24Anonymous__5048,Vvar__4___24Anonymous__5049)
=> ( ( Vvar__4___24Anonymous__5049 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__5042)
& Vvar__3___24Anonymous__5048 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__5041) )
| ? [Vvar__3__x__5065] :
( t(Vvar__3__x__5065,Vvar__0__A__5041)
& ? [Vvar__4__y__5066] :
( t(Vvar__4__y__5066,Vvar__1__B__5042)
& ? [Vvar__5__l__5067] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5041,Vvar__5__l__5067)
& ? [Vvar__6__l_27__5068] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__5042,Vvar__6__l_27__5068)
& p(happ(happ(Vvar__2__R__5043,Vvar__3__x__5065),Vvar__4__y__5066))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__5041,Vvar__1__B__5042,Vvar__2__R__5043,Vvar__5__l__5067,Vvar__6__l_27__5068)
& Vvar__4___24Anonymous__5049 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__5042,Vvar__4__y__5066,Vvar__6__l_27__5068)
& Vvar__3___24Anonymous__5048 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__5041,Vvar__3__x__5065,Vvar__5__l__5067) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__26716,Vvar__1__R__26717,Vvar__2___24Anonymous__26722] :
( cType___24t(Vvar__0__A__26716)
=> ( c_24__type__26749___24t(Vvar__0__A__26716,Vvar__1__R__26717,Vvar__2___24Anonymous__26722,Vvar__1__R__26717)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26716,Vvar__2___24Anonymous__26722)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__26716,Vvar__1__R__26717,Vvar__2___24Anonymous__26722)
=> ( Vvar__2___24Anonymous__26722 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26716)
| ? [Vvar__2__a__26736] :
( t(Vvar__2__a__26736,Vvar__0__A__26716)
& ? [Vvar__3__l__26737] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26716,Vvar__3__l__26737)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__26716,happ(Vvar__1__R__26717,Vvar__2__a__26736),Vvar__3__l__26737)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__26716,Vvar__1__R__26717,Vvar__3__l__26737)
& Vvar__2___24Anonymous__26722 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26716,Vvar__2__a__26736,Vvar__3__l__26737) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__5000,Vvar__1___24Anonymous__5001] :
( cType___24t(Vvar__0__A__5000)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5000,Vvar__1___24Anonymous__5001)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__5000,Vvar__1___24Anonymous__5001)
=> ( Vvar__1___24Anonymous__5001 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__5000)
| ? [Vvar__1__x__5005] :
( t(Vvar__1__x__5005,Vvar__0__A__5000)
& ? [Vvar__2__l__5006] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__5000,Vvar__2__l__5006)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__5000,Vvar__1__x__5005,Vvar__2__l__5006)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__5000,Vvar__2__l__5006)
& Vvar__1___24Anonymous__5001 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__5000,Vvar__1__x__5005,Vvar__2__l__5006) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__12194,Vvar__1__eqA__12195,Vvar__2__x__12200,Vvar__3___24Anonymous__12201] :
( cType___24t(Vvar__0__A__12194)
=> ( c_24__type__12234___24t(Vvar__0__A__12194,Vvar__1__eqA__12195,Vvar__2__x__12200,Vvar__3___24Anonymous__12201,Vvar__1__eqA__12195)
=> ( t(Vvar__2__x__12200,Vvar__0__A__12194)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12194,Vvar__3___24Anonymous__12201)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__12194,Vvar__1__eqA__12195,Vvar__2__x__12200,Vvar__3___24Anonymous__12201)
=> ( ? [Vvar__3__y__12210] :
( t(Vvar__3__y__12210,Vvar__0__A__12194)
& ? [Vvar__4__l__12211] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12194,Vvar__4__l__12211)
& p(happ(happ(Vvar__1__eqA__12195,Vvar__2__x__12200),Vvar__3__y__12210))
& Vvar__3___24Anonymous__12201 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12194,Vvar__3__y__12210,Vvar__4__l__12211) ) )
| ? [Vvar__3__y__12220] :
( t(Vvar__3__y__12220,Vvar__0__A__12194)
& ? [Vvar__4__l__12221] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12194,Vvar__4__l__12221)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__12194,Vvar__1__eqA__12195,Vvar__2__x__12200,Vvar__4__l__12221)
& Vvar__3___24Anonymous__12201 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12194,Vvar__3__y__12220,Vvar__4__l__12221) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__12242,Vvar__1__eqA__12243,Vvar__2___24Anonymous__12248] :
( cType___24t(Vvar__0__A__12242)
=> ( c_24__type__12275___24t(Vvar__0__A__12242,Vvar__1__eqA__12243,Vvar__2___24Anonymous__12248,Vvar__1__eqA__12243)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12242,Vvar__2___24Anonymous__12248)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__12242,Vvar__1__eqA__12243,Vvar__2___24Anonymous__12248)
=> ( Vvar__2___24Anonymous__12248 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12242)
| ? [Vvar__2__x__12262] :
( t(Vvar__2__x__12262,Vvar__0__A__12242)
& ? [Vvar__3__l__12263] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12242,Vvar__3__l__12263)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__12242,Vvar__1__eqA__12243,Vvar__2__x__12262,Vvar__3__l__12263)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__12242,Vvar__1__eqA__12243,Vvar__3__l__12263)
& Vvar__2___24Anonymous__12248 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12242,Vvar__2__x__12262,Vvar__3__l__12263) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__36600,Vvar__1__eqA__36601,Vvar__2___24Anonymous__36606,Vvar__3___24Anonymous__36607] :
( cType___24t(Vvar__0__A__36600)
=> ( c_24__type__36638___24t(Vvar__0__A__36600,Vvar__1__eqA__36601,Vvar__2___24Anonymous__36606,Vvar__3___24Anonymous__36607,Vvar__1__eqA__36601)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36600,Vvar__2___24Anonymous__36606)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36600,Vvar__3___24Anonymous__36607)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__36600,Vvar__1__eqA__36601,Vvar__2___24Anonymous__36606,Vvar__3___24Anonymous__36607)
=> ( ( Vvar__3___24Anonymous__36607 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36600)
& Vvar__2___24Anonymous__36606 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36600) )
| ? [Vvar__2__x__36621] :
( t(Vvar__2__x__36621,Vvar__0__A__36600)
& ? [Vvar__3__x_27__36622] :
( t(Vvar__3__x_27__36622,Vvar__0__A__36600)
& ? [Vvar__4__l__36623] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36600,Vvar__4__l__36623)
& ? [Vvar__5__l_27__36624] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36600,Vvar__5__l_27__36624)
& p(happ(happ(Vvar__1__eqA__36601,Vvar__2__x__36621),Vvar__3__x_27__36622))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__36600,Vvar__1__eqA__36601,Vvar__4__l__36623,Vvar__5__l_27__36624)
& Vvar__3___24Anonymous__36607 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36600,Vvar__3__x_27__36622,Vvar__5__l_27__36624)
& Vvar__2___24Anonymous__36606 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36600,Vvar__2__x__36621,Vvar__4__l__36623) ) ) ) ) ) ) ) ) ) ) ).
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__23716] :
( cProp___24t(Vvar__0__A__23716)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__23716)
=> ( ( ( p(Vvar__0__A__23716)
=> p(Vvar__0__A__23716) )
=> p(Vvar__0__A__23716) )
& ( ( p(Vvar__0__A__23716)
=> p(Vvar__0__A__23716) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__23692,Vvar__1__B__23693] :
( cProp___24t(Vvar__0__A__23692)
=> ( cProp___24t(Vvar__1__B__23693)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__23692,Vvar__1__B__23693)
=> ( ( p(Vvar__0__A__23692)
=> p(Vvar__1__B__23693) )
& ( p(Vvar__1__B__23693)
=> p(Vvar__0__A__23692) )
& ( p(Vvar__1__B__23693)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__24178,Vvar__1__P__24179,Vvar__2__p__24182,Vvar__3__x__24183,Vvar__4__q__24184,Vvar__5___24Anonymous__24185] :
( cType___24t(Vvar__0__U__24178)
=> ( c_24__type__24200___24t(Vvar__0__U__24178,Vvar__1__P__24179,Vvar__2__p__24182,Vvar__3__x__24183,Vvar__4__q__24184,Vvar__5___24Anonymous__24185,Vvar__1__P__24179)
=> ( t(Vvar__2__p__24182,Vvar__0__U__24178)
=> ( t(Vvar__3__x__24183,happ(Vvar__1__P__24179,Vvar__2__p__24182))
=> ( t(Vvar__4__q__24184,Vvar__0__U__24178)
=> ( t(Vvar__5___24Anonymous__24185,happ(Vvar__1__P__24179,Vvar__4__q__24184))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__24178,Vvar__1__P__24179,Vvar__2__p__24182,Vvar__3__x__24183,Vvar__4__q__24184,Vvar__5___24Anonymous__24185)
=> ( Vvar__5___24Anonymous__24185 = Vvar__3__x__24183
& Vvar__4__q__24184 = Vvar__2__p__24182 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__24202,Vvar__1__P__24203,Vvar__2__p__24206,Vvar__3__x__24207,Vvar__4__q__24208,Vvar__5__y__24209] :
( cType___24t(Vvar__0__U__24202)
=> ( c_24__type__24228___24t(Vvar__0__U__24202,Vvar__1__P__24203,Vvar__2__p__24206,Vvar__3__x__24207,Vvar__4__q__24208,Vvar__5__y__24209,Vvar__1__P__24203)
=> ( t(Vvar__2__p__24206,Vvar__0__U__24202)
=> ( t(Vvar__3__x__24207,happ(Vvar__1__P__24203,Vvar__2__p__24206))
=> ( t(Vvar__4__q__24208,Vvar__0__U__24202)
=> ( t(Vvar__5__y__24209,happ(Vvar__1__P__24203,Vvar__4__q__24208))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__24202,Vvar__1__P__24203,Vvar__2__p__24206,Vvar__3__x__24207,Vvar__4__q__24208,Vvar__5__y__24209)
=> ( Vvar__4__q__24208 = Vvar__2__p__24206
& Vvar__3__x__24207 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__24202,Vvar__4__q__24208,Vvar__1__P__24203,Vvar__5__y__24209,Vvar__2__p__24206)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX2837] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX2837)
=> ( VX2837 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__2838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2838)
& VX2837 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2838) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX2844] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX2844)
=> ( VX2844 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__2845] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2845)
& VX2844 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2845) )
| ? [Vvar__0___24Anonymous__2846] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2846)
& VX2844 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2846) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX2818] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX2818)
=> ( ? [Vvar__0___24Anonymous__2819] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2819)
& VX2818 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__2819) )
| ? [Vvar__0___24Anonymous__2820] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2820)
& VX2818 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__2820) )
| VX2818 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__37475,VX37476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__37475)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__37475,VX37476)
=> ( ( Vvar__0___24Anonymous__37475 = cCoq_2eNumbers_2eBinNums_2exH
& VX37476 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__37477] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__37477)
& ? [Vvar__1___24Anonymous__37478] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__37477,Vvar__1___24Anonymous__37478)
& Vvar__0___24Anonymous__37475 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2437513___24a2(Vvar__0___24Anonymous__37475,Vvar__0__p__37477)
& VX37476 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__37477,Vvar__1___24Anonymous__37478) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__22830,Vvar__1__q__22831,Vvar__2___24Anonymous__22832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__22830)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__22831)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__22832)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__22830,Vvar__1__q__22831,Vvar__2___24Anonymous__22832)
=> ( ( Vvar__0__p__22830 = Vvar__1__q__22831
& Vvar__2___24Anonymous__22832 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__22839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__22839)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__22831,Vvar__2__r__22839) = Vvar__0__p__22830
& Vvar__2___24Anonymous__22832 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__22839) )
| ? [Vvar__2__r__22843] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__22843)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__22830,Vvar__2__r__22843) = Vvar__1__q__22831
& Vvar__2___24Anonymous__22832 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX22505] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX22505)
=> ( VX22505 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__22506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22506)
& VX22505 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__22506) )
| VX22505 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX27587] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX27587)
=> ? [Vvar__0__Qnum__27588] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__27588)
& ? [Vvar__1__Qden__27589] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__27589)
& VX27587 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__27588,Vvar__1__Qden__27589) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX27630] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX27630)
=> ? [Vvar__0__neg__27631] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__27631)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__27631,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX27630 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__27631) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX27609] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX27609)
=> ? [Vvar__0__nonneg__27610] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__27610)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__27610)
& VX27609 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__27610) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX27623] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX27623)
=> ? [Vvar__0__nonpos__27624] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__27624)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__27624,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX27623 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__27624) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX27637] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX27637)
=> ? [Vvar__0__nonzero__27638] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__27638)
& Vvar__0__nonzero__27638 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX27637 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__27638) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX27616] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX27616)
=> ? [Vvar__0__pos__27617] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__27617)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__27617)
& VX27616 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__27617) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__28581,Vvar__1___24Anonymous__28582,VX28583] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__28581)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__28582)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__28581,Vvar__1___24Anonymous__28582,VX28583)
=> ( ( Vvar__0__x__28581 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__28582 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX28583 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__28581) )
| ? [Vvar__1__n__28587] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__28587)
& Vvar__0__x__28581 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__28587)
& Vvar__1___24Anonymous__28582 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2428607___24a3(Vvar__0__x__28581,Vvar__1___24Anonymous__28582,Vvar__1__n__28587)
& VX28583 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__28581,Vvar__1__n__28587) )
| ? [Vvar__1__n__28592] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__28592)
& Vvar__0__x__28581 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__28592))
& Vvar__1___24Anonymous__28582 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428624___24a3(Vvar__0__x__28581,Vvar__1___24Anonymous__28582,Vvar__1__n__28592)
& VX28583 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__28581,Vvar__1__n__28592) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__150778,Vvar__1__R__150779] :
( cType___24t(Vvar__0__A__150778)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150778,Vvar__1__R__150779)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__150778,Vvar__1__R__150779)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__150778,Vvar__1__R__150779)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__150778,Vvar__1__R__150779)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__27851,Vvar__1__R__27852] :
( cType___24t(Vvar__0__A__27851)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__27851,Vvar__1__R__27852)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__27851,Vvar__1__R__27852)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__27851,Vvar__1__R__27852)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__27851,Vvar__1__R__27852)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__27851,Vvar__1__R__27852)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__150763,Vvar__1__R__150764] :
( cType___24t(Vvar__0__A__150763)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150763,Vvar__1__R__150764)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__150763,Vvar__1__R__150764)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__150763,Vvar__1__R__150764)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__150763,Vvar__1__R__150764)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__28062,Vvar__1__leA__28063,Vvar__2___24Anonymous__28068] :
( cType___24t(Vvar__0__A__28062)
=> ( c_24__type__28158___24t(Vvar__0__A__28062,Vvar__1__leA__28063,Vvar__2___24Anonymous__28068,Vvar__1__leA__28063)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28062,Vvar__2___24Anonymous__28068)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__28062,Vvar__1__leA__28063,Vvar__2___24Anonymous__28068)
=> ( Vvar__2___24Anonymous__28068 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28062)
| ? [Vvar__2__x__28082] :
( t(Vvar__2__x__28082,Vvar__0__A__28062)
& Vvar__2___24Anonymous__28068 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28062,Vvar__2__x__28082,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28062)) )
| ? [Vvar__2__x__28089] :
( t(Vvar__2__x__28089,Vvar__0__A__28062)
& ? [Vvar__3__y__28090] :
( t(Vvar__3__y__28090,Vvar__0__A__28062)
& ? [Vvar__4__l__28091] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28062,Vvar__4__l__28091)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__28062,Vvar__1__leA__28063,Vvar__2__x__28089,Vvar__3__y__28090)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__28062,Vvar__1__leA__28063,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__28062,Vvar__4__l__28091,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28062,Vvar__3__y__28090,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28062))))
& Vvar__2___24Anonymous__28068 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2428356___24a6(Vvar__0__A__28062,Vvar__1__leA__28063,Vvar__2___24Anonymous__28068,Vvar__2__x__28089,Vvar__3__y__28090,Vvar__4__l__28091) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__28011,Vvar__1__leA__28012,Vvar__2___24Anonymous__28017,Vvar__3___24Anonymous__28018] :
( cType___24t(Vvar__0__A__28011)
=> ( c_24__type__28060___24t(Vvar__0__A__28011,Vvar__1__leA__28012,Vvar__2___24Anonymous__28017,Vvar__3___24Anonymous__28018,Vvar__1__leA__28012)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__2___24Anonymous__28017)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__3___24Anonymous__28018)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__28011,Vvar__1__leA__28012,Vvar__2___24Anonymous__28017,Vvar__3___24Anonymous__28018)
=> ( ? [Vvar__2__a__28026] :
( t(Vvar__2__a__28026,Vvar__0__A__28011)
& ? [Vvar__3__x__28027] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__3__x__28027)
& Vvar__3___24Anonymous__28018 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28011,Vvar__2__a__28026,Vvar__3__x__28027)
& Vvar__2___24Anonymous__28017 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28011) ) )
| ? [Vvar__2__a__28034] :
( t(Vvar__2__a__28034,Vvar__0__A__28011)
& ? [Vvar__3__b__28035] :
( t(Vvar__3__b__28035,Vvar__0__A__28011)
& p(happ(happ(Vvar__1__leA__28012,Vvar__2__a__28034),Vvar__3__b__28035))
& ? [Vvar__5__x__28037] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__5__x__28037)
& ? [Vvar__6__y__28038] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__6__y__28038)
& Vvar__3___24Anonymous__28018 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28011,Vvar__3__b__28035,Vvar__6__y__28038)
& Vvar__2___24Anonymous__28017 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28011,Vvar__2__a__28034,Vvar__5__x__28037) ) ) ) )
| ? [Vvar__2__a__28045] :
( t(Vvar__2__a__28045,Vvar__0__A__28011)
& ? [Vvar__3__x__28046] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__3__x__28046)
& ? [Vvar__4__y__28047] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28011,Vvar__4__y__28047)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__28011,Vvar__1__leA__28012,Vvar__3__x__28046,Vvar__4__y__28047)
& Vvar__3___24Anonymous__28018 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28011,Vvar__2__a__28045,Vvar__4__y__28047)
& Vvar__2___24Anonymous__28017 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28011,Vvar__2__a__28045,Vvar__3__x__28046) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__27859,Vvar__1__R__27860,Vvar__2__x__27861,Vvar__3___24Anonymous__27862] :
( cType___24t(Vvar__0__A__27859)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__27859,Vvar__1__R__27860)
=> ( t(Vvar__2__x__27861,Vvar__0__A__27859)
=> ( t(Vvar__3___24Anonymous__27862,Vvar__0__A__27859)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__27859,Vvar__1__R__27860,Vvar__2__x__27861,Vvar__3___24Anonymous__27862)
=> ( ? [Vvar__3__y__27867] :
( t(Vvar__3__y__27867,Vvar__0__A__27859)
& p(happ(happ(Vvar__1__R__27860,Vvar__2__x__27861),Vvar__3__y__27867))
& Vvar__3___24Anonymous__27862 = Vvar__3__y__27867 )
| Vvar__3___24Anonymous__27862 = Vvar__2__x__27861 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__150852,Vvar__1__R__150853,Vvar__2__x__150854,Vvar__3___24Anonymous__150855] :
( cType___24t(Vvar__0__A__150852)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150852,Vvar__1__R__150853)
=> ( t(Vvar__2__x__150854,Vvar__0__A__150852)
=> ( t(Vvar__3___24Anonymous__150855,Vvar__0__A__150852)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__150852,Vvar__1__R__150853,Vvar__2__x__150854,Vvar__3___24Anonymous__150855)
=> ( Vvar__3___24Anonymous__150855 = Vvar__2__x__150854
| ? [Vvar__3__y__150863] :
( t(Vvar__3__y__150863,Vvar__0__A__150852)
& ? [Vvar__4__z__150864] :
( t(Vvar__4__z__150864,Vvar__0__A__150852)
& ( p(happ(happ(Vvar__1__R__150853,Vvar__2__x__150854),Vvar__3__y__150863))
| p(happ(happ(Vvar__1__R__150853,Vvar__3__y__150863),Vvar__2__x__150854)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__150852,Vvar__1__R__150853,Vvar__3__y__150863,Vvar__4__z__150864)
& Vvar__3___24Anonymous__150855 = Vvar__4__z__150864 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__150867,Vvar__1__R__150868,Vvar__2__x__150869,Vvar__3___24Anonymous__150870] :
( cType___24t(Vvar__0__A__150867)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150867,Vvar__1__R__150868)
=> ( t(Vvar__2__x__150869,Vvar__0__A__150867)
=> ( t(Vvar__3___24Anonymous__150870,Vvar__0__A__150867)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__150867,Vvar__1__R__150868,Vvar__2__x__150869,Vvar__3___24Anonymous__150870)
=> ( Vvar__3___24Anonymous__150870 = Vvar__2__x__150869
| ? [Vvar__3__y__150878] :
( t(Vvar__3__y__150878,Vvar__0__A__150867)
& ? [Vvar__4__z__150879] :
( t(Vvar__4__z__150879,Vvar__0__A__150867)
& ( p(happ(happ(Vvar__1__R__150868,Vvar__3__y__150878),Vvar__4__z__150879))
| p(happ(happ(Vvar__1__R__150868,Vvar__4__z__150879),Vvar__3__y__150878)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__150867,Vvar__1__R__150868,Vvar__2__x__150869,Vvar__3__y__150878)
& Vvar__3___24Anonymous__150870 = Vvar__4__z__150879 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__150802,Vvar__1__R__150803,Vvar__2__x__150804,Vvar__3___24Anonymous__150805] :
( cType___24t(Vvar__0__A__150802)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150802,Vvar__1__R__150803)
=> ( t(Vvar__2__x__150804,Vvar__0__A__150802)
=> ( t(Vvar__3___24Anonymous__150805,Vvar__0__A__150802)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__150802,Vvar__1__R__150803,Vvar__2__x__150804,Vvar__3___24Anonymous__150805)
=> ( ? [Vvar__3__y__150810] :
( t(Vvar__3__y__150810,Vvar__0__A__150802)
& p(happ(happ(Vvar__1__R__150803,Vvar__2__x__150804),Vvar__3__y__150810))
& Vvar__3___24Anonymous__150805 = Vvar__3__y__150810 )
| Vvar__3___24Anonymous__150805 = Vvar__2__x__150804
| ? [Vvar__3__y__150818] :
( t(Vvar__3__y__150818,Vvar__0__A__150802)
& ? [Vvar__4__z__150819] :
( t(Vvar__4__z__150819,Vvar__0__A__150802)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__150802,Vvar__1__R__150803,Vvar__2__x__150804,Vvar__3__y__150818)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__150802,Vvar__1__R__150803,Vvar__3__y__150818,Vvar__4__z__150819)
& Vvar__3___24Anonymous__150805 = Vvar__4__z__150819 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__150822,Vvar__1__R__150823,Vvar__2__x__150824,Vvar__3___24Anonymous__150825] :
( cType___24t(Vvar__0__A__150822)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150822,Vvar__1__R__150823)
=> ( t(Vvar__2__x__150824,Vvar__0__A__150822)
=> ( t(Vvar__3___24Anonymous__150825,Vvar__0__A__150822)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__150822,Vvar__1__R__150823,Vvar__2__x__150824,Vvar__3___24Anonymous__150825)
=> ( Vvar__3___24Anonymous__150825 = Vvar__2__x__150824
| ? [Vvar__3__y__150833] :
( t(Vvar__3__y__150833,Vvar__0__A__150822)
& ? [Vvar__4__z__150834] :
( t(Vvar__4__z__150834,Vvar__0__A__150822)
& p(happ(happ(Vvar__1__R__150823,Vvar__2__x__150824),Vvar__3__y__150833))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__150822,Vvar__1__R__150823,Vvar__3__y__150833,Vvar__4__z__150834)
& Vvar__3___24Anonymous__150825 = Vvar__4__z__150834 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__150837,Vvar__1__R__150838,Vvar__2__x__150839,Vvar__3___24Anonymous__150840] :
( cType___24t(Vvar__0__A__150837)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150837,Vvar__1__R__150838)
=> ( t(Vvar__2__x__150839,Vvar__0__A__150837)
=> ( t(Vvar__3___24Anonymous__150840,Vvar__0__A__150837)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__150837,Vvar__1__R__150838,Vvar__2__x__150839,Vvar__3___24Anonymous__150840)
=> ( Vvar__3___24Anonymous__150840 = Vvar__2__x__150839
| ? [Vvar__3__y__150848] :
( t(Vvar__3__y__150848,Vvar__0__A__150837)
& ? [Vvar__4__z__150849] :
( t(Vvar__4__z__150849,Vvar__0__A__150837)
& p(happ(happ(Vvar__1__R__150838,Vvar__3__y__150848),Vvar__4__z__150849))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__150837,Vvar__1__R__150838,Vvar__2__x__150839,Vvar__3__y__150848)
& Vvar__3___24Anonymous__150840 = Vvar__4__z__150849 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__6239,Vvar__1__R__6240,Vvar__2__x__6241,Vvar__3___24Anonymous__6242] :
( cType___24t(Vvar__0__A__6239)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__6239,Vvar__1__R__6240)
=> ( t(Vvar__2__x__6241,Vvar__0__A__6239)
=> ( t(Vvar__3___24Anonymous__6242,Vvar__0__A__6239)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__6239,Vvar__1__R__6240,Vvar__2__x__6241,Vvar__3___24Anonymous__6242)
=> ( ? [Vvar__3__y__6247] :
( t(Vvar__3__y__6247,Vvar__0__A__6239)
& p(happ(happ(Vvar__1__R__6240,Vvar__2__x__6241),Vvar__3__y__6247))
& Vvar__3___24Anonymous__6242 = Vvar__3__y__6247 )
| ? [Vvar__3__y__6252] :
( t(Vvar__3__y__6252,Vvar__0__A__6239)
& ? [Vvar__4__z__6253] :
( t(Vvar__4__z__6253,Vvar__0__A__6239)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__6239,Vvar__1__R__6240,Vvar__2__x__6241,Vvar__3__y__6252)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__6239,Vvar__1__R__6240,Vvar__3__y__6252,Vvar__4__z__6253)
& Vvar__3___24Anonymous__6242 = Vvar__4__z__6253 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__6269,Vvar__1__R__6270,Vvar__2__x__6271,Vvar__3___24Anonymous__6272] :
( cType___24t(Vvar__0__A__6269)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__6269,Vvar__1__R__6270)
=> ( t(Vvar__2__x__6271,Vvar__0__A__6269)
=> ( t(Vvar__3___24Anonymous__6272,Vvar__0__A__6269)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__6269,Vvar__1__R__6270,Vvar__2__x__6271,Vvar__3___24Anonymous__6272)
=> ( ? [Vvar__3__y__6277] :
( t(Vvar__3__y__6277,Vvar__0__A__6269)
& p(happ(happ(Vvar__1__R__6270,Vvar__2__x__6271),Vvar__3__y__6277))
& Vvar__3___24Anonymous__6272 = Vvar__3__y__6277 )
| ? [Vvar__3__y__6282] :
( t(Vvar__3__y__6282,Vvar__0__A__6269)
& ? [Vvar__4__z__6283] :
( t(Vvar__4__z__6283,Vvar__0__A__6269)
& p(happ(happ(Vvar__1__R__6270,Vvar__2__x__6271),Vvar__3__y__6282))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__6269,Vvar__1__R__6270,Vvar__3__y__6282,Vvar__4__z__6283)
& Vvar__3___24Anonymous__6272 = Vvar__4__z__6283 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__150785,Vvar__1__R__150786,Vvar__2__x__150787,Vvar__3___24Anonymous__150788] :
( cType___24t(Vvar__0__A__150785)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__150785,Vvar__1__R__150786)
=> ( t(Vvar__2__x__150787,Vvar__0__A__150785)
=> ( t(Vvar__3___24Anonymous__150788,Vvar__0__A__150785)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__150785,Vvar__1__R__150786,Vvar__2__x__150787,Vvar__3___24Anonymous__150788)
=> ( ? [Vvar__3__y__150793] :
( t(Vvar__3__y__150793,Vvar__0__A__150785)
& p(happ(happ(Vvar__1__R__150786,Vvar__2__x__150787),Vvar__3__y__150793))
& Vvar__3___24Anonymous__150788 = Vvar__3__y__150793 )
| ? [Vvar__3__y__150798] :
( t(Vvar__3__y__150798,Vvar__0__A__150785)
& ? [Vvar__4__z__150799] :
( t(Vvar__4__z__150799,Vvar__0__A__150785)
& p(happ(happ(Vvar__1__R__150786,Vvar__3__y__150798),Vvar__4__z__150799))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__150785,Vvar__1__R__150786,Vvar__2__x__150787,Vvar__3__y__150798)
& Vvar__3___24Anonymous__150788 = Vvar__4__z__150799 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
! [Vvar__0__A__27969,Vvar__1__R__27970,Vvar__2___24Anonymous__27975,Vvar__3___24Anonymous__27976] :
( cType___24t(Vvar__0__A__27969)
=> ( c_24__type__28009___24t(Vvar__0__A__27969,Vvar__1__R__27970,Vvar__2___24Anonymous__27975,Vvar__3___24Anonymous__27976,Vvar__1__R__27970)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__2___24Anonymous__27975)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__3___24Anonymous__27976)
=> ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__27969,Vvar__1__R__27970,Vvar__2___24Anonymous__27975,Vvar__3___24Anonymous__27976)
=> ( ? [Vvar__2__x__27984] :
( t(Vvar__2__x__27984,Vvar__0__A__27969)
& ? [Vvar__3__y__27985] :
( t(Vvar__3__y__27985,Vvar__0__A__27969)
& ? [Vvar__4__p__27986] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__4__p__27986)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__1__R__27970,Vvar__1__R__27970,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__2__x__27984,Vvar__3__y__27985),Vvar__4__p__27986)
& Vvar__3___24Anonymous__27976 = Vvar__4__p__27986
& Vvar__2___24Anonymous__27975 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__2__x__27984,Vvar__3__y__27985) ) ) )
| ? [Vvar__2__x__27994] :
( t(Vvar__2__x__27994,Vvar__0__A__27969)
& ? [Vvar__3__y__27995] :
( t(Vvar__3__y__27995,Vvar__0__A__27969)
& ? [Vvar__4__p__27996] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__4__p__27996)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__1__R__27970,Vvar__1__R__27970,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__2__x__27994,Vvar__3__y__27995),Vvar__4__p__27996)
& Vvar__3___24Anonymous__27976 = Vvar__4__p__27996
& Vvar__2___24Anonymous__27975 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27969,Vvar__0__A__27969,Vvar__3__y__27995,Vvar__2__x__27994) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
! [Vvar__0__A__27872,Vvar__1__B__27873,Vvar__2__leA__27874,Vvar__3__leB__27879,Vvar__4___24Anonymous__27884,Vvar__5___24Anonymous__27885] :
( cType___24t(Vvar__0__A__27872)
=> ( cType___24t(Vvar__1__B__27873)
=> ( c_24__type__27942___24t(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__2__leA__27874,Vvar__3__leB__27879,Vvar__4___24Anonymous__27884,Vvar__5___24Anonymous__27885,Vvar__2__leA__27874)
=> ( c_24__type__27967___24t(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__2__leA__27874,Vvar__3__leB__27879,Vvar__4___24Anonymous__27884,Vvar__5___24Anonymous__27885,Vvar__3__leB__27879)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__4___24Anonymous__27884)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__5___24Anonymous__27885)
=> ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__2__leA__27874,Vvar__3__leB__27879,Vvar__4___24Anonymous__27884,Vvar__5___24Anonymous__27885)
=> ( ? [Vvar__4__x__27899] :
( t(Vvar__4__x__27899,Vvar__0__A__27872)
& ? [Vvar__5__x_27__27900] :
( t(Vvar__5__x_27__27900,Vvar__0__A__27872)
& p(happ(happ(Vvar__2__leA__27874,Vvar__4__x__27899),Vvar__5__x_27__27900))
& ? [Vvar__7__y__27902] :
( t(Vvar__7__y__27902,Vvar__1__B__27873)
& Vvar__5___24Anonymous__27885 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__5__x_27__27900,Vvar__7__y__27902)
& Vvar__4___24Anonymous__27884 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__4__x__27899,Vvar__7__y__27902) ) ) )
| ? [Vvar__4__y__27915] :
( t(Vvar__4__y__27915,Vvar__1__B__27873)
& ? [Vvar__5__y_27__27916] :
( t(Vvar__5__y_27__27916,Vvar__1__B__27873)
& p(happ(happ(Vvar__3__leB__27879,Vvar__4__y__27915),Vvar__5__y_27__27916))
& ? [Vvar__7__x__27918] :
( t(Vvar__7__x__27918,Vvar__0__A__27872)
& Vvar__5___24Anonymous__27885 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__7__x__27918,Vvar__5__y_27__27916)
& Vvar__4___24Anonymous__27884 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__27872,Vvar__1__B__27873,Vvar__7__x__27918,Vvar__4__y__27915) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Bottom',axiom,
! [Vvar__0__U__1807,Vvar__1__D__1808,Vvar__2__bot__1809] :
( cType___24t(Vvar__0__U__1807)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1807,Vvar__1__D__1808)
=> ( t(Vvar__2__bot__1809,Vvar__0__U__1807)
=> ( cCoq_2eSets_2eCpo_2eBottom___24a3(Vvar__0__U__1807,Vvar__1__D__1808,Vvar__2__bot__1809)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1807,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1807,Vvar__1__D__1808),Vvar__2__bot__1809)
& ! [Vvar__var__var__var__var__4__y__1816__1818__1820__1822__1824] :
( t(Vvar__var__var__var__var__4__y__1816__1818__1820__1822__1824,Vvar__0__U__1807)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1807,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1807,Vvar__1__D__1808),Vvar__var__var__var__var__4__y__1816__1818__1820__1822__1824)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1807,Vvar__1__D__1808,Vvar__2__bot__1809,Vvar__var__var__var__var__4__y__1816__1818__1820__1822__1824) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Chain',axiom,
! [Vvar__0__U__23778,VX23779] :
( cType___24t(Vvar__0__U__23778)
=> ( cCoq_2eSets_2eCpo_2eChain___24t(Vvar__0__U__23778,VX23779)
=> ? [Vvar__1__PO__of__chain__23781] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__23778,Vvar__1__PO__of__chain__23781)
& cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vvar__0__U__23778,Vvar__1__PO__of__chain__23781,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__23778,Vvar__1__PO__of__chain__23781))
& VX23779 = cCoq_2eSets_2eCpo_2eDefinition__of__chain___24a2(Vvar__0__U__23778,Vvar__1__PO__of__chain__23781) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Complete',axiom,
! [Vvar__0__U__2388,Vvar__1__D__2389] :
( cType___24t(Vvar__0__U__2388)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__2388,Vvar__1__D__2389)
=> ( cCoq_2eSets_2eCpo_2eComplete___24a2(Vvar__0__U__2388,Vvar__1__D__2389)
=> ( ? [Vvar__var__var__var__2__bot__2394__2395__2403__2404] :
( t(Vvar__var__var__var__2__bot__2394__2395__2403__2404,Vvar__0__U__2388)
& cCoq_2eSets_2eCpo_2eBottom___24a3(Vvar__0__U__2388,Vvar__1__D__2389,Vvar__var__var__var__2__bot__2394__2395__2403__2404) )
& ! [Vvar__var__var__var__3__X__2397__2400__2405__2408] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2388,Vvar__var__var__var__3__X__2397__2400__2405__2408)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vvar__0__U__2388,Vvar__1__D__2389,Vvar__var__var__var__3__X__2397__2400__2405__2408)
=> ? [Vvar__var__var__var__5__bsup__2398__2401__2406__2409] :
( t(Vvar__var__var__var__5__bsup__2398__2401__2406__2409,Vvar__0__U__2388)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__2388,Vvar__1__D__2389,Vvar__var__var__var__3__X__2397__2400__2405__2408,Vvar__var__var__var__5__bsup__2398__2401__2406__2409) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Conditionally_complete',axiom,
! [Vvar__0__U__782,Vvar__1__D__783] :
( cType___24t(Vvar__0__U__782)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__782,Vvar__1__D__783)
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(Vvar__0__U__782,Vvar__1__D__783)
=> ( ! [Vvar__var__var__var__2__X__788__793__798__803] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__782,Vvar__var__var__var__2__X__788__793__798__803)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__782,Vvar__var__var__var__2__X__788__793__798__803,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__782,Vvar__1__D__783))
=> ( ? [Vvar__var__var__var__4__maj__789__794__799__804] :
( t(Vvar__var__var__var__4__maj__789__794__799__804,Vvar__0__U__782)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__782,Vvar__1__D__783,Vvar__var__var__var__2__X__788__793__798__803,Vvar__var__var__var__4__maj__789__794__799__804) )
=> ? [Vvar__var__var__var__5__bsup__790__795__800__805] :
( t(Vvar__var__var__var__5__bsup__790__795__800__805,Vvar__0__U__782)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__782,Vvar__1__D__783,Vvar__var__var__var__2__X__788__793__798__803,Vvar__var__var__var__5__bsup__790__795__800__805) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Cpo',axiom,
! [Vvar__0__U__23767,VX23768] :
( cType___24t(Vvar__0__U__23767)
=> ( cCoq_2eSets_2eCpo_2eCpo___24t(Vvar__0__U__23767,VX23768)
=> ? [Vvar__1__PO__of__cpo__23770] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__23767,Vvar__1__PO__of__cpo__23770)
& cCoq_2eSets_2eCpo_2eComplete___24a2(Vvar__0__U__23767,Vvar__1__PO__of__cpo__23770)
& VX23768 = cCoq_2eSets_2eCpo_2eDefinition__of__cpo___24a2(Vvar__0__U__23767,Vvar__1__PO__of__cpo__23770) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Directed',axiom,
! [Vvar__0__U__2029,Vvar__1__D__2030,Vvar__2__X__2031] :
( cType___24t(Vvar__0__U__2029)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__2029,Vvar__1__D__2030)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2029,Vvar__2__X__2031)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vvar__0__U__2029,Vvar__1__D__2030,Vvar__2__X__2031)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__2029,Vvar__2__X__2031,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__2029,Vvar__1__D__2030))
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__2029,Vvar__2__X__2031)
& ! [Vvar__var__var__var__var__5__x1__2039__2043__2047__2051__2055] :
( t(Vvar__var__var__var__var__5__x1__2039__2043__2047__2051__2055,Vvar__0__U__2029)
=> ! [Vvar__var__var__var__var__6__x2__2040__2044__2048__2052__2056] :
( t(Vvar__var__var__var__var__6__x2__2040__2044__2048__2052__2056,Vvar__0__U__2029)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__2029,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__2029,Vvar__var__var__var__var__5__x1__2039__2043__2047__2051__2055,Vvar__var__var__var__var__6__x2__2040__2044__2048__2052__2056),Vvar__2__X__2031)
=> ? [Vvar__var__var__var__var__8__x3__2041__2045__2049__2053__2057] :
( t(Vvar__var__var__var__var__8__x3__2041__2045__2049__2053__2057,Vvar__0__U__2029)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__2029,Vvar__2__X__2031,Vvar__var__var__var__var__8__x3__2041__2045__2049__2053__2057)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__2029,Vvar__1__D__2030,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__2029,Vvar__var__var__var__var__5__x1__2039__2043__2047__2051__2055,Vvar__var__var__var__var__6__x2__2040__2044__2048__2052__2056),Vvar__var__var__var__var__8__x3__2041__2045__2049__2053__2057) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Glb',axiom,
! [Vvar__0__U__1780,Vvar__1__D__1781,Vvar__2__B__1782,Vvar__3__x__1783] :
( cType___24t(Vvar__0__U__1780)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1780,Vvar__1__D__1781)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1780,Vvar__2__B__1782)
=> ( t(Vvar__3__x__1783,Vvar__0__U__1780)
=> ( cCoq_2eSets_2eCpo_2eGlb___24a4(Vvar__0__U__1780,Vvar__1__D__1781,Vvar__2__B__1782,Vvar__3__x__1783)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__1780,Vvar__1__D__1781,Vvar__2__B__1782,Vvar__3__x__1783)
& ! [Vvar__var__var__var__var__var__5__y__1791__1793__1795__1797__1799__1801] :
( t(Vvar__var__var__var__var__var__5__y__1791__1793__1795__1797__1799__1801,Vvar__0__U__1780)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__1780,Vvar__1__D__1781,Vvar__2__B__1782,Vvar__var__var__var__var__var__5__y__1791__1793__1795__1797__1799__1801)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1780,Vvar__1__D__1781,Vvar__var__var__var__var__var__5__y__1791__1793__1795__1797__1799__1801,Vvar__3__x__1783) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Lower_Bound',axiom,
! [Vvar__0__U__1326,Vvar__1__D__1327,Vvar__2__B__1328,Vvar__3__x__1329] :
( cType___24t(Vvar__0__U__1326)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1326,Vvar__1__D__1327)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1326,Vvar__2__B__1328)
=> ( t(Vvar__3__x__1329,Vvar__0__U__1326)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__1326,Vvar__1__D__1327,Vvar__2__B__1328,Vvar__3__x__1329)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1326,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1326,Vvar__1__D__1327),Vvar__3__x__1329)
& ! [Vvar__var__var__var__var__var__5__y__1337__1339__1341__1343__1345__1347] :
( t(Vvar__var__var__var__var__var__5__y__1337__1339__1341__1343__1345__1347,Vvar__0__U__1326)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1326,Vvar__2__B__1328,Vvar__var__var__var__var__var__5__y__1337__1339__1341__1343__1345__1347)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1326,Vvar__1__D__1327,Vvar__3__x__1329,Vvar__var__var__var__var__var__5__y__1337__1339__1341__1343__1345__1347) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Lub',axiom,
! [Vvar__0__U__757,Vvar__1__D__758,Vvar__2__B__759,Vvar__3__x__760] :
( cType___24t(Vvar__0__U__757)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__757,Vvar__1__D__758)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__757,Vvar__2__B__759)
=> ( t(Vvar__3__x__760,Vvar__0__U__757)
=> ( cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__757,Vvar__1__D__758,Vvar__2__B__759,Vvar__3__x__760)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__757,Vvar__1__D__758,Vvar__2__B__759,Vvar__3__x__760)
& ! [Vvar__var__var__var__var__var__5__y__768__770__772__774__776__778] :
( t(Vvar__var__var__var__var__var__5__y__768__770__772__774__776__778,Vvar__0__U__757)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__757,Vvar__1__D__758,Vvar__2__B__759,Vvar__var__var__var__var__var__5__y__768__770__772__774__776__778)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__757,Vvar__1__D__758,Vvar__3__x__760,Vvar__var__var__var__var__var__5__y__768__770__772__774__776__778) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Totally_ordered',axiom,
! [Vvar__0__U__1830,Vvar__1__D__1831,Vvar__2__B__1832] :
( cType___24t(Vvar__0__U__1830)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1830,Vvar__1__D__1831)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1830,Vvar__2__B__1832)
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vvar__0__U__1830,Vvar__1__D__1831,Vvar__2__B__1832)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__1830,Vvar__2__B__1832,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1830,Vvar__1__D__1831))
=> ! [Vvar__var__var__var__var__4__x__1838__1842__1846__1850__1854] :
( t(Vvar__var__var__var__var__4__x__1838__1842__1846__1850__1854,Vvar__0__U__1830)
=> ! [Vvar__var__var__var__var__5__y__1839__1843__1847__1851__1855] :
( t(Vvar__var__var__var__var__5__y__1839__1843__1847__1851__1855,Vvar__0__U__1830)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__1830,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__1830,Vvar__var__var__var__var__4__x__1838__1842__1846__1850__1854,Vvar__var__var__var__var__5__y__1839__1843__1847__1851__1855),Vvar__2__B__1832)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1830,Vvar__1__D__1831,Vvar__var__var__var__var__4__x__1838__1842__1846__1850__1854,Vvar__var__var__var__var__5__y__1839__1843__1847__1851__1855)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1830,Vvar__1__D__1831,Vvar__var__var__var__var__5__y__1839__1843__1847__1851__1855,Vvar__var__var__var__var__4__x__1838__1842__1846__1850__1854) ) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Upper_Bound',axiom,
! [Vvar__0__U__560,Vvar__1__D__561,Vvar__2__B__562,Vvar__3__x__563] :
( cType___24t(Vvar__0__U__560)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__560,Vvar__1__D__561)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__560,Vvar__2__B__562)
=> ( t(Vvar__3__x__563,Vvar__0__U__560)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__560,Vvar__1__D__561,Vvar__2__B__562,Vvar__3__x__563)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__560,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__560,Vvar__1__D__561),Vvar__3__x__563)
& ! [Vvar__var__var__var__var__var__5__y__571__573__575__577__579__581] :
( t(Vvar__var__var__var__var__var__5__y__571__573__575__577__579__581,Vvar__0__U__560)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__560,Vvar__2__B__562,Vvar__var__var__var__var__var__5__y__571__573__575__577__579__581)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__560,Vvar__1__D__561,Vvar__var__var__var__var__var__5__y__571__573__575__577__579__581,Vvar__3__x__563) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Couple',axiom,
! [Vvar__0__U__47,Vvar__1__x__48,Vvar__2__y__49,Vvar__1___24Anonymous__50] :
( cType___24t(Vvar__0__U__47)
=> ( t(Vvar__1__x__48,Vvar__0__U__47)
=> ( t(Vvar__2__y__49,Vvar__0__U__47)
=> ( t(Vvar__1___24Anonymous__50,Vvar__0__U__47)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(Vvar__0__U__47,Vvar__1__x__48,Vvar__2__y__49,Vvar__1___24Anonymous__50)
=> ( Vvar__1___24Anonymous__50 = Vvar__1__x__48
| Vvar__1___24Anonymous__50 = Vvar__2__y__49 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Disjoint',axiom,
! [Vvar__0__U__1062,Vvar__1__B__1063,Vvar__2__C__1064] :
( cType___24t(Vvar__0__U__1062)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1062,Vvar__1__B__1063)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1062,Vvar__2__C__1064)
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(Vvar__0__U__1062,Vvar__1__B__1063,Vvar__2__C__1064)
=> ( ! [Vvar__var__var__var__var__3__x__1070__1071__1072__1073__1074] :
( t(Vvar__var__var__var__var__3__x__1070__1071__1072__1073__1074,Vvar__0__U__1062)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1062,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__U__1062,Vvar__1__B__1063,Vvar__2__C__1064),Vvar__var__var__var__var__3__x__1070__1071__1072__1073__1074) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Full_set',axiom,
! [Vvar__0__U__16,Vvar__1___24Anonymous__17] :
( cType___24t(Vvar__0__U__16)
=> ( t(Vvar__1___24Anonymous__17,Vvar__0__U__16)
=> ( cCoq_2eSets_2eEnsembles_2eFull__set___24a2(Vvar__0__U__16,Vvar__1___24Anonymous__17)
=> ? [Vvar__1__x__20] :
( t(Vvar__1__x__20,Vvar__0__U__16)
& Vvar__1___24Anonymous__17 = Vvar__1__x__20 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Inhabited',axiom,
! [Vvar__0__U__1077,Vvar__1__B__1078] :
( cType___24t(Vvar__0__U__1077)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1077,Vvar__1__B__1078)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__1077,Vvar__1__B__1078)
=> ? [Vvar__2__x__1082] :
( t(Vvar__2__x__1082,Vvar__0__U__1077)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1077,Vvar__1__B__1078,Vvar__2__x__1082)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Intersection',axiom,
! [Vvar__0__U__36,Vvar__1__B__37,Vvar__2__C__38,Vvar__1___24Anonymous__39] :
( cType___24t(Vvar__0__U__36)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__36,Vvar__1__B__37)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__36,Vvar__2__C__38)
=> ( t(Vvar__1___24Anonymous__39,Vvar__0__U__36)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(Vvar__0__U__36,Vvar__1__B__37,Vvar__2__C__38,Vvar__1___24Anonymous__39)
=> ? [Vvar__3__x__44] :
( t(Vvar__3__x__44,Vvar__0__U__36)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__36,Vvar__1__B__37,Vvar__3__x__44)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__36,Vvar__2__C__38,Vvar__3__x__44)
& Vvar__1___24Anonymous__39 = Vvar__3__x__44 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Singleton',axiom,
! [Vvar__0__U__1038,Vvar__1__x__1039,Vvar__1___24Anonymous__1040] :
( cType___24t(Vvar__0__U__1038)
=> ( t(Vvar__1__x__1039,Vvar__0__U__1038)
=> ( t(Vvar__1___24Anonymous__1040,Vvar__0__U__1038)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(Vvar__0__U__1038,Vvar__1__x__1039,Vvar__1___24Anonymous__1040)
=> Vvar__1___24Anonymous__1040 = Vvar__1__x__1039 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Triple',axiom,
! [Vvar__0__U__4622,Vvar__1__x__4623,Vvar__2__y__4624,Vvar__3__z__4625,Vvar__1___24Anonymous__4626] :
( cType___24t(Vvar__0__U__4622)
=> ( t(Vvar__1__x__4623,Vvar__0__U__4622)
=> ( t(Vvar__2__y__4624,Vvar__0__U__4622)
=> ( t(Vvar__3__z__4625,Vvar__0__U__4622)
=> ( t(Vvar__1___24Anonymous__4626,Vvar__0__U__4622)
=> ( cCoq_2eSets_2eEnsembles_2eTriple___24a5(Vvar__0__U__4622,Vvar__1__x__4623,Vvar__2__y__4624,Vvar__3__z__4625,Vvar__1___24Anonymous__4626)
=> ( Vvar__1___24Anonymous__4626 = Vvar__1__x__4623
| Vvar__1___24Anonymous__4626 = Vvar__2__y__4624
| Vvar__1___24Anonymous__4626 = Vvar__3__z__4625 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Union',axiom,
! [Vvar__0__U__21,Vvar__1__B__22,Vvar__2__C__23,Vvar__1___24Anonymous__24] :
( cType___24t(Vvar__0__U__21)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__21,Vvar__1__B__22)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__21,Vvar__2__C__23)
=> ( t(Vvar__1___24Anonymous__24,Vvar__0__U__21)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(Vvar__0__U__21,Vvar__1__B__22,Vvar__2__C__23,Vvar__1___24Anonymous__24)
=> ( ? [Vvar__3__x__29] :
( t(Vvar__3__x__29,Vvar__0__U__21)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__21,Vvar__1__B__22,Vvar__3__x__29)
& Vvar__1___24Anonymous__24 = Vvar__3__x__29 )
| ? [Vvar__3__x__34] :
( t(Vvar__3__x__34,Vvar__0__U__21)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__21,Vvar__2__C__23,Vvar__3__x__34)
& Vvar__1___24Anonymous__24 = Vvar__3__x__34 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.Finite',axiom,
! [Vvar__0__U__2640,Vvar__1___24Anonymous__2641] :
( cType___24t(Vvar__0__U__2640)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2640,Vvar__1___24Anonymous__2641)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(Vvar__0__U__2640,Vvar__1___24Anonymous__2641)
=> ( Vvar__1___24Anonymous__2641 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__2640)
| ? [Vvar__1__A__2645] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2640,Vvar__1__A__2645)
& cCoq_2eSets_2eFinite__sets_2eFinite___24a2(Vvar__0__U__2640,Vvar__1__A__2645)
& ? [Vvar__3__x__2647] :
( t(Vvar__3__x__2647,Vvar__0__U__2640)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__2640,Vvar__1__A__2645,Vvar__3__x__2647)
& Vvar__1___24Anonymous__2641 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__2640,Vvar__1__A__2645,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__2640,Vvar__3__x__2647)) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.cardinal',axiom,
! [Vvar__0__U__1089,Vvar__1___24Anonymous__1090,Vvar__2___24Anonymous__1091] :
( cType___24t(Vvar__0__U__1089)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1089,Vvar__1___24Anonymous__1090)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__1091)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__1089,Vvar__1___24Anonymous__1090,Vvar__2___24Anonymous__1091)
=> ( ( Vvar__2___24Anonymous__1091 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__1090 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__1089) )
| ? [Vvar__1__A__1095] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1089,Vvar__1__A__1095)
& ? [Vvar__2__n__1096] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__1096)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__1089,Vvar__1__A__1095,Vvar__2__n__1096)
& ? [Vvar__4__x__1098] :
( t(Vvar__4__x__1098,Vvar__0__U__1089)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1089,Vvar__1__A__1095,Vvar__4__x__1098)
& Vvar__2___24Anonymous__1091 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__1096)
& Vvar__1___24Anonymous__1090 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__1089,Vvar__1__A__1095,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__1089,Vvar__4__x__1098)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Image.Im',axiom,
! [Vvar__0__U__71,Vvar__1__V__72,Vvar__2__X__73,Vvar__3__f__74,Vvar__1___24Anonymous__77] :
( cType___24t(Vvar__0__U__71)
=> ( cType___24t(Vvar__1__V__72)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__71,Vvar__2__X__73)
=> ( c_24__type__97___24t(Vvar__0__U__71,Vvar__1__V__72,Vvar__2__X__73,Vvar__3__f__74,Vvar__1___24Anonymous__77,Vvar__3__f__74)
=> ( t(Vvar__1___24Anonymous__77,Vvar__1__V__72)
=> ( cCoq_2eSets_2eImage_2eIm___24a5(Vvar__0__U__71,Vvar__1__V__72,Vvar__2__X__73,Vvar__3__f__74,Vvar__1___24Anonymous__77)
=> ? [Vvar__4__x__85] :
( t(Vvar__4__x__85,Vvar__0__U__71)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__71,Vvar__2__X__73,Vvar__4__x__85)
& ? [Vvar__6__y__87] :
( t(Vvar__6__y__87,Vvar__1__V__72)
& Vvar__6__y__87 = happ(Vvar__3__f__74,Vvar__4__x__85)
& Vvar__1___24Anonymous__77 = Vvar__6__y__87 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.PO',axiom,
! [Vvar__0__U__1135,VX1136] :
( cType___24t(Vvar__0__U__1135)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1135,VX1136)
=> ? [Vvar__1__Carrier__of__1138] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1135,Vvar__1__Carrier__of__1138)
& ? [Vvar__2__Rel__of__1139] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__1135,Vvar__2__Rel__of__1139)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__1135,Vvar__1__Carrier__of__1138)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__1135,Vvar__2__Rel__of__1139)
& VX1136 = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__1135,Vvar__1__Carrier__of__1138,Vvar__2__Rel__of__1139) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.covers',axiom,
! [Vvar__0__U__2742,Vvar__1__p__2743,Vvar__2__y__2744,Vvar__3__x__2745] :
( cType___24t(Vvar__0__U__2742)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__2742,Vvar__1__p__2743)
=> ( t(Vvar__2__y__2744,Vvar__0__U__2742)
=> ( t(Vvar__3__x__2745,Vvar__0__U__2742)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(Vvar__0__U__2742,Vvar__1__p__2743,Vvar__2__y__2744,Vvar__3__x__2745)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__2742,Vvar__1__p__2743,Vvar__3__x__2745,Vvar__2__y__2744)
& ~ ? [Vvar__var__var__var__var__var__5__z__2753__2754__2755__2756__2757__2758] :
( t(Vvar__var__var__var__var__var__5__z__2753__2754__2755__2756__2757__2758,Vvar__0__U__2742)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__2742,Vvar__1__p__2743,Vvar__3__x__2745,Vvar__var__var__var__var__var__5__z__2753__2754__2755__2756__2757__2758)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__2742,Vvar__1__p__2743,Vvar__var__var__var__var__var__5__z__2753__2754__2755__2756__2757__2758,Vvar__2__y__2744) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Powerset.Power_set',axiom,
! [Vvar__0__U__2767,Vvar__1__A__2768,Vvar__1___24Anonymous__2769] :
( cType___24t(Vvar__0__U__2767)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2767,Vvar__1__A__2768)
=> ( c_24__type__2782___24t(Vvar__0__U__2767,Vvar__1__A__2768,Vvar__1___24Anonymous__2769,Vvar__1___24Anonymous__2769)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(Vvar__0__U__2767,Vvar__1__A__2768,Vvar__1___24Anonymous__2769)
=> ? [Vvar__2__X__2775] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2767,Vvar__2__X__2775)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__2767,Vvar__2__X__2775,Vvar__1__A__2768)
& Vvar__1___24Anonymous__2769 = Vvar__2__X__2775 ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Order',axiom,
! [Vvar__0__U__6308,Vvar__1__R__6309] :
( cType___24t(Vvar__0__U__6308)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__6308,Vvar__1__R__6309)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__6308,Vvar__1__R__6309)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__6308,Vvar__1__R__6309)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__6308,Vvar__1__R__6309)
& cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(Vvar__0__U__6308,Vvar__1__R__6309)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__36780,Vvar__1__R__36781,Vvar__2__a__36786,Vvar__3___24Anonymous__36787] :
( cType___24t(Vvar__0__A__36780)
=> ( c_24__type__36817___24t(Vvar__0__A__36780,Vvar__1__R__36781,Vvar__2__a__36786,Vvar__3___24Anonymous__36787,Vvar__1__R__36781)
=> ( t(Vvar__2__a__36786,Vvar__0__A__36780)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36780,Vvar__3___24Anonymous__36787)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__36780,Vvar__1__R__36781,Vvar__2__a__36786,Vvar__3___24Anonymous__36787)
=> ( Vvar__3___24Anonymous__36787 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36780)
| ? [Vvar__3__b__36803] :
( t(Vvar__3__b__36803,Vvar__0__A__36780)
& ? [Vvar__4__l__36804] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36780,Vvar__4__l__36804)
& p(happ(happ(Vvar__1__R__36781,Vvar__2__a__36786),Vvar__3__b__36803))
& Vvar__3___24Anonymous__36787 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36780,Vvar__3__b__36803,Vvar__4__l__36804) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__36737,Vvar__1__R__36738,Vvar__2___24Anonymous__36743] :
( cType___24t(Vvar__0__A__36737)
=> ( c_24__type__36778___24t(Vvar__0__A__36737,Vvar__1__R__36738,Vvar__2___24Anonymous__36743,Vvar__1__R__36738)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36737,Vvar__2___24Anonymous__36743)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__36737,Vvar__1__R__36738,Vvar__2___24Anonymous__36743)
=> ( Vvar__2___24Anonymous__36743 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36737)
| ? [Vvar__2__a__36757] :
( t(Vvar__2__a__36757,Vvar__0__A__36737)
& Vvar__2___24Anonymous__36743 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36737,Vvar__2__a__36757,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36737)) )
| ? [Vvar__2__a__36764] :
( t(Vvar__2__a__36764,Vvar__0__A__36737)
& ? [Vvar__3__b__36765] :
( t(Vvar__3__b__36765,Vvar__0__A__36737)
& ? [Vvar__4__l__36766] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36737,Vvar__4__l__36766)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__36737,Vvar__1__R__36738,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36737,Vvar__3__b__36765,Vvar__4__l__36766))
& p(happ(happ(Vvar__1__R__36738,Vvar__2__a__36764),Vvar__3__b__36765))
& Vvar__2___24Anonymous__36743 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36737,Vvar__2__a__36764,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36737,Vvar__3__b__36765,Vvar__4__l__36766)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__36819,Vvar__1__R__36820,Vvar__2___24Anonymous__36825] :
( cType___24t(Vvar__0__A__36819)
=> ( c_24__type__36852___24t(Vvar__0__A__36819,Vvar__1__R__36820,Vvar__2___24Anonymous__36825,Vvar__1__R__36820)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36819,Vvar__2___24Anonymous__36825)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__36819,Vvar__1__R__36820,Vvar__2___24Anonymous__36825)
=> ( Vvar__2___24Anonymous__36825 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36819)
| ? [Vvar__2__a__36839] :
( t(Vvar__2__a__36839,Vvar__0__A__36819)
& ? [Vvar__3__l__36840] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36819,Vvar__3__l__36840)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__36819,Vvar__1__R__36820,Vvar__3__l__36840)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__36819,Vvar__1__R__36820,Vvar__2__a__36839,Vvar__3__l__36840)
& Vvar__2___24Anonymous__36825 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36819,Vvar__2__a__36839,Vvar__3__l__36840) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__36854,Vvar__1__R__36855,Vvar__2___24Anonymous__36860] :
( cType___24t(Vvar__0__A__36854)
=> ( c_24__type__36887___24t(Vvar__0__A__36854,Vvar__1__R__36855,Vvar__2___24Anonymous__36860,Vvar__1__R__36855)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36854,Vvar__2___24Anonymous__36860)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__36854,Vvar__1__R__36855,Vvar__2___24Anonymous__36860)
=> ( Vvar__2___24Anonymous__36860 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36854)
| ? [Vvar__2__a__36874] :
( t(Vvar__2__a__36874,Vvar__0__A__36854)
& ? [Vvar__3__l__36875] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36854,Vvar__3__l__36875)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__36854,Vvar__1__R__36855,Vvar__3__l__36875)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__36854,happ(Vvar__1__R__36855,Vvar__2__a__36874),Vvar__3__l__36875)
& Vvar__2___24Anonymous__36860 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36854,Vvar__2__a__36874,Vvar__3__l__36875) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX2793] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX2793)
=> ? [Vvar__0___24Anonymous__2794] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__2794)
& ? [Vvar__1___24Anonymous__2795] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__2795)
& ? [Vvar__2___24Anonymous__2796] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__2796)
& ? [Vvar__3___24Anonymous__2797] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__2797)
& ? [Vvar__4___24Anonymous__2798] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__2798)
& ? [Vvar__5___24Anonymous__2799] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__2799)
& ? [Vvar__6___24Anonymous__2800] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__2800)
& ? [Vvar__7___24Anonymous__2801] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__2801)
& VX2793 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2794,Vvar__1___24Anonymous__2795,Vvar__2___24Anonymous__2796,Vvar__3___24Anonymous__2797,Vvar__4___24Anonymous__2798,Vvar__5___24Anonymous__2799,Vvar__6___24Anonymous__2800,Vvar__7___24Anonymous__2801) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX20154] :
( cCoq_2eStrings_2eString_2estring___24t(VX20154)
=> ( VX20154 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__20155] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__20155)
& ? [Vvar__1___24Anonymous__20156] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__20156)
& VX20154 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__20155,Vvar__1___24Anonymous__20156) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402,VX27403] :
( cType___24t(Vvar__0__X__27390)
=> ( c_24__type__27463___24t(Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402,Vvar__1__lt__27391)
=> ( c_24__type__27482___24t(Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402,Vvar__2__eq__27396)
=> ( t(Vvar__3__x__27401,Vvar__0__X__27390)
=> ( t(Vvar__4__y__27402,Vvar__0__X__27390)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402,VX27403)
=> ( ( p(happ(happ(Vvar__1__lt__27391,Vvar__3__x__27401),Vvar__4__y__27402))
& VX27403 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402) )
| ( p(happ(happ(Vvar__2__eq__27396,Vvar__3__x__27401),Vvar__4__y__27402))
& VX27403 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402) )
| ( p(happ(happ(Vvar__1__lt__27391,Vvar__4__y__27402),Vvar__3__x__27401))
& VX27403 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__27390,Vvar__1__lt__27391,Vvar__2__eq__27396,Vvar__3__x__27401,Vvar__4__y__27402) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__37555,Vvar__1___24Anonymous__37556] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__37555)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__37556)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__37555,Vvar__1___24Anonymous__37556)
=> ( ? [Vvar__0__a__37558] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__37558)
& ? [Vvar__1__s__37559] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__37559)
& Vvar__1___24Anonymous__37556 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__37558,Vvar__1__s__37559)
& Vvar__0___24Anonymous__37555 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__37560] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__37560)
& ? [Vvar__1__s1__37561] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__37561)
& ? [Vvar__2__s2__37562] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__37562)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__37561,Vvar__2__s2__37562)
& Vvar__1___24Anonymous__37556 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__37560,Vvar__2__s2__37562)
& Vvar__0___24Anonymous__37555 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__37560,Vvar__1__s1__37561) ) ) )
| ? [Vvar__0__a__37564] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__37564)
& ? [Vvar__1__b__37565] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__37565)
& ? [Vvar__2__s1__37566] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__37566)
& ? [Vvar__3__s2__37567] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__37567)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__37564),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__37565))
& Vvar__1___24Anonymous__37556 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__37565,Vvar__3__s2__37567)
& Vvar__0___24Anonymous__37555 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__37564,Vvar__2__s1__37566) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX6223] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX6223)
=> ( VX6223 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX6223 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX6223 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__26468,VX26469] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26468)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__26468,VX26469)
=> ( ? [Vvar__0__n__26470] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__26470)
& Vvar__0___24Anonymous__26468 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__26470)
& VX26469 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__26470) )
| ? [Vvar__0__n__26471] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__26471)
& ? [Vvar__1___24Anonymous__26472] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__26471,Vvar__1___24Anonymous__26472)
& Vvar__0___24Anonymous__26468 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__26471)
& VX26469 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__26471,Vvar__1___24Anonymous__26472) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__21696,Vvar__1___24Anonymous__21697,VX21698] :
( cType___24t(Vvar__0__A__21696)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__21697)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__21696,Vvar__1___24Anonymous__21697,VX21698)
=> ( ( Vvar__1___24Anonymous__21697 = cCoq_2eInit_2eDatatypes_2eO
& VX21698 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21696) )
| ? [Vvar__1__h__21701] :
( t(Vvar__1__h__21701,Vvar__0__A__21696)
& ? [Vvar__2__n__21702] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__21702)
& ? [Vvar__3___24Anonymous__21703] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__21696,Vvar__2__n__21702,Vvar__3___24Anonymous__21703)
& Vvar__1___24Anonymous__21697 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__21702)
& VX21698 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21696,Vvar__1__h__21701,Vvar__2__n__21702,Vvar__3___24Anonymous__21703) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__37245,Vvar__1__b__37246,Vvar__2__d__37247] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__37245)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__37246)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__37247)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__37245,Vvar__1__b__37246,Vvar__2__d__37247)
=> ? [Vvar__3__u__37252] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__37252)
& ? [Vvar__4__v__37253] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__37253)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__37252,Vvar__0__a__37245),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__37253,Vvar__1__b__37246)) = Vvar__2__d__37247
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__37220,Vvar__1__b__37221,VX37222] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__37220)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__37221)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__37220,Vvar__1__b__37221,VX37222)
=> ? [Vvar__2__u__37225] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__37225)
& ? [Vvar__3__v__37226] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__37226)
& ? [Vvar__4__d__37227] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__37227)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__37225,Vvar__0__a__37220),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__37226,Vvar__1__b__37221)) = Vvar__4__d__37227
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__37220,Vvar__1__b__37221,Vvar__4__d__37227)
& VX37222 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__37220,Vvar__1__b__37221,Vvar__2__u__37225,Vvar__3__v__37226,Vvar__4__d__37227) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__37192,Vvar__1__b__37193,Vvar__2__g__37194] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__37192)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__37193)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__37194)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__37192,Vvar__1__b__37193,Vvar__2__g__37194)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__37194,Vvar__0__a__37192)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__37194,Vvar__1__b__37193)
& ! [Vvar__var__var__var__var__5__x__37202__37205__37208__37211__37214] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__37202__37205__37208__37211__37214)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__37202__37205__37208__37211__37214,Vvar__0__a__37192)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__37202__37205__37208__37211__37214,Vvar__1__b__37193)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__37202__37205__37208__37211__37214,Vvar__2__g__37194) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__37255] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__37255)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__37255)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__37255)
& ! [Vvar__var__var__2__n__37260__37262__37264] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__37260__37262__37264)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__37260__37262__37264)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__37260__37262__37264,Vvar__0__p__37255) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__37260__37262__37264,Vvar__0__p__37255) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__37268,Vvar__1__p__37269,VX37270] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__37268)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__37269)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__37268,Vvar__1__p__37269,VX37270)
=> ? [Vvar__2__q__37273] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__37273)
& ? [Vvar__3__r__37274] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__37274)
& Vvar__0__x__37268 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__37273,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__37269)),Vvar__3__r__37274)
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__37274)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__37274,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__37269))
& VX37270 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__37268,Vvar__1__p__37269,Vvar__2__q__37273,Vvar__3__r__37274) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__4617,Vvar__1__F__4618] :
( cType___24t(Vvar__0__T__4617)
=> ( t(Vvar__1__F__4618,Vvar__0__T__4617)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__4617,Vvar__1__F__4618)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__23949,Vvar__1__F__23950] :
( cType___24t(Vvar__0__T__23949)
=> ( t(Vvar__1__F__23950,Vvar__0__T__23949)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__23949,Vvar__1__F__23950)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX4746] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX4746)
=> ( VX4746 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__4747] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4747)
& ? [Vvar__1___24Anonymous__4748] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__4748)
& VX4746 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__4747,Vvar__1___24Anonymous__4748) ) )
| ? [Vvar__0___24Anonymous__4749] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4749)
& ? [Vvar__1___24Anonymous__4750] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__4750)
& VX4746 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__4749,Vvar__1___24Anonymous__4750) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__23954,VX23955] :
( cType___24t(Vvar__0__C__23954)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,VX23955)
=> ( ? [Vvar__1___24Anonymous__23957] :
( t(Vvar__1___24Anonymous__23957,Vvar__0__C__23954)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__23954,Vvar__1___24Anonymous__23957) )
| ? [Vvar__1___24Anonymous__23959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__23959)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__23954,Vvar__1___24Anonymous__23959) )
| ? [Vvar__1___24Anonymous__23961] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__1___24Anonymous__23961)
& ? [Vvar__2___24Anonymous__23962] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__2___24Anonymous__23962)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__23954,Vvar__1___24Anonymous__23961,Vvar__2___24Anonymous__23962) ) )
| ? [Vvar__1___24Anonymous__23964] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__1___24Anonymous__23964)
& ? [Vvar__2___24Anonymous__23965] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__2___24Anonymous__23965)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__23954,Vvar__1___24Anonymous__23964,Vvar__2___24Anonymous__23965) ) )
| ? [Vvar__1___24Anonymous__23967] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__1___24Anonymous__23967)
& ? [Vvar__2___24Anonymous__23968] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__2___24Anonymous__23968)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__23954,Vvar__1___24Anonymous__23967,Vvar__2___24Anonymous__23968) ) )
| ? [Vvar__1___24Anonymous__23970] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__1___24Anonymous__23970)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__23954,Vvar__1___24Anonymous__23970) )
| ? [Vvar__1___24Anonymous__23972] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__23954,Vvar__1___24Anonymous__23972)
& ? [Vvar__2___24Anonymous__23973] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__23973)
& VX23955 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__23954,Vvar__1___24Anonymous__23972,Vvar__2___24Anonymous__23973) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__24121,VX24122] :
( cType___24t(Vvar__0__C__24121)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__24121,VX24122)
=> ( ? [Vvar__1___24Anonymous__24124] :
( t(Vvar__1___24Anonymous__24124,Vvar__0__C__24121)
& VX24122 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__24121,Vvar__1___24Anonymous__24124) )
| ? [Vvar__1___24Anonymous__24126] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__24126)
& ? [Vvar__2___24Anonymous__24127] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__24121,Vvar__2___24Anonymous__24127)
& VX24122 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__24121,Vvar__1___24Anonymous__24126,Vvar__2___24Anonymous__24127) ) )
| ? [Vvar__1___24Anonymous__24129] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__24121,Vvar__1___24Anonymous__24129)
& ? [Vvar__2___24Anonymous__24130] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__24130)
& ? [Vvar__3___24Anonymous__24131] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__24121,Vvar__3___24Anonymous__24131)
& VX24122 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__24121,Vvar__1___24Anonymous__24129,Vvar__2___24Anonymous__24130,Vvar__3___24Anonymous__24131) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157] :
( cType___24t(Vvar__0__R__5126)
=> ( t(Vvar__1__rO__5127,Vvar__0__R__5126)
=> ( t(Vvar__2__rI__5128,Vvar__0__R__5126)
=> ( c_24__type__5558___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__3__rplus__5129)
=> ( c_24__type__5659___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__4__rtimes__5134)
=> ( c_24__type__5760___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__5__rminus__5139)
=> ( c_24__type__5850___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__6__ropp__5144)
=> ( c_24__type__5951___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__7__req__5147)
=> ( c_24__type__6052___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__8__rle__5152)
=> ( c_24__type__6153___24t(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157,Vvar__9__rlt__5157)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147,Vvar__8__rle__5152,Vvar__9__rlt__5157)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__5126,Vvar__7__req__5147)
& ! [Vvar__var__var__var__var__11__x1__5201__5207__5312__5318__5324] :
( t(Vvar__var__var__var__var__11__x1__5201__5207__5312__5318__5324,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__12__x2__5202__5208__5313__5319__5325] :
( t(Vvar__var__var__var__var__12__x2__5202__5208__5313__5319__5325,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__11__x1__5201__5207__5312__5318__5324),Vvar__var__var__var__var__12__x2__5202__5208__5313__5319__5325))
=> ! [Vvar__var__var__var__var__14__y1__5203__5209__5314__5320__5326] :
( t(Vvar__var__var__var__var__14__y1__5203__5209__5314__5320__5326,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__15__y2__5204__5210__5315__5321__5327] :
( t(Vvar__var__var__var__var__15__y2__5204__5210__5315__5321__5327,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__14__y1__5203__5209__5314__5320__5326),Vvar__var__var__var__var__15__y2__5204__5210__5315__5321__5327))
=> p(happ(happ(Vvar__7__req__5147,happ(happ(Vvar__3__rplus__5129,Vvar__var__var__var__var__11__x1__5201__5207__5312__5318__5324),Vvar__var__var__var__var__14__y1__5203__5209__5314__5320__5326)),happ(happ(Vvar__3__rplus__5129,Vvar__var__var__var__var__12__x2__5202__5208__5313__5319__5325),Vvar__var__var__var__var__15__y2__5204__5210__5315__5321__5327))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__5214__5220__5330__5336__5342] :
( t(Vvar__var__var__var__var__12__x1__5214__5220__5330__5336__5342,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__13__x2__5215__5221__5331__5337__5343] :
( t(Vvar__var__var__var__var__13__x2__5215__5221__5331__5337__5343,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__12__x1__5214__5220__5330__5336__5342),Vvar__var__var__var__var__13__x2__5215__5221__5331__5337__5343))
=> ! [Vvar__var__var__var__var__15__y1__5216__5222__5332__5338__5344] :
( t(Vvar__var__var__var__var__15__y1__5216__5222__5332__5338__5344,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__16__y2__5217__5223__5333__5339__5345] :
( t(Vvar__var__var__var__var__16__y2__5217__5223__5333__5339__5345,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__15__y1__5216__5222__5332__5338__5344),Vvar__var__var__var__var__16__y2__5217__5223__5333__5339__5345))
=> p(happ(happ(Vvar__7__req__5147,happ(happ(Vvar__4__rtimes__5134,Vvar__var__var__var__var__12__x1__5214__5220__5330__5336__5342),Vvar__var__var__var__var__15__y1__5216__5222__5332__5338__5344)),happ(happ(Vvar__4__rtimes__5134,Vvar__var__var__var__var__13__x2__5215__5221__5331__5337__5343),Vvar__var__var__var__var__16__y2__5217__5223__5333__5339__5345))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__5227__5230__5348__5351__5354] :
( t(Vvar__var__var__var__var__13__x1__5227__5230__5348__5351__5354,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__14__x2__5228__5231__5349__5352__5355] :
( t(Vvar__var__var__var__var__14__x2__5228__5231__5349__5352__5355,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__13__x1__5227__5230__5348__5351__5354),Vvar__var__var__var__var__14__x2__5228__5231__5349__5352__5355))
=> p(happ(happ(Vvar__7__req__5147,happ(Vvar__6__ropp__5144,Vvar__var__var__var__var__13__x1__5227__5230__5348__5351__5354)),happ(Vvar__6__ropp__5144,Vvar__var__var__var__var__14__x2__5228__5231__5349__5352__5355))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__5234__5240__5357__5363__5369] :
( t(Vvar__var__var__var__var__14__x1__5234__5240__5357__5363__5369,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__15__x2__5235__5241__5358__5364__5370] :
( t(Vvar__var__var__var__var__15__x2__5235__5241__5358__5364__5370,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__14__x1__5234__5240__5357__5363__5369),Vvar__var__var__var__var__15__x2__5235__5241__5358__5364__5370))
=> ! [Vvar__var__var__var__var__17__y1__5236__5242__5359__5365__5371] :
( t(Vvar__var__var__var__var__17__y1__5236__5242__5359__5365__5371,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__18__y2__5237__5243__5360__5366__5372] :
( t(Vvar__var__var__var__var__18__y2__5237__5243__5360__5366__5372,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__17__y1__5236__5242__5359__5365__5371),Vvar__var__var__var__var__18__y2__5237__5243__5360__5366__5372))
=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__var__14__x1__5234__5240__5357__5363__5369),Vvar__var__var__var__var__17__y1__5236__5242__5359__5365__5371))
<=> p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__var__15__x2__5235__5241__5358__5364__5370),Vvar__var__var__var__var__18__y2__5237__5243__5360__5366__5372)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__5247__5253__5375__5381__5387] :
( t(Vvar__var__var__var__var__15__x1__5247__5253__5375__5381__5387,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__16__x2__5248__5254__5376__5382__5388] :
( t(Vvar__var__var__var__var__16__x2__5248__5254__5376__5382__5388,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__15__x1__5247__5253__5375__5381__5387),Vvar__var__var__var__var__16__x2__5248__5254__5376__5382__5388))
=> ! [Vvar__var__var__var__var__18__y1__5249__5255__5377__5383__5389] :
( t(Vvar__var__var__var__var__18__y1__5249__5255__5377__5383__5389,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__19__y2__5250__5256__5378__5384__5390] :
( t(Vvar__var__var__var__var__19__y2__5250__5256__5378__5384__5390,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__18__y1__5249__5255__5377__5383__5389),Vvar__var__var__var__var__19__y2__5250__5256__5378__5384__5390))
=> ( p(happ(happ(Vvar__9__rlt__5157,Vvar__var__var__var__var__15__x1__5247__5253__5375__5381__5387),Vvar__var__var__var__var__18__y1__5249__5255__5377__5383__5389))
<=> p(happ(happ(Vvar__9__rlt__5157,Vvar__var__var__var__var__16__x2__5248__5254__5376__5382__5388),Vvar__var__var__var__var__19__y2__5250__5256__5378__5384__5390)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__5126,Vvar__1__rO__5127,Vvar__2__rI__5128,Vvar__3__rplus__5129,Vvar__4__rtimes__5134,Vvar__5__rminus__5139,Vvar__6__ropp__5144,Vvar__7__req__5147)
& ! [Vvar__var__var__var__17__n__5261__5262__5393__5394] :
( t(Vvar__var__var__var__17__n__5261__5262__5393__5394,Vvar__0__R__5126)
=> p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__17__n__5261__5262__5393__5394),Vvar__var__var__var__17__n__5261__5262__5393__5394)) )
& ! [Vvar__var__var__var__var__18__n__5264__5268__5395__5399__5403] :
( t(Vvar__var__var__var__var__18__n__5264__5268__5395__5399__5403,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__19__m__5265__5269__5396__5400__5404] :
( t(Vvar__var__var__var__var__19__m__5265__5269__5396__5400__5404,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__var__18__n__5264__5268__5395__5399__5403),Vvar__var__var__var__var__19__m__5265__5269__5396__5400__5404))
=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__var__19__m__5265__5269__5396__5400__5404),Vvar__var__var__var__var__18__n__5264__5268__5395__5399__5403))
=> p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__18__n__5264__5268__5395__5399__5403),Vvar__var__var__var__var__19__m__5265__5269__5396__5400__5404)) ) ) ) )
& ! [Vvar__var__var__var__19__n__5273__5278__5407__5412] :
( t(Vvar__var__var__var__19__n__5273__5278__5407__5412,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__20__m__5274__5279__5408__5413] :
( t(Vvar__var__var__var__20__m__5274__5279__5408__5413,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__21__p__5275__5280__5409__5414] :
( t(Vvar__var__var__var__21__p__5275__5280__5409__5414,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__19__n__5273__5278__5407__5412),Vvar__var__var__var__20__m__5274__5279__5408__5413))
=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__20__m__5274__5279__5408__5413),Vvar__var__var__var__21__p__5275__5280__5409__5414))
=> p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__19__n__5273__5278__5407__5412),Vvar__var__var__var__21__p__5275__5280__5409__5414)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__5284__5286__5417__5419__5421__5423] :
( t(Vvar__var__var__var__var__var__20__n__5284__5286__5417__5419__5421__5423,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__var__21__m__5285__5287__5418__5420__5422__5424] :
( t(Vvar__var__var__var__var__var__21__m__5285__5287__5418__5420__5422__5424,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__9__rlt__5157,Vvar__var__var__var__var__var__20__n__5284__5286__5417__5419__5421__5423),Vvar__var__var__var__var__var__21__m__5285__5287__5418__5420__5422__5424))
<=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__var__var__20__n__5284__5286__5417__5419__5421__5423),Vvar__var__var__var__var__var__21__m__5285__5287__5418__5420__5422__5424))
& ~ p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__var__20__n__5284__5286__5417__5419__5421__5423),Vvar__var__var__var__var__var__21__m__5285__5287__5418__5420__5422__5424)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__5289__5291__5425__5427__5429] :
( t(Vvar__var__var__var__var__21__n__5289__5291__5425__5427__5429,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__22__m__5290__5292__5426__5428__5430] :
( t(Vvar__var__var__var__var__22__m__5290__5292__5426__5428__5430,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__9__rlt__5157,Vvar__var__var__var__var__21__n__5289__5291__5425__5427__5429),Vvar__var__var__var__var__22__m__5290__5292__5426__5428__5430))
| p(happ(happ(Vvar__7__req__5147,Vvar__var__var__var__var__21__n__5289__5291__5425__5427__5429),Vvar__var__var__var__var__22__m__5290__5292__5426__5428__5430))
| p(happ(happ(Vvar__9__rlt__5157,Vvar__var__var__var__var__22__m__5290__5292__5426__5428__5430),Vvar__var__var__var__var__21__n__5289__5291__5425__5427__5429)) ) ) )
& ! [Vvar__var__var__var__var__22__n__5294__5298__5431__5435__5439] :
( t(Vvar__var__var__var__var__22__n__5294__5298__5431__5435__5439,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__23__m__5295__5299__5432__5436__5440] :
( t(Vvar__var__var__var__var__23__m__5295__5299__5432__5436__5440,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__24__p__5296__5300__5433__5437__5441] :
( t(Vvar__var__var__var__var__24__p__5296__5300__5433__5437__5441,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__8__rle__5152,Vvar__var__var__var__var__22__n__5294__5298__5431__5435__5439),Vvar__var__var__var__var__23__m__5295__5299__5432__5436__5440))
=> p(happ(happ(Vvar__8__rle__5152,happ(happ(Vvar__3__rplus__5129,Vvar__var__var__var__var__24__p__5296__5300__5433__5437__5441),Vvar__var__var__var__var__22__n__5294__5298__5431__5435__5439)),happ(happ(Vvar__3__rplus__5129,Vvar__var__var__var__var__24__p__5296__5300__5433__5437__5441),Vvar__var__var__var__var__23__m__5295__5299__5432__5436__5440))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__5303__5307__5443__5447__5451__5455] :
( t(Vvar__var__var__var__var__var__23__n__5303__5307__5443__5447__5451__5455,Vvar__0__R__5126)
=> ! [Vvar__var__var__var__var__var__24__m__5304__5308__5444__5448__5452__5456] :
( t(Vvar__var__var__var__var__var__24__m__5304__5308__5444__5448__5452__5456,Vvar__0__R__5126)
=> ( p(happ(happ(Vvar__9__rlt__5157,Vvar__1__rO__5127),Vvar__var__var__var__var__var__23__n__5303__5307__5443__5447__5451__5455))
=> ( p(happ(happ(Vvar__9__rlt__5157,Vvar__1__rO__5127),Vvar__var__var__var__var__var__24__m__5304__5308__5444__5448__5452__5456))
=> p(happ(happ(Vvar__9__rlt__5157,Vvar__1__rO__5127),happ(happ(Vvar__4__rtimes__5134,Vvar__var__var__var__var__var__23__n__5303__5307__5443__5447__5451__5455),Vvar__var__var__var__var__var__24__m__5304__5308__5444__5448__5452__5456))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__5147,Vvar__1__rO__5127),Vvar__2__rI__5128))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX27644] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX27644)
=> ( VX27644 = cCoq_2emicromega_2eRMicromega_2eC0
| VX27644 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__27645] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__27645)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__27645) )
| ? [Vvar__0__r__27646] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__27646)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__27646) )
| ? [Vvar__0__r1__27647] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__27647)
& ? [Vvar__1__r2__27648] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__27648)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__27647,Vvar__1__r2__27648) ) )
| ? [Vvar__0__r1__27649] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__27649)
& ? [Vvar__1__r2__27650] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__27650)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__27649,Vvar__1__r2__27650) ) )
| ? [Vvar__0__r1__27651] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__27651)
& ? [Vvar__1__r2__27652] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__27652)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__27651,Vvar__1__r2__27652) ) )
| ? [Vvar__0__r1__27653] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__27653)
& ? [Vvar__1__z__27654] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__27654)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__27653,Vvar__1__z__27654) ) )
| ? [Vvar__0__r__27655] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__27655)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__27655) )
| ? [Vvar__0__r__27656] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__27656)
& VX27644 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__27656) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__34110,VX34111] :
( cType___24t(Vvar__0__T__34110)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__34110,VX34111)
=> ? [Vvar__1__Flhs__34113] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__34110,Vvar__1__Flhs__34113)
& ? [Vvar__2__Fop__34114] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__34114)
& ? [Vvar__3__Frhs__34115] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__34110,Vvar__3__Frhs__34115)
& VX34111 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__34110,Vvar__1__Flhs__34113,Vvar__2__Fop__34114,Vvar__3__Frhs__34115) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX6319] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX6319)
=> ( VX6319 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX6319 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX6319 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX6319 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX34109] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX34109)
=> ( VX34109 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX34109 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX34109 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX34109 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX34109 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX34109 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__33963,VX33964] :
( cType___24t(Vvar__0__C__33963)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__33963,VX33964)
=> ( ? [Vvar__1___24Anonymous__33966] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__33966)
& VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__33963,Vvar__1___24Anonymous__33966) )
| ? [Vvar__1___24Anonymous__33968] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__33963,Vvar__1___24Anonymous__33968)
& VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__33963,Vvar__1___24Anonymous__33968) )
| ? [Vvar__1___24Anonymous__33970] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__33963,Vvar__1___24Anonymous__33970)
& ? [Vvar__2___24Anonymous__33971] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__33963,Vvar__2___24Anonymous__33971)
& VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__33963,Vvar__1___24Anonymous__33970,Vvar__2___24Anonymous__33971) ) )
| ? [Vvar__1___24Anonymous__33973] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__33963,Vvar__1___24Anonymous__33973)
& ? [Vvar__2___24Anonymous__33974] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__33963,Vvar__2___24Anonymous__33974)
& VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__33963,Vvar__1___24Anonymous__33973,Vvar__2___24Anonymous__33974) ) )
| ? [Vvar__1___24Anonymous__33976] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__33963,Vvar__1___24Anonymous__33976)
& ? [Vvar__2___24Anonymous__33977] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__33963,Vvar__2___24Anonymous__33977)
& VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__33963,Vvar__1___24Anonymous__33976,Vvar__2___24Anonymous__33977) ) )
| ? [Vvar__1___24Anonymous__33979] :
( t(Vvar__1___24Anonymous__33979,Vvar__0__C__33963)
& VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__33963,Vvar__1___24Anonymous__33979) )
| VX33964 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__33963) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739] :
( cType___24t(Vvar__0__R__28670)
=> ( t(Vvar__1__rO__28671,Vvar__0__R__28670)
=> ( t(Vvar__2__rI__28672,Vvar__0__R__28670)
=> ( c_24__type__29203___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__3__rplus__28673)
=> ( c_24__type__29549___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__4__rtimes__28678)
=> ( c_24__type__29895___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__5__rminus__28683)
=> ( c_24__type__30218___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__6__ropp__28688)
=> ( c_24__type__30564___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__7__req__28691)
=> ( c_24__type__30910___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__8__rle__28696)
=> ( cType___24t(Vvar__9__C__28701)
=> ( t(Vvar__10__cO__28702,Vvar__9__C__28701)
=> ( t(Vvar__11__cI__28703,Vvar__9__C__28701)
=> ( c_24__type__31256___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__12__cplus__28704)
=> ( c_24__type__31602___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__13__ctimes__28709)
=> ( c_24__type__31948___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__14__cminus__28714)
=> ( c_24__type__32271___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__15__copp__28719)
=> ( c_24__type__32617___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__16__ceqb__28722)
=> ( c_24__type__32963___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__17__cleb__28727)
=> ( c_24__type__33286___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__18__phi__28732)
=> ( cType___24t(Vvar__19__E__28735)
=> ( c_24__type__33609___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__20__pow__phi__28736)
=> ( c_24__type__33955___24t(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739,Vvar__21__rpow__28739)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__8__rle__28696,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__17__cleb__28727,Vvar__18__phi__28732,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__28670,Vvar__1__rO__28671,Vvar__2__rI__28672,Vvar__3__rplus__28673,Vvar__4__rtimes__28678,Vvar__5__rminus__28683,Vvar__6__ropp__28688,Vvar__7__req__28691,Vvar__9__C__28701,Vvar__10__cO__28702,Vvar__11__cI__28703,Vvar__12__cplus__28704,Vvar__13__ctimes__28709,Vvar__14__cminus__28714,Vvar__15__copp__28719,Vvar__16__ceqb__28722,Vvar__18__phi__28732)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__28670,Vvar__2__rI__28672,Vvar__4__rtimes__28678,Vvar__7__req__28691,Vvar__19__E__28735,Vvar__20__pow__phi__28736,Vvar__21__rpow__28739)
& ! [Vvar__var__var__var__var__var__24__x__28822__28825__28835__28838__28841__28844] :
( t(Vvar__var__var__var__var__var__24__x__28822__28825__28835__28838__28841__28844,Vvar__9__C__28701)
=> ! [Vvar__var__var__var__var__var__25__y__28823__28826__28836__28839__28842__28845] :
( t(Vvar__var__var__var__var__var__25__y__28823__28826__28836__28839__28842__28845,Vvar__9__C__28701)
=> ( happ(happ(Vvar__16__ceqb__28722,Vvar__var__var__var__var__var__24__x__28822__28825__28835__28838__28841__28844),Vvar__var__var__var__var__var__25__y__28823__28826__28836__28839__28842__28845) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__28691,happ(Vvar__18__phi__28732,Vvar__var__var__var__var__var__24__x__28822__28825__28835__28838__28841__28844)),happ(Vvar__18__phi__28732,Vvar__var__var__var__var__var__25__y__28823__28826__28836__28839__28842__28845))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__28829__28832__28847__28850__28853__28856] :
( t(Vvar__var__var__var__var__var__25__x__28829__28832__28847__28850__28853__28856,Vvar__9__C__28701)
=> ! [Vvar__var__var__var__var__var__26__y__28830__28833__28848__28851__28854__28857] :
( t(Vvar__var__var__var__var__var__26__y__28830__28833__28848__28851__28854__28857,Vvar__9__C__28701)
=> ( happ(happ(Vvar__17__cleb__28727,Vvar__var__var__var__var__var__25__x__28829__28832__28847__28850__28853__28856),Vvar__var__var__var__var__var__26__y__28830__28833__28848__28851__28854__28857) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__28696,happ(Vvar__18__phi__28732,Vvar__var__var__var__var__var__25__x__28829__28832__28847__28850__28853__28856)),happ(Vvar__18__phi__28732,Vvar__var__var__var__var__var__26__y__28830__28833__28848__28851__28854__28857))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,VX20261] :
( cType___24t(Vvar__0__TA__20257)
=> ( cType___24t(Vvar__1__TX__20258)
=> ( cType___24t(Vvar__2__AA__20259)
=> ( cType___24t(Vvar__3__AF__20260)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,VX20261)
=> ( VX20261 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260)
| VX20261 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260)
| ? [Vvar__4___24Anonymous__20274] :
( t(Vvar__4___24Anonymous__20274,Vvar__1__TX__20258)
& VX20261 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20274) )
| ? [Vvar__4___24Anonymous__20279] :
( t(Vvar__4___24Anonymous__20279,Vvar__0__TA__20257)
& ? [Vvar__5___24Anonymous__20280] :
( t(Vvar__5___24Anonymous__20280,Vvar__2__AA__20259)
& VX20261 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20279,Vvar__5___24Anonymous__20280) ) )
| ? [Vvar__4___24Anonymous__20285] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20285)
& ? [Vvar__5___24Anonymous__20286] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__5___24Anonymous__20286)
& VX20261 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20285,Vvar__5___24Anonymous__20286) ) )
| ? [Vvar__4___24Anonymous__20291] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20291)
& ? [Vvar__5___24Anonymous__20292] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__5___24Anonymous__20292)
& VX20261 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20291,Vvar__5___24Anonymous__20292) ) )
| ? [Vvar__4___24Anonymous__20297] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20297)
& VX20261 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20297) )
| ? [Vvar__4___24Anonymous__20302] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20302)
& ? [Vvar__5___24Anonymous__20303] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__20260,Vvar__5___24Anonymous__20303)
& ? [Vvar__6___24Anonymous__20304] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__6___24Anonymous__20304)
& VX20261 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__20257,Vvar__1__TX__20258,Vvar__2__AA__20259,Vvar__3__AF__20260,Vvar__4___24Anonymous__20302,Vvar__5___24Anonymous__20303,Vvar__6___24Anonymous__20304) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__36989,VX36990] :
( cType___24t(Vvar__0__A__36989)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__36989,VX36990)
=> ( VX36990 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__36989)
| ? [Vvar__1___24Anonymous__36993] :
( t(Vvar__1___24Anonymous__36993,Vvar__0__A__36989)
& VX36990 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__36989,Vvar__1___24Anonymous__36993) )
| ? [Vvar__1___24Anonymous__36995] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__36989,Vvar__1___24Anonymous__36995)
& ? [Vvar__2___24Anonymous__36996] :
( t(Vvar__2___24Anonymous__36996,Vvar__0__A__36989)
& ? [Vvar__3___24Anonymous__36997] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__36989,Vvar__3___24Anonymous__36997)
& VX36990 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__36989,Vvar__1___24Anonymous__36995,Vvar__2___24Anonymous__36996,Vvar__3___24Anonymous__36997) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__37355] :
( cProp___24t(Vvar__0___24Anonymous__37355)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__37355)
=> ( ? [Vvar__0__P__37357] :
( cProp___24t(Vvar__0__P__37357)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__37357)
& Vvar__0___24Anonymous__37355 = Vvar__0__P__37357 )
| ? [Vvar__0__s__37359] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__37359)
& Vvar__0___24Anonymous__37355 = c_24__prop__37368___24a2(Vvar__0___24Anonymous__37355,Vvar__0__s__37359) )
| ? [Vvar__0__s1__37361] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__37361)
& ? [Vvar__1__s2__37362] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__37362)
& Vvar__0___24Anonymous__37355 = c_24__prop__37369___24a3(Vvar__0___24Anonymous__37355,Vvar__0__s1__37361,Vvar__1__s2__37362) ) )
| ? [Vvar__0__s1__37365] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__37365)
& ? [Vvar__1__s2__37366] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__37366)
& Vvar__0___24Anonymous__37355 = c_24__prop__37370___24a3(Vvar__0___24Anonymous__37355,Vvar__0__s1__37365,Vvar__1__s2__37366) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__37324] :
( cProp___24t(Vvar__0___24Anonymous__37324)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__37324)
=> ( ? [Vvar__0__S__37326] :
( cType___24t(Vvar__0__S__37326)
& ? [Vvar__1__x__37327] :
( t(Vvar__1__x__37327,Vvar__0__S__37326)
& ? [Vvar__2__y__37328] :
( t(Vvar__2__y__37328,Vvar__0__S__37326)
& Vvar__0___24Anonymous__37324 = c_24__prop__37348___24a4(Vvar__0___24Anonymous__37324,Vvar__0__S__37326,Vvar__1__x__37327,Vvar__2__y__37328) ) ) )
| ? [Vvar__0__x__37329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__37329)
& ? [Vvar__1__y__37330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__37330)
& Vvar__0___24Anonymous__37324 = c_24__prop__37349___24a3(Vvar__0___24Anonymous__37324,Vvar__0__x__37329,Vvar__1__y__37330) ) )
| ? [Vvar__0__x__37331] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__37331)
& ? [Vvar__1__s__37332] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__37332)
& Vvar__0___24Anonymous__37324 = c_24__prop__37350___24a3(Vvar__0___24Anonymous__37324,Vvar__0__x__37331,Vvar__1__s__37332) ) )
| Vvar__0___24Anonymous__37324 = c_24True
| Vvar__0___24Anonymous__37324 = c_24False
| ? [Vvar__0__P__37333] :
( cProp___24t(Vvar__0__P__37333)
& ? [Vvar__1__Q__37334] :
( cProp___24t(Vvar__1__Q__37334)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__37333)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__37334)
& Vvar__0___24Anonymous__37324 = c_24__prop__37351___24a3(Vvar__0___24Anonymous__37324,Vvar__0__P__37333,Vvar__1__Q__37334) ) )
| ? [Vvar__0__P__37337] :
( cProp___24t(Vvar__0__P__37337)
& ? [Vvar__1__Q__37338] :
( cProp___24t(Vvar__1__Q__37338)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__37337)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__37338)
& Vvar__0___24Anonymous__37324 = c_24__prop__37352___24a3(Vvar__0___24Anonymous__37324,Vvar__0__P__37337,Vvar__1__Q__37338) ) )
| ? [Vvar__0__P__37341] :
( cProp___24t(Vvar__0__P__37341)
& ? [Vvar__1__Q__37342] :
( cProp___24t(Vvar__1__Q__37342)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__37341)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__37342)
& Vvar__0___24Anonymous__37324 = c_24__prop__37353___24a3(Vvar__0___24Anonymous__37324,Vvar__0__P__37341,Vvar__1__Q__37342) ) )
| ? [Vvar__0__P__37346] :
( cProp___24t(Vvar__0__P__37346)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__37346)
& Vvar__0___24Anonymous__37324 = c_24__prop__37354___24a2(Vvar__0___24Anonymous__37324,Vvar__0__P__37346) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX22171] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX22171)
=> ( VX22171 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__22172] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__22172)
& ? [Vvar__1___24Anonymous__22173] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__22173)
& VX22171 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__22172,Vvar__1___24Anonymous__22173) ) )
| ? [Vvar__0___24Anonymous__22174] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__22174)
& ? [Vvar__1___24Anonymous__22175] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__22175)
& VX22171 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__22174,Vvar__1___24Anonymous__22175) ) )
| ? [Vvar__0___24Anonymous__22176] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__22176)
& ? [Vvar__1___24Anonymous__22177] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__22177)
& ? [Vvar__2___24Anonymous__22178] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__22178)
& VX22171 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__22176,Vvar__1___24Anonymous__22177,Vvar__2___24Anonymous__22178) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__37149,Vvar__1__env__37150,Vvar__2__env_27__37153,Vvar__3__x__37156] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__37149)
=> ( c_24__type__37177___24t(Vvar__0__fr__37149,Vvar__1__env__37150,Vvar__2__env_27__37153,Vvar__3__x__37156,Vvar__1__env__37150)
=> ( c_24__type__37186___24t(Vvar__0__fr__37149,Vvar__1__env__37150,Vvar__2__env_27__37153,Vvar__3__x__37156,Vvar__2__env_27__37153)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__37156)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__37149,Vvar__1__env__37150,Vvar__2__env_27__37153,Vvar__3__x__37156)
=> ( happ(Vvar__1__env__37150,Vvar__3__x__37156) = happ(Vvar__2__env_27__37153,Vvar__3__x__37156)
& happ(Vvar__1__env__37150,Vvar__3__x__37156) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__37153,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__37149,Vvar__3__x__37156))),happ(Vvar__2__env_27__37153,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__37149,Vvar__3__x__37156))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__37153,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__37149,Vvar__3__x__37156))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__37153,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__37149,Vvar__3__x__37156))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__24974,VX24975] :
( cType___24t(Vvar__0__C__24974)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,VX24975)
=> ( VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__24974)
| VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__24974)
| ? [Vvar__1___24Anonymous__24979] :
( t(Vvar__1___24Anonymous__24979,Vvar__0__C__24974)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__24974,Vvar__1___24Anonymous__24979) )
| ? [Vvar__1___24Anonymous__24981] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__24981)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__24974,Vvar__1___24Anonymous__24981) )
| ? [Vvar__1___24Anonymous__24983] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24983)
& ? [Vvar__2___24Anonymous__24984] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__2___24Anonymous__24984)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__24974,Vvar__1___24Anonymous__24983,Vvar__2___24Anonymous__24984) ) )
| ? [Vvar__1___24Anonymous__24986] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24986)
& ? [Vvar__2___24Anonymous__24987] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__2___24Anonymous__24987)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__24974,Vvar__1___24Anonymous__24986,Vvar__2___24Anonymous__24987) ) )
| ? [Vvar__1___24Anonymous__24989] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24989)
& ? [Vvar__2___24Anonymous__24990] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__2___24Anonymous__24990)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__24974,Vvar__1___24Anonymous__24989,Vvar__2___24Anonymous__24990) ) )
| ? [Vvar__1___24Anonymous__24992] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24992)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__24974,Vvar__1___24Anonymous__24992) )
| ? [Vvar__1___24Anonymous__24994] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24994)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__24974,Vvar__1___24Anonymous__24994) )
| ? [Vvar__1___24Anonymous__24996] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24996)
& ? [Vvar__2___24Anonymous__24997] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__2___24Anonymous__24997)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__24974,Vvar__1___24Anonymous__24996,Vvar__2___24Anonymous__24997) ) )
| ? [Vvar__1___24Anonymous__24999] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__24974,Vvar__1___24Anonymous__24999)
& ? [Vvar__2___24Anonymous__25000] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__25000)
& VX24975 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__24974,Vvar__1___24Anonymous__24999,Vvar__2___24Anonymous__25000) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267] :
( cType___24t(Vvar__0__R__24238)
=> ( t(Vvar__1__rO__24239,Vvar__0__R__24238)
=> ( t(Vvar__2__rI__24240,Vvar__0__R__24238)
=> ( c_24__type__24432___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__3__radd__24241)
=> ( c_24__type__24525___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__4__rmul__24246)
=> ( c_24__type__24618___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__5__rsub__24251)
=> ( c_24__type__24700___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__6__ropp__24256)
=> ( c_24__type__24793___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__7__rdiv__24259)
=> ( c_24__type__24875___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__8__rinv__24264)
=> ( c_24__type__24968___24t(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267,Vvar__9__req__24267)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__7__rdiv__24259,Vvar__8__rinv__24264,Vvar__9__req__24267)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__24238,Vvar__1__rO__24239,Vvar__2__rI__24240,Vvar__3__radd__24241,Vvar__4__rmul__24246,Vvar__5__rsub__24251,Vvar__6__ropp__24256,Vvar__9__req__24267)
& ~ p(happ(happ(Vvar__9__req__24267,Vvar__2__rI__24240),Vvar__1__rO__24239))
& ! [Vvar__var__var__var__var__var__var__12__p__24310__24312__24319__24321__24323__24325__24327] :
( t(Vvar__var__var__var__var__var__var__12__p__24310__24312__24319__24321__24323__24325__24327,Vvar__0__R__24238)
=> ! [Vvar__var__var__var__var__var__var__13__q__24311__24313__24320__24322__24324__24326__24328] :
( t(Vvar__var__var__var__var__var__var__13__q__24311__24313__24320__24322__24324__24326__24328,Vvar__0__R__24238)
=> p(happ(happ(Vvar__9__req__24267,happ(happ(Vvar__7__rdiv__24259,Vvar__var__var__var__var__var__var__12__p__24310__24312__24319__24321__24323__24325__24327),Vvar__var__var__var__var__var__var__13__q__24311__24313__24320__24322__24324__24326__24328)),happ(happ(Vvar__4__rmul__24246,Vvar__var__var__var__var__var__var__12__p__24310__24312__24319__24321__24323__24325__24327),happ(Vvar__8__rinv__24264,Vvar__var__var__var__var__var__var__13__q__24311__24313__24320__24322__24324__24326__24328)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__24315__24317__24329__24331__24333__24335__24337__24339] :
( t(Vvar__var__var__var__var__var__var__var__13__p__24315__24317__24329__24331__24333__24335__24337__24339,Vvar__0__R__24238)
=> ( ~ p(happ(happ(Vvar__9__req__24267,Vvar__var__var__var__var__var__var__var__13__p__24315__24317__24329__24331__24333__24335__24337__24339),Vvar__1__rO__24239))
=> p(happ(happ(Vvar__9__req__24267,happ(happ(Vvar__4__rmul__24246,happ(Vvar__8__rinv__24264,Vvar__var__var__var__var__var__var__var__13__p__24315__24317__24329__24331__24333__24335__24337__24339)),Vvar__var__var__var__var__var__var__var__13__p__24315__24317__24329__24331__24333__24335__24337__24339)),Vvar__2__rI__24240)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364] :
( cType___24t(Vvar__0__R__25335)
=> ( t(Vvar__1__rO__25336,Vvar__0__R__25335)
=> ( t(Vvar__2__rI__25337,Vvar__0__R__25335)
=> ( c_24__type__25529___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__3__radd__25338)
=> ( c_24__type__25622___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__4__rmul__25343)
=> ( c_24__type__25715___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__5__rsub__25348)
=> ( c_24__type__25797___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__6__ropp__25353)
=> ( c_24__type__25890___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__7__rdiv__25356)
=> ( c_24__type__25972___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__8__rinv__25361)
=> ( c_24__type__26065___24t(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364,Vvar__9__req__25364)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__7__rdiv__25356,Vvar__8__rinv__25361,Vvar__9__req__25364)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__25335,Vvar__1__rO__25336,Vvar__2__rI__25337,Vvar__3__radd__25338,Vvar__4__rmul__25343,Vvar__5__rsub__25348,Vvar__6__ropp__25353,Vvar__9__req__25364)
& ~ p(happ(happ(Vvar__9__req__25364,Vvar__2__rI__25337),Vvar__1__rO__25336))
& ! [Vvar__var__var__var__var__var__var__12__p__25407__25409__25416__25418__25420__25422__25424] :
( t(Vvar__var__var__var__var__var__var__12__p__25407__25409__25416__25418__25420__25422__25424,Vvar__0__R__25335)
=> ! [Vvar__var__var__var__var__var__var__13__q__25408__25410__25417__25419__25421__25423__25425] :
( t(Vvar__var__var__var__var__var__var__13__q__25408__25410__25417__25419__25421__25423__25425,Vvar__0__R__25335)
=> p(happ(happ(Vvar__9__req__25364,happ(happ(Vvar__7__rdiv__25356,Vvar__var__var__var__var__var__var__12__p__25407__25409__25416__25418__25420__25422__25424),Vvar__var__var__var__var__var__var__13__q__25408__25410__25417__25419__25421__25423__25425)),happ(happ(Vvar__4__rmul__25343,Vvar__var__var__var__var__var__var__12__p__25407__25409__25416__25418__25420__25422__25424),happ(Vvar__8__rinv__25361,Vvar__var__var__var__var__var__var__13__q__25408__25410__25417__25419__25421__25423__25425)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__25412__25414__25426__25428__25430__25432__25434__25436] :
( t(Vvar__var__var__var__var__var__var__var__13__p__25412__25414__25426__25428__25430__25432__25434__25436,Vvar__0__R__25335)
=> ( ~ p(happ(happ(Vvar__9__req__25364,Vvar__var__var__var__var__var__var__var__13__p__25412__25414__25426__25428__25430__25432__25434__25436),Vvar__1__rO__25336))
=> p(happ(happ(Vvar__9__req__25364,happ(happ(Vvar__4__rmul__25343,happ(Vvar__8__rinv__25361,Vvar__var__var__var__var__var__var__var__13__p__25412__25414__25426__25428__25430__25432__25434__25436)),Vvar__var__var__var__var__var__var__var__13__p__25412__25414__25426__25428__25430__25432__25434__25436)),Vvar__2__rI__25337)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__25307,VX25308] :
( cType___24t(Vvar__0__C__25307)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__25307,VX25308)
=> ? [Vvar__1__num__25310] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__25307,Vvar__1__num__25310)
& ? [Vvar__2__denum__25311] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__25307,Vvar__2__denum__25311)
& ? [Vvar__3__condition__25312] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__25307),Vvar__3__condition__25312)
& VX25308 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__25307,Vvar__1__num__25310,Vvar__2__denum__25311,Vvar__3__condition__25312) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__25321,VX25322] :
( cType___24t(Vvar__0__C__25321)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__25321,VX25322)
=> ? [Vvar__1__rsplit__left__25324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__25321,Vvar__1__rsplit__left__25324)
& ? [Vvar__2__rsplit__common__25325] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__25321,Vvar__2__rsplit__common__25325)
& ? [Vvar__3__rsplit__right__25326] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__25321,Vvar__3__rsplit__right__25326)
& VX25322 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__25321,Vvar__1__rsplit__left__25324,Vvar__2__rsplit__common__25325,Vvar__3__rsplit__right__25326) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092] :
( cType___24t(Vvar__0__R__26071)
=> ( t(Vvar__1__rO__26072,Vvar__0__R__26071)
=> ( t(Vvar__2__rI__26073,Vvar__0__R__26071)
=> ( c_24__type__26219___24t(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092,Vvar__3__radd__26074)
=> ( c_24__type__26282___24t(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092,Vvar__4__rmul__26079)
=> ( c_24__type__26345___24t(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092,Vvar__5__rdiv__26084)
=> ( c_24__type__26399___24t(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092,Vvar__6__rinv__26089)
=> ( c_24__type__26462___24t(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092,Vvar__7__req__26092)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__5__rdiv__26084,Vvar__6__rinv__26089,Vvar__7__req__26092)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__26071,Vvar__1__rO__26072,Vvar__2__rI__26073,Vvar__3__radd__26074,Vvar__4__rmul__26079,Vvar__7__req__26092)
& ~ p(happ(happ(Vvar__7__req__26092,Vvar__2__rI__26073),Vvar__1__rO__26072))
& ! [Vvar__var__var__var__var__var__var__10__p__26127__26129__26136__26138__26140__26142__26144] :
( t(Vvar__var__var__var__var__var__var__10__p__26127__26129__26136__26138__26140__26142__26144,Vvar__0__R__26071)
=> ! [Vvar__var__var__var__var__var__var__11__q__26128__26130__26137__26139__26141__26143__26145] :
( t(Vvar__var__var__var__var__var__var__11__q__26128__26130__26137__26139__26141__26143__26145,Vvar__0__R__26071)
=> p(happ(happ(Vvar__7__req__26092,happ(happ(Vvar__5__rdiv__26084,Vvar__var__var__var__var__var__var__10__p__26127__26129__26136__26138__26140__26142__26144),Vvar__var__var__var__var__var__var__11__q__26128__26130__26137__26139__26141__26143__26145)),happ(happ(Vvar__4__rmul__26079,Vvar__var__var__var__var__var__var__10__p__26127__26129__26136__26138__26140__26142__26144),happ(Vvar__6__rinv__26089,Vvar__var__var__var__var__var__var__11__q__26128__26130__26137__26139__26141__26143__26145)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__26132__26134__26146__26148__26150__26152__26154__26156] :
( t(Vvar__var__var__var__var__var__var__var__11__p__26132__26134__26146__26148__26150__26152__26154__26156,Vvar__0__R__26071)
=> ( ~ p(happ(happ(Vvar__7__req__26092,Vvar__var__var__var__var__var__var__var__11__p__26132__26134__26146__26148__26150__26152__26154__26156),Vvar__1__rO__26072))
=> p(happ(happ(Vvar__7__req__26092,happ(happ(Vvar__4__rmul__26079,happ(Vvar__6__rinv__26089,Vvar__var__var__var__var__var__var__var__11__p__26132__26134__26146__26148__26150__26152__26154__26156)),Vvar__var__var__var__var__var__var__var__11__p__26132__26134__26146__26148__26150__26152__26154__26156)),Vvar__2__rI__26073)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX26640] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX26640)
=> ? [Vvar__0__hypo__type__26641] :
( cType___24t(Vvar__0__hypo__type__26641)
& ? [Vvar__1__hypo__proof__26642] :
( t(Vvar__1__hypo__proof__26642,Vvar__0__hypo__type__26641)
& VX26640 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__26641,Vvar__1__hypo__proof__26642) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX6635] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX6635)
=> ( VX6635 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__6636] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6636)
& ? [Vvar__1___24Anonymous__6637] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__6637)
& VX6635 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__6636,Vvar__1___24Anonymous__6637) ) )
| ? [Vvar__0___24Anonymous__6638] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__6638)
& ? [Vvar__1___24Anonymous__6639] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__6639)
& VX6635 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__6638,Vvar__1___24Anonymous__6639) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__6699,VX6700] :
( cType___24t(Vvar__0__C__6699)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,VX6700)
=> ( VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__6699)
| VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__6699)
| ? [Vvar__1___24Anonymous__6704] :
( t(Vvar__1___24Anonymous__6704,Vvar__0__C__6699)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__6699,Vvar__1___24Anonymous__6704) )
| ? [Vvar__1___24Anonymous__6706] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6706)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__6699,Vvar__1___24Anonymous__6706) )
| ? [Vvar__1___24Anonymous__6708] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__1___24Anonymous__6708)
& ? [Vvar__2___24Anonymous__6709] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__2___24Anonymous__6709)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__6699,Vvar__1___24Anonymous__6708,Vvar__2___24Anonymous__6709) ) )
| ? [Vvar__1___24Anonymous__6711] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__1___24Anonymous__6711)
& ? [Vvar__2___24Anonymous__6712] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__2___24Anonymous__6712)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__6699,Vvar__1___24Anonymous__6711,Vvar__2___24Anonymous__6712) ) )
| ? [Vvar__1___24Anonymous__6714] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__1___24Anonymous__6714)
& ? [Vvar__2___24Anonymous__6715] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__2___24Anonymous__6715)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__6699,Vvar__1___24Anonymous__6714,Vvar__2___24Anonymous__6715) ) )
| ? [Vvar__1___24Anonymous__6717] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__1___24Anonymous__6717)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__6699,Vvar__1___24Anonymous__6717) )
| ? [Vvar__1___24Anonymous__6719] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__6699,Vvar__1___24Anonymous__6719)
& ? [Vvar__2___24Anonymous__6720] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__6720)
& VX6700 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__6699,Vvar__1___24Anonymous__6719,Vvar__2___24Anonymous__6720) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__6454,VX6455] :
( cType___24t(Vvar__0__C__6454)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__6454,VX6455)
=> ( ? [Vvar__1___24Anonymous__6457] :
( t(Vvar__1___24Anonymous__6457,Vvar__0__C__6454)
& VX6455 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__6454,Vvar__1___24Anonymous__6457) )
| ? [Vvar__1___24Anonymous__6459] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__6459)
& ? [Vvar__2___24Anonymous__6460] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__6454,Vvar__2___24Anonymous__6460)
& VX6455 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__6454,Vvar__1___24Anonymous__6459,Vvar__2___24Anonymous__6460) ) )
| ? [Vvar__1___24Anonymous__6462] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__6454,Vvar__1___24Anonymous__6462)
& ? [Vvar__2___24Anonymous__6463] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__6463)
& ? [Vvar__3___24Anonymous__6464] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__6454,Vvar__3___24Anonymous__6464)
& VX6455 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__6454,Vvar__1___24Anonymous__6462,Vvar__2___24Anonymous__6463,Vvar__3___24Anonymous__6464) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118] :
( cType___24t(Vvar__0__R__8097)
=> ( t(Vvar__1__rO__8098,Vvar__0__R__8097)
=> ( t(Vvar__2__rI__8099,Vvar__0__R__8097)
=> ( c_24__type__8346___24t(Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118,Vvar__3__radd__8100)
=> ( c_24__type__8409___24t(Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118,Vvar__4__rmul__8105)
=> ( c_24__type__8472___24t(Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118,Vvar__5__rsub__8110)
=> ( c_24__type__8526___24t(Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118,Vvar__6__ropp__8115)
=> ( c_24__type__8589___24t(Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118,Vvar__7__req__8118)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__8097,Vvar__1__rO__8098,Vvar__2__rI__8099,Vvar__3__radd__8100,Vvar__4__rmul__8105,Vvar__5__rsub__8110,Vvar__6__ropp__8115,Vvar__7__req__8118)
=> ( ! [Vvar__var__var__var__var__var__8__x__8151__8152__8205__8206__8207__8208] :
( t(Vvar__var__var__var__var__var__8__x__8151__8152__8205__8206__8207__8208,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__3__radd__8100,Vvar__1__rO__8098),Vvar__var__var__var__var__var__8__x__8151__8152__8205__8206__8207__8208)),Vvar__var__var__var__var__var__8__x__8151__8152__8205__8206__8207__8208)) )
& ! [Vvar__var__var__var__var__9__x__8154__8156__8209__8211__8213] :
( t(Vvar__var__var__var__var__9__x__8154__8156__8209__8211__8213,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__10__y__8155__8157__8210__8212__8214] :
( t(Vvar__var__var__var__var__10__y__8155__8157__8210__8212__8214,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__9__x__8154__8156__8209__8211__8213),Vvar__var__var__var__var__10__y__8155__8157__8210__8212__8214)),happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__10__y__8155__8157__8210__8212__8214),Vvar__var__var__var__var__9__x__8154__8156__8209__8211__8213))) ) )
& ! [Vvar__var__var__var__var__10__x__8159__8162__8215__8218__8221] :
( t(Vvar__var__var__var__var__10__x__8159__8162__8215__8218__8221,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__11__y__8160__8163__8216__8219__8222] :
( t(Vvar__var__var__var__var__11__y__8160__8163__8216__8219__8222,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__12__z__8161__8164__8217__8220__8223] :
( t(Vvar__var__var__var__var__12__z__8161__8164__8217__8220__8223,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__10__x__8159__8162__8215__8218__8221),happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__11__y__8160__8163__8216__8219__8222),Vvar__var__var__var__var__12__z__8161__8164__8217__8220__8223))),happ(happ(Vvar__3__radd__8100,happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__10__x__8159__8162__8215__8218__8221),Vvar__var__var__var__var__11__y__8160__8163__8216__8219__8222)),Vvar__var__var__var__var__12__z__8161__8164__8217__8220__8223))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__8166__8167__8224__8225__8226__8227] :
( t(Vvar__var__var__var__var__var__11__x__8166__8167__8224__8225__8226__8227,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__4__rmul__8105,Vvar__2__rI__8099),Vvar__var__var__var__var__var__11__x__8166__8167__8224__8225__8226__8227)),Vvar__var__var__var__var__var__11__x__8166__8167__8224__8225__8226__8227)) )
& ! [Vvar__var__var__var__var__var__12__x__8169__8170__8228__8229__8230__8231] :
( t(Vvar__var__var__var__var__var__12__x__8169__8170__8228__8229__8230__8231,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__4__rmul__8105,Vvar__1__rO__8098),Vvar__var__var__var__var__var__12__x__8169__8170__8228__8229__8230__8231)),Vvar__1__rO__8098)) )
& ! [Vvar__var__var__var__var__13__x__8172__8174__8232__8234__8236] :
( t(Vvar__var__var__var__var__13__x__8172__8174__8232__8234__8236,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__14__y__8173__8175__8233__8235__8237] :
( t(Vvar__var__var__var__var__14__y__8173__8175__8233__8235__8237,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__13__x__8172__8174__8232__8234__8236),Vvar__var__var__var__var__14__y__8173__8175__8233__8235__8237)),happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__14__y__8173__8175__8233__8235__8237),Vvar__var__var__var__var__13__x__8172__8174__8232__8234__8236))) ) )
& ! [Vvar__var__var__var__var__14__x__8177__8180__8238__8241__8244] :
( t(Vvar__var__var__var__var__14__x__8177__8180__8238__8241__8244,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__15__y__8178__8181__8239__8242__8245] :
( t(Vvar__var__var__var__var__15__y__8178__8181__8239__8242__8245,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__16__z__8179__8182__8240__8243__8246] :
( t(Vvar__var__var__var__var__16__z__8179__8182__8240__8243__8246,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__14__x__8177__8180__8238__8241__8244),happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__15__y__8178__8181__8239__8242__8245),Vvar__var__var__var__var__16__z__8179__8182__8240__8243__8246))),happ(happ(Vvar__4__rmul__8105,happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__14__x__8177__8180__8238__8241__8244),Vvar__var__var__var__var__15__y__8178__8181__8239__8242__8245)),Vvar__var__var__var__var__16__z__8179__8182__8240__8243__8246))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__8184__8187__8247__8250__8253__8256] :
( t(Vvar__var__var__var__var__var__15__x__8184__8187__8247__8250__8253__8256,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__var__16__y__8185__8188__8248__8251__8254__8257] :
( t(Vvar__var__var__var__var__var__16__y__8185__8188__8248__8251__8254__8257,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__var__17__z__8186__8189__8249__8252__8255__8258] :
( t(Vvar__var__var__var__var__var__17__z__8186__8189__8249__8252__8255__8258,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__4__rmul__8105,happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__var__15__x__8184__8187__8247__8250__8253__8256),Vvar__var__var__var__var__var__16__y__8185__8188__8248__8251__8254__8257)),Vvar__var__var__var__var__var__17__z__8186__8189__8249__8252__8255__8258)),happ(happ(Vvar__3__radd__8100,happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__var__15__x__8184__8187__8247__8250__8253__8256),Vvar__var__var__var__var__var__17__z__8186__8189__8249__8252__8255__8258)),happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__var__16__y__8185__8188__8248__8251__8254__8257),Vvar__var__var__var__var__var__17__z__8186__8189__8249__8252__8255__8258)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__8191__8193__8259__8261__8263__8265] :
( t(Vvar__var__var__var__var__var__16__x__8191__8193__8259__8261__8263__8265,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__var__17__y__8192__8194__8260__8262__8264__8266] :
( t(Vvar__var__var__var__var__var__17__y__8192__8194__8260__8262__8264__8266,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(Vvar__6__ropp__8115,happ(happ(Vvar__4__rmul__8105,Vvar__var__var__var__var__var__16__x__8191__8193__8259__8261__8263__8265),Vvar__var__var__var__var__var__17__y__8192__8194__8260__8262__8264__8266))),happ(happ(Vvar__4__rmul__8105,happ(Vvar__6__ropp__8115,Vvar__var__var__var__var__var__16__x__8191__8193__8259__8261__8263__8265)),Vvar__var__var__var__var__var__17__y__8192__8194__8260__8262__8264__8266))) ) )
& ! [Vvar__var__var__var__var__var__17__x__8196__8198__8267__8269__8271__8273] :
( t(Vvar__var__var__var__var__var__17__x__8196__8198__8267__8269__8271__8273,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__var__18__y__8197__8199__8268__8270__8272__8274] :
( t(Vvar__var__var__var__var__var__18__y__8197__8199__8268__8270__8272__8274,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(Vvar__6__ropp__8115,happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__var__17__x__8196__8198__8267__8269__8271__8273),Vvar__var__var__var__var__var__18__y__8197__8199__8268__8270__8272__8274))),happ(happ(Vvar__3__radd__8100,happ(Vvar__6__ropp__8115,Vvar__var__var__var__var__var__17__x__8196__8198__8267__8269__8271__8273)),happ(Vvar__6__ropp__8115,Vvar__var__var__var__var__var__18__y__8197__8199__8268__8270__8272__8274)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__8201__8203__8275__8277__8279__8281__8283] :
( t(Vvar__var__var__var__var__var__var__18__x__8201__8203__8275__8277__8279__8281__8283,Vvar__0__R__8097)
=> ! [Vvar__var__var__var__var__var__var__19__y__8202__8204__8276__8278__8280__8282__8284] :
( t(Vvar__var__var__var__var__var__var__19__y__8202__8204__8276__8278__8280__8282__8284,Vvar__0__R__8097)
=> p(happ(happ(Vvar__7__req__8118,happ(happ(Vvar__5__rsub__8110,Vvar__var__var__var__var__var__var__18__x__8201__8203__8275__8277__8279__8281__8283),Vvar__var__var__var__var__var__var__19__y__8202__8204__8276__8278__8280__8282__8284)),happ(happ(Vvar__3__radd__8100,Vvar__var__var__var__var__var__var__18__x__8201__8203__8275__8277__8279__8281__8283),happ(Vvar__6__ropp__8115,Vvar__var__var__var__var__var__var__19__y__8202__8204__8276__8278__8280__8282__8284)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763] :
( cType___24t(Vvar__0__R__35743)
=> ( c_24__type__35883___24t(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763,Vvar__1__req__35744)
=> ( cType___24t(Vvar__2__C__35749)
=> ( c_24__type__35933___24t(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763,Vvar__3__cadd__35750)
=> ( c_24__type__35983___24t(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763,Vvar__4__cmul__35755)
=> ( c_24__type__36025___24t(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763,Vvar__5__phi__35760)
=> ( c_24__type__36075___24t(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763,Vvar__6__cdiv__35763)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__35795__35800__35805__35810__35815__35820__35825__35830] :
( t(Vvar__var__var__var__var__var__var__var__7__a__35795__35800__35805__35810__35815__35820__35825__35830,Vvar__2__C__35749)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__35796__35801__35806__35811__35816__35821__35826__35831] :
( t(Vvar__var__var__var__var__var__var__var__8__b__35796__35801__35806__35811__35816__35821__35826__35831,Vvar__2__C__35749)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2436138___24a9(Vvar__0__R__35743,Vvar__1__req__35744,Vvar__2__C__35749,Vvar__3__cadd__35750,Vvar__4__cmul__35755,Vvar__5__phi__35760,Vvar__6__cdiv__35763,Vvar__var__var__var__var__var__var__var__7__a__35795__35800__35805__35810__35815__35820__35825__35830,Vvar__var__var__var__var__var__var__var__8__b__35796__35801__35806__35811__35816__35821__35826__35831) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__3__req__36165,Vvar__4__Cpow__36170,Vvar__5__Cp__phi__36171,Vvar__6__rpow__36174] :
( cType___24t(Vvar__0__R__36158)
=> ( t(Vvar__1__rI__36159,Vvar__0__R__36158)
=> ( c_24__type__36260___24t(Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__3__req__36165,Vvar__4__Cpow__36170,Vvar__5__Cp__phi__36171,Vvar__6__rpow__36174,Vvar__2__rmul__36160)
=> ( c_24__type__36304___24t(Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__3__req__36165,Vvar__4__Cpow__36170,Vvar__5__Cp__phi__36171,Vvar__6__rpow__36174,Vvar__3__req__36165)
=> ( cType___24t(Vvar__4__Cpow__36170)
=> ( c_24__type__36340___24t(Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__3__req__36165,Vvar__4__Cpow__36170,Vvar__5__Cp__phi__36171,Vvar__6__rpow__36174,Vvar__5__Cp__phi__36171)
=> ( c_24__type__36384___24t(Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__3__req__36165,Vvar__4__Cpow__36170,Vvar__5__Cp__phi__36171,Vvar__6__rpow__36174,Vvar__6__rpow__36174)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__3__req__36165,Vvar__4__Cpow__36170,Vvar__5__Cp__phi__36171,Vvar__6__rpow__36174)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__36202__36204__36206__36208__36210__36212__36214__36216] :
( t(Vvar__var__var__var__var__var__var__var__7__r__36202__36204__36206__36208__36210__36212__36214__36216,Vvar__0__R__36158)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__36203__36205__36207__36209__36211__36213__36215__36217] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__36203__36205__36207__36209__36211__36213__36215__36217)
=> p(happ(happ(Vvar__3__req__36165,happ(happ(Vvar__6__rpow__36174,Vvar__var__var__var__var__var__var__var__7__r__36202__36204__36206__36208__36210__36212__36214__36216),happ(Vvar__5__Cp__phi__36171,Vvar__var__var__var__var__var__var__var__8__n__36203__36205__36207__36209__36211__36213__36215__36217))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__36158,Vvar__1__rI__36159,Vvar__2__rmul__36160,Vvar__var__var__var__var__var__var__var__7__r__36202__36204__36206__36208__36210__36212__36214__36216,Vvar__var__var__var__var__var__var__var__8__n__36203__36205__36207__36209__36211__36213__36215__36217))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171] :
( cType___24t(Vvar__0__R__9157)
=> ( c_24__type__9262___24t(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171,Vvar__1__radd__9158)
=> ( c_24__type__9292___24t(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171,Vvar__2__rmul__9163)
=> ( c_24__type__9316___24t(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171,Vvar__3__ropp__9168)
=> ( c_24__type__9346___24t(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171,Vvar__4__req__9171)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9376___24a5(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9157,c_24__type__9400___24a5(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171),Vvar__4__req__9171,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9157,Vvar__0__R__9157,Vvar__4__req__9171,Vvar__4__req__9171)),Vvar__1__radd__9158)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9433___24a5(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9157,c_24__type__9457___24a5(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171),Vvar__4__req__9171,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9157,Vvar__0__R__9157,Vvar__4__req__9171,Vvar__4__req__9171)),Vvar__2__rmul__9163)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9484___24a5(Vvar__0__R__9157,Vvar__1__radd__9158,Vvar__2__rmul__9163,Vvar__3__ropp__9168,Vvar__4__req__9171),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9157,Vvar__0__R__9157,Vvar__4__req__9171,Vvar__4__req__9171),Vvar__3__ropp__9168)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX36388] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX36388)
=> ( VX36388 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__36389] :
( cType___24t(Vvar__0__R__36389)
& ? [Vvar__1__req__36390] :
( c_24__type__1189___24t(Vvar__0__R__36389,Vvar__1__req__36390)
& ? [Vvar__2__reqb__36395] :
( c_24__type__6619___24t(Vvar__0__R__36389,Vvar__2__reqb__36395)
& ! [Vvar__var__3__x__36401__36404] :
( t(Vvar__var__3__x__36401__36404,Vvar__0__R__36389)
=> ! [Vvar__var__4__y__36402__36405] :
( t(Vvar__var__4__y__36402__36405,Vvar__0__R__36389)
=> ( happ(happ(Vvar__2__reqb__36395,Vvar__var__3__x__36401__36404),Vvar__var__4__y__36402__36405) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__36390,Vvar__var__3__x__36401__36404),Vvar__var__4__y__36402__36405)) ) ) )
& VX36388 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__36389,Vvar__1__req__36390,Vvar__2__reqb__36395) ) ) )
| ? [Vvar__0__R__36407] :
( cType___24t(Vvar__0__R__36407)
& ? [Vvar__1__rO__36408] :
( t(Vvar__1__rO__36408,Vvar__0__R__36407)
& ? [Vvar__2__rI__36409] :
( t(Vvar__2__rI__36409,Vvar__0__R__36407)
& ? [Vvar__3__radd__36410] :
( c_24__type__4728___24t(Vvar__0__R__36407,Vvar__3__radd__36410)
& ? [Vvar__4__rmul__36415] :
( c_24__type__4728___24t(Vvar__0__R__36407,Vvar__4__rmul__36415)
& ? [Vvar__5__rsub__36420] :
( c_24__type__4728___24t(Vvar__0__R__36407,Vvar__5__rsub__36420)
& ? [Vvar__6__ropp__36425] :
( c_24__type__4737___24t(Vvar__0__R__36407,Vvar__6__ropp__36425)
& ? [Vvar__7__req__36428] :
( c_24__type__1189___24t(Vvar__0__R__36407,Vvar__7__req__36428)
& ? [Vvar__8__C__36433] :
( cType___24t(Vvar__8__C__36433)
& ? [Vvar__9__cO__36434] :
( t(Vvar__9__cO__36434,Vvar__8__C__36433)
& ? [Vvar__10__cI__36435] :
( t(Vvar__10__cI__36435,Vvar__8__C__36433)
& ? [Vvar__11__cadd__36436] :
( c_24__type__6674___24t(Vvar__0__R__36407,Vvar__8__C__36433,Vvar__11__cadd__36436)
& ? [Vvar__12__cmul__36441] :
( c_24__type__6674___24t(Vvar__0__R__36407,Vvar__8__C__36433,Vvar__12__cmul__36441)
& ? [Vvar__13__csub__36446] :
( c_24__type__6674___24t(Vvar__0__R__36407,Vvar__8__C__36433,Vvar__13__csub__36446)
& ? [Vvar__14__copp__36451] :
( c_24__type__6688___24t(Vvar__0__R__36407,Vvar__8__C__36433,Vvar__14__copp__36451)
& ? [Vvar__15__ceqb__36454] :
( c_24__type__6695___24t(Vvar__0__R__36407,Vvar__8__C__36433,Vvar__15__ceqb__36454)
& ? [Vvar__16__phi__36459] :
( c_24__type__4812___24t(Vvar__0__R__36407,Vvar__8__C__36433,Vvar__16__phi__36459)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__36407,Vvar__1__rO__36408,Vvar__2__rI__36409,Vvar__3__radd__36410,Vvar__4__rmul__36415,Vvar__5__rsub__36420,Vvar__6__ropp__36425,Vvar__7__req__36428,Vvar__8__C__36433,Vvar__9__cO__36434,Vvar__10__cI__36435,Vvar__11__cadd__36436,Vvar__12__cmul__36441,Vvar__13__csub__36446,Vvar__14__copp__36451,Vvar__15__ceqb__36454,Vvar__16__phi__36459)
& VX36388 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__36407,Vvar__1__rO__36408,Vvar__2__rI__36409,Vvar__3__radd__36410,Vvar__4__rmul__36415,Vvar__5__rsub__36420,Vvar__6__ropp__36425,Vvar__7__req__36428,Vvar__8__C__36433,Vvar__9__cO__36434,Vvar__10__cI__36435,Vvar__11__cadd__36436,Vvar__12__cmul__36441,Vvar__13__csub__36446,Vvar__14__copp__36451,Vvar__15__ceqb__36454,Vvar__16__phi__36459) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539] :
( cType___24t(Vvar__0__R__9487)
=> ( t(Vvar__1__rO__9488,Vvar__0__R__9487)
=> ( t(Vvar__2__rI__9489,Vvar__0__R__9487)
=> ( c_24__type__9883___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__3__radd__9490)
=> ( c_24__type__10096___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__4__rmul__9495)
=> ( c_24__type__10309___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__5__rsub__9500)
=> ( c_24__type__10504___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__6__ropp__9505)
=> ( c_24__type__10717___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__7__req__9508)
=> ( cType___24t(Vvar__8__C__9513)
=> ( t(Vvar__9__cO__9514,Vvar__8__C__9513)
=> ( t(Vvar__10__cI__9515,Vvar__8__C__9513)
=> ( c_24__type__10930___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__11__cadd__9516)
=> ( c_24__type__11143___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__12__cmul__9521)
=> ( c_24__type__11356___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__13__csub__9526)
=> ( c_24__type__11551___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__14__copp__9531)
=> ( c_24__type__11764___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__15__ceqb__9534)
=> ( c_24__type__11959___24t(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539,Vvar__16__phi__9539)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__9487,Vvar__1__rO__9488,Vvar__2__rI__9489,Vvar__3__radd__9490,Vvar__4__rmul__9495,Vvar__5__rsub__9500,Vvar__6__ropp__9505,Vvar__7__req__9508,Vvar__8__C__9513,Vvar__9__cO__9514,Vvar__10__cI__9515,Vvar__11__cadd__9516,Vvar__12__cmul__9521,Vvar__13__csub__9526,Vvar__14__copp__9531,Vvar__15__ceqb__9534,Vvar__16__phi__9539)
=> ( p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,Vvar__9__cO__9514)),Vvar__1__rO__9488))
& p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,Vvar__10__cI__9515)),Vvar__2__rI__9489))
& ! [Vvar__var__var__var__var__var__var__19__x__9601__9603__9625__9627__9629__9631__9633] :
( t(Vvar__var__var__var__var__var__var__19__x__9601__9603__9625__9627__9629__9631__9633,Vvar__8__C__9513)
=> ! [Vvar__var__var__var__var__var__var__20__y__9602__9604__9626__9628__9630__9632__9634] :
( t(Vvar__var__var__var__var__var__var__20__y__9602__9604__9626__9628__9630__9632__9634,Vvar__8__C__9513)
=> p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,happ(happ(Vvar__11__cadd__9516,Vvar__var__var__var__var__var__var__19__x__9601__9603__9625__9627__9629__9631__9633),Vvar__var__var__var__var__var__var__20__y__9602__9604__9626__9628__9630__9632__9634))),happ(happ(Vvar__3__radd__9490,happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__19__x__9601__9603__9625__9627__9629__9631__9633)),happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__20__y__9602__9604__9626__9628__9630__9632__9634)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__9606__9608__9635__9637__9639__9641__9643] :
( t(Vvar__var__var__var__var__var__var__20__x__9606__9608__9635__9637__9639__9641__9643,Vvar__8__C__9513)
=> ! [Vvar__var__var__var__var__var__var__21__y__9607__9609__9636__9638__9640__9642__9644] :
( t(Vvar__var__var__var__var__var__var__21__y__9607__9609__9636__9638__9640__9642__9644,Vvar__8__C__9513)
=> p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,happ(happ(Vvar__13__csub__9526,Vvar__var__var__var__var__var__var__20__x__9606__9608__9635__9637__9639__9641__9643),Vvar__var__var__var__var__var__var__21__y__9607__9609__9636__9638__9640__9642__9644))),happ(happ(Vvar__5__rsub__9500,happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__20__x__9606__9608__9635__9637__9639__9641__9643)),happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__21__y__9607__9609__9636__9638__9640__9642__9644)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__9611__9613__9645__9647__9649__9651__9653] :
( t(Vvar__var__var__var__var__var__var__21__x__9611__9613__9645__9647__9649__9651__9653,Vvar__8__C__9513)
=> ! [Vvar__var__var__var__var__var__var__22__y__9612__9614__9646__9648__9650__9652__9654] :
( t(Vvar__var__var__var__var__var__var__22__y__9612__9614__9646__9648__9650__9652__9654,Vvar__8__C__9513)
=> p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,happ(happ(Vvar__12__cmul__9521,Vvar__var__var__var__var__var__var__21__x__9611__9613__9645__9647__9649__9651__9653),Vvar__var__var__var__var__var__var__22__y__9612__9614__9646__9648__9650__9652__9654))),happ(happ(Vvar__4__rmul__9495,happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__21__x__9611__9613__9645__9647__9649__9651__9653)),happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__22__y__9612__9614__9646__9648__9650__9652__9654)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__9616__9617__9655__9656__9657__9658__9659] :
( t(Vvar__var__var__var__var__var__var__22__x__9616__9617__9655__9656__9657__9658__9659,Vvar__8__C__9513)
=> p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,happ(Vvar__14__copp__9531,Vvar__var__var__var__var__var__var__22__x__9616__9617__9655__9656__9657__9658__9659))),happ(Vvar__6__ropp__9505,happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__var__22__x__9616__9617__9655__9656__9657__9658__9659)))) )
& ! [Vvar__var__var__var__var__var__23__x__9619__9622__9660__9663__9666__9669] :
( t(Vvar__var__var__var__var__var__23__x__9619__9622__9660__9663__9666__9669,Vvar__8__C__9513)
=> ! [Vvar__var__var__var__var__var__24__y__9620__9623__9661__9664__9667__9670] :
( t(Vvar__var__var__var__var__var__24__y__9620__9623__9661__9664__9667__9670,Vvar__8__C__9513)
=> ( happ(happ(Vvar__15__ceqb__9534,Vvar__var__var__var__var__var__23__x__9619__9622__9660__9663__9666__9669),Vvar__var__var__var__var__var__24__y__9620__9623__9661__9664__9667__9670) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__9508,happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__23__x__9619__9622__9660__9663__9666__9669)),happ(Vvar__16__phi__9539,Vvar__var__var__var__var__var__24__y__9620__9623__9661__9664__9667__9670))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660] :
( cType___24t(Vvar__0__R__8639)
=> ( t(Vvar__1__rO__8640,Vvar__0__R__8639)
=> ( t(Vvar__2__rI__8641,Vvar__0__R__8639)
=> ( c_24__type__8863___24t(Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660,Vvar__3__radd__8642)
=> ( c_24__type__8926___24t(Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660,Vvar__4__rmul__8647)
=> ( c_24__type__8989___24t(Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660,Vvar__5__rsub__8652)
=> ( c_24__type__9043___24t(Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660,Vvar__6__ropp__8657)
=> ( c_24__type__9106___24t(Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660,Vvar__7__req__8660)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__8639,Vvar__1__rO__8640,Vvar__2__rI__8641,Vvar__3__radd__8642,Vvar__4__rmul__8647,Vvar__5__rsub__8652,Vvar__6__ropp__8657,Vvar__7__req__8660)
=> ( ! [Vvar__var__var__var__var__var__8__x__8693__8694__8737__8738__8739__8740] :
( t(Vvar__var__var__var__var__var__8__x__8693__8694__8737__8738__8739__8740,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__3__radd__8642,Vvar__1__rO__8640),Vvar__var__var__var__var__var__8__x__8693__8694__8737__8738__8739__8740)),Vvar__var__var__var__var__var__8__x__8693__8694__8737__8738__8739__8740)) )
& ! [Vvar__var__var__var__var__9__x__8696__8698__8741__8743__8745] :
( t(Vvar__var__var__var__var__9__x__8696__8698__8741__8743__8745,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__10__y__8697__8699__8742__8744__8746] :
( t(Vvar__var__var__var__var__10__y__8697__8699__8742__8744__8746,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__9__x__8696__8698__8741__8743__8745),Vvar__var__var__var__var__10__y__8697__8699__8742__8744__8746)),happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__10__y__8697__8699__8742__8744__8746),Vvar__var__var__var__var__9__x__8696__8698__8741__8743__8745))) ) )
& ! [Vvar__var__var__var__var__10__x__8701__8704__8747__8750__8753] :
( t(Vvar__var__var__var__var__10__x__8701__8704__8747__8750__8753,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__11__y__8702__8705__8748__8751__8754] :
( t(Vvar__var__var__var__var__11__y__8702__8705__8748__8751__8754,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__12__z__8703__8706__8749__8752__8755] :
( t(Vvar__var__var__var__var__12__z__8703__8706__8749__8752__8755,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__10__x__8701__8704__8747__8750__8753),happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__11__y__8702__8705__8748__8751__8754),Vvar__var__var__var__var__12__z__8703__8706__8749__8752__8755))),happ(happ(Vvar__3__radd__8642,happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__10__x__8701__8704__8747__8750__8753),Vvar__var__var__var__var__11__y__8702__8705__8748__8751__8754)),Vvar__var__var__var__var__12__z__8703__8706__8749__8752__8755))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__8708__8709__8756__8757__8758__8759] :
( t(Vvar__var__var__var__var__var__11__x__8708__8709__8756__8757__8758__8759,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__4__rmul__8647,Vvar__2__rI__8641),Vvar__var__var__var__var__var__11__x__8708__8709__8756__8757__8758__8759)),Vvar__var__var__var__var__var__11__x__8708__8709__8756__8757__8758__8759)) )
& ! [Vvar__var__var__var__var__12__x__8711__8713__8760__8762__8764] :
( t(Vvar__var__var__var__var__12__x__8711__8713__8760__8762__8764,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__13__y__8712__8714__8761__8763__8765] :
( t(Vvar__var__var__var__var__13__y__8712__8714__8761__8763__8765,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__12__x__8711__8713__8760__8762__8764),Vvar__var__var__var__var__13__y__8712__8714__8761__8763__8765)),happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__13__y__8712__8714__8761__8763__8765),Vvar__var__var__var__var__12__x__8711__8713__8760__8762__8764))) ) )
& ! [Vvar__var__var__var__var__13__x__8716__8719__8766__8769__8772] :
( t(Vvar__var__var__var__var__13__x__8716__8719__8766__8769__8772,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__14__y__8717__8720__8767__8770__8773] :
( t(Vvar__var__var__var__var__14__y__8717__8720__8767__8770__8773,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__15__z__8718__8721__8768__8771__8774] :
( t(Vvar__var__var__var__var__15__z__8718__8721__8768__8771__8774,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__13__x__8716__8719__8766__8769__8772),happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__14__y__8717__8720__8767__8770__8773),Vvar__var__var__var__var__15__z__8718__8721__8768__8771__8774))),happ(happ(Vvar__4__rmul__8647,happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__13__x__8716__8719__8766__8769__8772),Vvar__var__var__var__var__14__y__8717__8720__8767__8770__8773)),Vvar__var__var__var__var__15__z__8718__8721__8768__8771__8774))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__8723__8726__8775__8778__8781__8784] :
( t(Vvar__var__var__var__var__var__14__x__8723__8726__8775__8778__8781__8784,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__var__15__y__8724__8727__8776__8779__8782__8785] :
( t(Vvar__var__var__var__var__var__15__y__8724__8727__8776__8779__8782__8785,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__var__16__z__8725__8728__8777__8780__8783__8786] :
( t(Vvar__var__var__var__var__var__16__z__8725__8728__8777__8780__8783__8786,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__4__rmul__8647,happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__var__14__x__8723__8726__8775__8778__8781__8784),Vvar__var__var__var__var__var__15__y__8724__8727__8776__8779__8782__8785)),Vvar__var__var__var__var__var__16__z__8725__8728__8777__8780__8783__8786)),happ(happ(Vvar__3__radd__8642,happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__var__14__x__8723__8726__8775__8778__8781__8784),Vvar__var__var__var__var__var__16__z__8725__8728__8777__8780__8783__8786)),happ(happ(Vvar__4__rmul__8647,Vvar__var__var__var__var__var__15__y__8724__8727__8776__8779__8782__8785),Vvar__var__var__var__var__var__16__z__8725__8728__8777__8780__8783__8786)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__8730__8732__8787__8789__8791__8793__8795] :
( t(Vvar__var__var__var__var__var__var__15__x__8730__8732__8787__8789__8791__8793__8795,Vvar__0__R__8639)
=> ! [Vvar__var__var__var__var__var__var__16__y__8731__8733__8788__8790__8792__8794__8796] :
( t(Vvar__var__var__var__var__var__var__16__y__8731__8733__8788__8790__8792__8794__8796,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__5__rsub__8652,Vvar__var__var__var__var__var__var__15__x__8730__8732__8787__8789__8791__8793__8795),Vvar__var__var__var__var__var__var__16__y__8731__8733__8788__8790__8792__8794__8796)),happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__var__var__15__x__8730__8732__8787__8789__8791__8793__8795),happ(Vvar__6__ropp__8657,Vvar__var__var__var__var__var__var__16__y__8731__8733__8788__8790__8792__8794__8796)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__8735__8736__8797__8798__8799__8800__8801] :
( t(Vvar__var__var__var__var__var__var__16__x__8735__8736__8797__8798__8799__8800__8801,Vvar__0__R__8639)
=> p(happ(happ(Vvar__7__req__8660,happ(happ(Vvar__3__radd__8642,Vvar__var__var__var__var__var__var__16__x__8735__8736__8797__8798__8799__8800__8801),happ(Vvar__6__ropp__8657,Vvar__var__var__var__var__var__var__16__x__8735__8736__8797__8798__8799__8800__8801))),Vvar__1__rO__8640)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781] :
( cType___24t(Vvar__0__R__34745)
=> ( t(Vvar__1__rO__34746,Vvar__0__R__34745)
=> ( t(Vvar__2__rI__34747,Vvar__0__R__34745)
=> ( c_24__type__34998___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__3__radd__34748)
=> ( c_24__type__35123___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__4__rmul__34753)
=> ( c_24__type__35248___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__5__req__34758)
=> ( cType___24t(Vvar__6__C__34763)
=> ( t(Vvar__7__cO__34764,Vvar__6__C__34763)
=> ( t(Vvar__8__cI__34765,Vvar__6__C__34763)
=> ( c_24__type__35373___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__9__cadd__34766)
=> ( c_24__type__35498___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__10__cmul__34771)
=> ( c_24__type__35623___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__11__ceqb__34776)
=> ( c_24__type__35734___24t(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781,Vvar__12__phi__34781)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__34745,Vvar__1__rO__34746,Vvar__2__rI__34747,Vvar__3__radd__34748,Vvar__4__rmul__34753,Vvar__5__req__34758,Vvar__6__C__34763,Vvar__7__cO__34764,Vvar__8__cI__34765,Vvar__9__cadd__34766,Vvar__10__cmul__34771,Vvar__11__ceqb__34776,Vvar__12__phi__34781)
=> ( p(happ(happ(Vvar__5__req__34758,happ(Vvar__12__phi__34781,Vvar__7__cO__34764)),Vvar__1__rO__34746))
& p(happ(happ(Vvar__5__req__34758,happ(Vvar__12__phi__34781,Vvar__8__cI__34765)),Vvar__2__rI__34747))
& ! [Vvar__var__var__var__var__var__var__15__x__34827__34829__34843__34845__34847__34849__34851] :
( t(Vvar__var__var__var__var__var__var__15__x__34827__34829__34843__34845__34847__34849__34851,Vvar__6__C__34763)
=> ! [Vvar__var__var__var__var__var__var__16__y__34828__34830__34844__34846__34848__34850__34852] :
( t(Vvar__var__var__var__var__var__var__16__y__34828__34830__34844__34846__34848__34850__34852,Vvar__6__C__34763)
=> p(happ(happ(Vvar__5__req__34758,happ(Vvar__12__phi__34781,happ(happ(Vvar__9__cadd__34766,Vvar__var__var__var__var__var__var__15__x__34827__34829__34843__34845__34847__34849__34851),Vvar__var__var__var__var__var__var__16__y__34828__34830__34844__34846__34848__34850__34852))),happ(happ(Vvar__3__radd__34748,happ(Vvar__12__phi__34781,Vvar__var__var__var__var__var__var__15__x__34827__34829__34843__34845__34847__34849__34851)),happ(Vvar__12__phi__34781,Vvar__var__var__var__var__var__var__16__y__34828__34830__34844__34846__34848__34850__34852)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__34832__34834__34853__34855__34857__34859__34861] :
( t(Vvar__var__var__var__var__var__var__16__x__34832__34834__34853__34855__34857__34859__34861,Vvar__6__C__34763)
=> ! [Vvar__var__var__var__var__var__var__17__y__34833__34835__34854__34856__34858__34860__34862] :
( t(Vvar__var__var__var__var__var__var__17__y__34833__34835__34854__34856__34858__34860__34862,Vvar__6__C__34763)
=> p(happ(happ(Vvar__5__req__34758,happ(Vvar__12__phi__34781,happ(happ(Vvar__10__cmul__34771,Vvar__var__var__var__var__var__var__16__x__34832__34834__34853__34855__34857__34859__34861),Vvar__var__var__var__var__var__var__17__y__34833__34835__34854__34856__34858__34860__34862))),happ(happ(Vvar__4__rmul__34753,happ(Vvar__12__phi__34781,Vvar__var__var__var__var__var__var__16__x__34832__34834__34853__34855__34857__34859__34861)),happ(Vvar__12__phi__34781,Vvar__var__var__var__var__var__var__17__y__34833__34835__34854__34856__34858__34860__34862)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__34837__34840__34863__34866__34869__34872] :
( t(Vvar__var__var__var__var__var__17__x__34837__34840__34863__34866__34869__34872,Vvar__6__C__34763)
=> ! [Vvar__var__var__var__var__var__18__y__34838__34841__34864__34867__34870__34873] :
( t(Vvar__var__var__var__var__var__18__y__34838__34841__34864__34867__34870__34873,Vvar__6__C__34763)
=> ( happ(happ(Vvar__11__ceqb__34776,Vvar__var__var__var__var__var__17__x__34837__34840__34863__34866__34869__34872),Vvar__var__var__var__var__var__18__y__34838__34841__34864__34867__34870__34873) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__34758,happ(Vvar__12__phi__34781,Vvar__var__var__var__var__var__17__x__34837__34840__34863__34866__34869__34872)),happ(Vvar__12__phi__34781,Vvar__var__var__var__var__var__18__y__34838__34841__34864__34867__34870__34873))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__34207,Vvar__1__rO__34208,Vvar__2__rI__34209,Vvar__3__radd__34210,Vvar__4__rmul__34215,Vvar__5__req__34220] :
( cType___24t(Vvar__0__R__34207)
=> ( t(Vvar__1__rO__34208,Vvar__0__R__34207)
=> ( t(Vvar__2__rI__34209,Vvar__0__R__34207)
=> ( c_24__type__34375___24t(Vvar__0__R__34207,Vvar__1__rO__34208,Vvar__2__rI__34209,Vvar__3__radd__34210,Vvar__4__rmul__34215,Vvar__5__req__34220,Vvar__3__radd__34210)
=> ( c_24__type__34414___24t(Vvar__0__R__34207,Vvar__1__rO__34208,Vvar__2__rI__34209,Vvar__3__radd__34210,Vvar__4__rmul__34215,Vvar__5__req__34220,Vvar__4__rmul__34215)
=> ( c_24__type__34453___24t(Vvar__0__R__34207,Vvar__1__rO__34208,Vvar__2__rI__34209,Vvar__3__radd__34210,Vvar__4__rmul__34215,Vvar__5__req__34220,Vvar__5__req__34220)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__34207,Vvar__1__rO__34208,Vvar__2__rI__34209,Vvar__3__radd__34210,Vvar__4__rmul__34215,Vvar__5__req__34220)
=> ( ! [Vvar__var__var__var__var__var__6__n__34245__34246__34284__34285__34286__34287] :
( t(Vvar__var__var__var__var__var__6__n__34245__34246__34284__34285__34286__34287,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__3__radd__34210,Vvar__1__rO__34208),Vvar__var__var__var__var__var__6__n__34245__34246__34284__34285__34286__34287)),Vvar__var__var__var__var__var__6__n__34245__34246__34284__34285__34286__34287)) )
& ! [Vvar__var__var__var__var__7__n__34248__34250__34288__34290__34292] :
( t(Vvar__var__var__var__var__7__n__34248__34250__34288__34290__34292,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__8__m__34249__34251__34289__34291__34293] :
( t(Vvar__var__var__var__var__8__m__34249__34251__34289__34291__34293,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__3__radd__34210,Vvar__var__var__var__var__7__n__34248__34250__34288__34290__34292),Vvar__var__var__var__var__8__m__34249__34251__34289__34291__34293)),happ(happ(Vvar__3__radd__34210,Vvar__var__var__var__var__8__m__34249__34251__34289__34291__34293),Vvar__var__var__var__var__7__n__34248__34250__34288__34290__34292))) ) )
& ! [Vvar__var__var__var__var__8__n__34253__34256__34294__34297__34300] :
( t(Vvar__var__var__var__var__8__n__34253__34256__34294__34297__34300,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__9__m__34254__34257__34295__34298__34301] :
( t(Vvar__var__var__var__var__9__m__34254__34257__34295__34298__34301,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__10__p__34255__34258__34296__34299__34302] :
( t(Vvar__var__var__var__var__10__p__34255__34258__34296__34299__34302,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__3__radd__34210,Vvar__var__var__var__var__8__n__34253__34256__34294__34297__34300),happ(happ(Vvar__3__radd__34210,Vvar__var__var__var__var__9__m__34254__34257__34295__34298__34301),Vvar__var__var__var__var__10__p__34255__34258__34296__34299__34302))),happ(happ(Vvar__3__radd__34210,happ(happ(Vvar__3__radd__34210,Vvar__var__var__var__var__8__n__34253__34256__34294__34297__34300),Vvar__var__var__var__var__9__m__34254__34257__34295__34298__34301)),Vvar__var__var__var__var__10__p__34255__34258__34296__34299__34302))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__34260__34261__34303__34304__34305__34306] :
( t(Vvar__var__var__var__var__var__9__n__34260__34261__34303__34304__34305__34306,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__4__rmul__34215,Vvar__2__rI__34209),Vvar__var__var__var__var__var__9__n__34260__34261__34303__34304__34305__34306)),Vvar__var__var__var__var__var__9__n__34260__34261__34303__34304__34305__34306)) )
& ! [Vvar__var__var__var__var__var__10__n__34263__34264__34307__34308__34309__34310] :
( t(Vvar__var__var__var__var__var__10__n__34263__34264__34307__34308__34309__34310,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__4__rmul__34215,Vvar__1__rO__34208),Vvar__var__var__var__var__var__10__n__34263__34264__34307__34308__34309__34310)),Vvar__1__rO__34208)) )
& ! [Vvar__var__var__var__var__11__n__34266__34268__34311__34313__34315] :
( t(Vvar__var__var__var__var__11__n__34266__34268__34311__34313__34315,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__12__m__34267__34269__34312__34314__34316] :
( t(Vvar__var__var__var__var__12__m__34267__34269__34312__34314__34316,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__11__n__34266__34268__34311__34313__34315),Vvar__var__var__var__var__12__m__34267__34269__34312__34314__34316)),happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__12__m__34267__34269__34312__34314__34316),Vvar__var__var__var__var__11__n__34266__34268__34311__34313__34315))) ) )
& ! [Vvar__var__var__var__var__12__n__34271__34274__34317__34320__34323] :
( t(Vvar__var__var__var__var__12__n__34271__34274__34317__34320__34323,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__13__m__34272__34275__34318__34321__34324] :
( t(Vvar__var__var__var__var__13__m__34272__34275__34318__34321__34324,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__14__p__34273__34276__34319__34322__34325] :
( t(Vvar__var__var__var__var__14__p__34273__34276__34319__34322__34325,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__12__n__34271__34274__34317__34320__34323),happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__13__m__34272__34275__34318__34321__34324),Vvar__var__var__var__var__14__p__34273__34276__34319__34322__34325))),happ(happ(Vvar__4__rmul__34215,happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__12__n__34271__34274__34317__34320__34323),Vvar__var__var__var__var__13__m__34272__34275__34318__34321__34324)),Vvar__var__var__var__var__14__p__34273__34276__34319__34322__34325))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__34278__34281__34326__34329__34332__34335] :
( t(Vvar__var__var__var__var__var__13__n__34278__34281__34326__34329__34332__34335,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__var__14__m__34279__34282__34327__34330__34333__34336] :
( t(Vvar__var__var__var__var__var__14__m__34279__34282__34327__34330__34333__34336,Vvar__0__R__34207)
=> ! [Vvar__var__var__var__var__var__15__p__34280__34283__34328__34331__34334__34337] :
( t(Vvar__var__var__var__var__var__15__p__34280__34283__34328__34331__34334__34337,Vvar__0__R__34207)
=> p(happ(happ(Vvar__5__req__34220,happ(happ(Vvar__4__rmul__34215,happ(happ(Vvar__3__radd__34210,Vvar__var__var__var__var__var__13__n__34278__34281__34326__34329__34332__34335),Vvar__var__var__var__var__var__14__m__34279__34282__34327__34330__34333__34336)),Vvar__var__var__var__var__var__15__p__34280__34283__34328__34331__34334__34337)),happ(happ(Vvar__3__radd__34210,happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__var__13__n__34278__34281__34326__34329__34332__34335),Vvar__var__var__var__var__var__15__p__34280__34283__34328__34331__34334__34337)),happ(happ(Vvar__4__rmul__34215,Vvar__var__var__var__var__var__14__m__34279__34282__34327__34330__34333__34336),Vvar__var__var__var__var__var__15__p__34280__34283__34328__34331__34334__34337)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534] :
( cType___24t(Vvar__0__R__34523)
=> ( c_24__type__34609___24t(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534,Vvar__1__radd__34524)
=> ( c_24__type__34632___24t(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534,Vvar__2__rmul__34529)
=> ( c_24__type__34655___24t(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534,Vvar__3__req__34534)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34678___24a4(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__34523,c_24__type__34696___24a4(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534),Vvar__3__req__34534,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__34523,Vvar__0__R__34523,Vvar__3__req__34534,Vvar__3__req__34534)),Vvar__1__radd__34524)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34722___24a4(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__34523,c_24__type__34740___24a4(Vvar__0__R__34523,Vvar__1__radd__34524,Vvar__2__rmul__34529,Vvar__3__req__34534),Vvar__3__req__34534,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__34523,Vvar__0__R__34523,Vvar__3__req__34534,Vvar__3__req__34534)),Vvar__2__rmul__34529)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX27802] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX27802)
=> ( VX27802 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX27802 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_Topology.TopologicalSpaces.TopologicalSpace',axiom,
! [VX122] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(VX122)
=> ? [Vvar__0__point__set__123] :
( cType___24t(Vvar__0__point__set__123)
& ? [Vvar__1__open__124] :
( c_24__type__147___24t(Vvar__0__point__set__123,Vvar__1__open__124)
& ! [Vvar__var__2__F__128__132] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__point__set__123,Vvar__var__2__F__128__132)
=> ( ! [Vvar__var__3__S__129__133] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__123,Vvar__var__3__S__129__133)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__point__set__123),Vvar__var__2__F__128__132,Vvar__var__3__S__129__133)
=> p(happ(Vvar__1__open__124,Vvar__var__3__S__129__133)) ) )
=> p(happ(Vvar__1__open__124,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vvar__0__point__set__123,Vvar__var__2__F__128__132))) ) )
& ! [Vvar__var__3__U__137__141] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__123,Vvar__var__3__U__137__141)
=> ! [Vvar__var__4__V__138__142] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__point__set__123,Vvar__var__4__V__138__142)
=> ( p(happ(Vvar__1__open__124,Vvar__var__3__U__137__141))
=> ( p(happ(Vvar__1__open__124,Vvar__var__4__V__138__142))
=> p(happ(Vvar__1__open__124,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__point__set__123,Vvar__var__3__U__137__141,Vvar__var__4__V__138__142))) ) ) ) )
& p(happ(Vvar__1__open__124,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vvar__0__point__set__123)))
& VX122 = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(Vvar__0__point__set__123,Vvar__1__open__124) ) ) ) ).
fof('$_inversion_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction',axiom,
! [Vvar__0__X__331,Vvar__1__P__332,Vvar__2__x__335] :
( cType___24t(Vvar__0__X__331)
=> ( c_24__type__347___24t(Vvar__0__X__331,Vvar__1__P__332,Vvar__2__x__335,Vvar__1__P__332)
=> ( t(Vvar__2__x__335,Vvar__0__X__331)
=> ( cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(Vvar__0__X__331,Vvar__1__P__332,Vvar__2__x__335)
=> ( p(happ(Vvar__1__P__332,Vvar__2__x__335))
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyIntersection',axiom,
! [Vvar__0__T__355,Vvar__1__F__356,Vvar__1___24Anonymous__357] :
( cType___24t(Vvar__0__T__355)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__355,Vvar__1__F__356)
=> ( t(Vvar__1___24Anonymous__357,Vvar__0__T__355)
=> ( cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(Vvar__0__T__355,Vvar__1__F__356,Vvar__1___24Anonymous__357)
=> ? [Vvar__2__x__361] :
( t(Vvar__2__x__361,Vvar__0__T__355)
& ! [Vvar__var__var__var__3__S__363__365__367__369] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__355,Vvar__var__var__var__3__S__363__365__367__369)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__355),Vvar__1__F__356,Vvar__var__var__var__3__S__363__365__367__369)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__355,Vvar__var__var__var__3__S__363__365__367__369,Vvar__2__x__361) ) )
& Vvar__1___24Anonymous__357 = Vvar__2__x__361 ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyUnion',axiom,
! [Vvar__0__T__61,Vvar__1__F__62,Vvar__1___24Anonymous__63] :
( cType___24t(Vvar__0__T__61)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__61,Vvar__1__F__62)
=> ( t(Vvar__1___24Anonymous__63,Vvar__0__T__61)
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a3(Vvar__0__T__61,Vvar__1__F__62,Vvar__1___24Anonymous__63)
=> ? [Vvar__2__S__67] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__61,Vvar__2__S__67)
& ? [Vvar__3__x__68] :
( t(Vvar__3__x__68,Vvar__0__T__61)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__61),Vvar__1__F__62,Vvar__2__S__67)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__61,Vvar__2__S__67,Vvar__3__x__68)
& Vvar__1___24Anonymous__63 = Vvar__3__x__68 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.FiniteTypes.FiniteT',axiom,
! [Vvar__0___24Anonymous__375] :
( cType___24t(Vvar__0___24Anonymous__375)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__0___24Anonymous__375)
=> ( Vvar__0___24Anonymous__375 = c_24False
| ? [Vvar__0__T__377] :
( cType___24t(Vvar__0__T__377)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__0__T__377)
& Vvar__0___24Anonymous__375 = cCoq_2eInit_2eDatatypes_2eoption___24a1(Vvar__0__T__377) )
| ? [Vvar__0__X__379] :
( cType___24t(Vvar__0__X__379)
& ? [Vvar__1__Y__380] :
( cType___24t(Vvar__1__Y__380)
& ? [Vvar__2__f__381] :
( c_24__type__389___24t(Vvar__0___24Anonymous__375,Vvar__0__X__379,Vvar__1__Y__380,Vvar__2__f__381)
& cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(Vvar__0__X__379)
& cZornsLemma_2eFunctionProperties_2einvertible___24a3(Vvar__0__X__379,Vvar__1__Y__380,Vvar__2__f__381)
& Vvar__0___24Anonymous__375 = Vvar__1__Y__380 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.FunctionProperties.invertible',axiom,
! [Vvar__0__X__407,Vvar__1__Y__408,Vvar__2__f__409] :
( cType___24t(Vvar__0__X__407)
=> ( cType___24t(Vvar__1__Y__408)
=> ( c_24__type__438___24t(Vvar__0__X__407,Vvar__1__Y__408,Vvar__2__f__409,Vvar__2__f__409)
=> ( cZornsLemma_2eFunctionProperties_2einvertible___24a3(Vvar__0__X__407,Vvar__1__Y__408,Vvar__2__f__409)
=> ? [Vvar__3__g__418] :
( c_24__type__445___24t(Vvar__0__X__407,Vvar__1__Y__408,Vvar__2__f__409,Vvar__3__g__418)
& ! [Vvar__var__var__var__4__x__422__423__429__430] :
( t(Vvar__var__var__var__4__x__422__423__429__430,Vvar__0__X__407)
=> happ(Vvar__3__g__418,happ(Vvar__2__f__409,Vvar__var__var__var__4__x__422__423__429__430)) = Vvar__var__var__var__4__x__422__423__429__430 )
& ! [Vvar__var__var__var__5__y__425__426__431__432] :
( t(Vvar__var__var__var__5__y__425__426__431__432,Vvar__1__Y__408)
=> happ(Vvar__2__f__409,happ(Vvar__3__g__418,Vvar__var__var__var__5__y__425__426__431__432)) = Vvar__var__var__var__5__y__425__426__431__432 )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.IndexedFamilies.IndexedIntersection',axiom,
! [Vvar__0__A__449,Vvar__1__T__450,Vvar__2__F__451,Vvar__1___24Anonymous__452] :
( cType___24t(Vvar__0__A__449)
=> ( cType___24t(Vvar__1__T__450)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vvar__0__A__449,Vvar__1__T__450,Vvar__2__F__451)
=> ( t(Vvar__1___24Anonymous__452,Vvar__1__T__450)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a4(Vvar__0__A__449,Vvar__1__T__450,Vvar__2__F__451,Vvar__1___24Anonymous__452)
=> ? [Vvar__3__x__457] :
( t(Vvar__3__x__457,Vvar__1__T__450)
& ! [Vvar__var__var__var__var__4__a__459__460__461__462__463] :
( t(Vvar__var__var__var__var__4__a__459__460__461__462__463,Vvar__0__A__449)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__1__T__450,happ(Vvar__2__F__451,Vvar__var__var__var__var__4__a__459__460__461__462__463),Vvar__3__x__457) )
& Vvar__1___24Anonymous__452 = Vvar__3__x__457 ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.IndexedFamilies.IndexedUnion',axiom,
! [Vvar__0__A__106,Vvar__1__T__107,Vvar__2__F__108,Vvar__1___24Anonymous__109] :
( cType___24t(Vvar__0__A__106)
=> ( cType___24t(Vvar__1__T__107)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vvar__0__A__106,Vvar__1__T__107,Vvar__2__F__108)
=> ( t(Vvar__1___24Anonymous__109,Vvar__1__T__107)
=> ( cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a4(Vvar__0__A__106,Vvar__1__T__107,Vvar__2__F__108,Vvar__1___24Anonymous__109)
=> ? [Vvar__3__a__114] :
( t(Vvar__3__a__114,Vvar__0__A__106)
& ? [Vvar__4__x__115] :
( t(Vvar__4__x__115,Vvar__1__T__107)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__1__T__107,happ(Vvar__2__F__108,Vvar__3__a__114),Vvar__4__x__115)
& Vvar__1___24Anonymous__109 = Vvar__4__x__115 ) ) ) ) ) ) ) ).
fof('$_lam_150748',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__150748___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1,Vv__CANONICAL__2) ) ) ).
fof('$_lam_150754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__150754___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__1) ) ) ).
fof('$_lam_157541',axiom,
! [Vv__CANONICAL__0] : c_24__lam__157541___24a1(Vv__CANONICAL__0) = cInteriorsClosures_2eclosure___24a2(cX,cInteriorsClosures_2einterior___24a2(cX,Vv__CANONICAL__0)) ).
fof('$_lam_157542',axiom,
! [Vv__CANONICAL__0] : c_24__lam__157542___24a1(Vv__CANONICAL__0) = cInteriorsClosures_2einterior___24a2(cX,cInteriorsClosures_2eclosure___24a2(cX,Vv__CANONICAL__0)) ).
fof('$_lam_23691',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__23691___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_26531',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__26531___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_26539',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__26539___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_37398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__37398___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_4708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__4708___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_prop_37348',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__S__37326,Vvar__1__x__37327,Vvar__2__y__37328] :
( p(c_24__prop__37348___24a4(Vvar__0___24Anonymous__37324,Vvar__0__S__37326,Vvar__1__x__37327,Vvar__2__y__37328))
<=> Vvar__1__x__37327 = Vvar__2__y__37328 ) ).
fof('$_prop_37349',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__x__37329,Vvar__1__y__37330] :
( p(c_24__prop__37349___24a3(Vvar__0___24Anonymous__37324,Vvar__0__x__37329,Vvar__1__y__37330))
<=> Vvar__0__x__37329 = Vvar__1__y__37330 ) ).
fof('$_prop_37350',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__x__37331,Vvar__1__s__37332] :
( p(c_24__prop__37350___24a3(Vvar__0___24Anonymous__37324,Vvar__0__x__37331,Vvar__1__s__37332))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__37331,Vvar__1__s__37332) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_37351',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__P__37333,Vvar__1__Q__37334] :
( p(c_24__prop__37351___24a3(Vvar__0___24Anonymous__37324,Vvar__0__P__37333,Vvar__1__Q__37334))
<=> ( p(Vvar__0__P__37333)
& p(Vvar__1__Q__37334) ) ) ).
fof('$_prop_37352',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__P__37337,Vvar__1__Q__37338] :
( p(c_24__prop__37352___24a3(Vvar__0___24Anonymous__37324,Vvar__0__P__37337,Vvar__1__Q__37338))
<=> ( p(Vvar__0__P__37337)
| p(Vvar__1__Q__37338) ) ) ).
fof('$_prop_37353',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__P__37341,Vvar__1__Q__37342] :
( p(c_24__prop__37353___24a3(Vvar__0___24Anonymous__37324,Vvar__0__P__37341,Vvar__1__Q__37342))
<=> ( p(Vvar__0__P__37341)
=> p(Vvar__1__Q__37342) ) ) ).
fof('$_prop_37354',axiom,
! [Vvar__0___24Anonymous__37324,Vvar__0__P__37346] :
( p(c_24__prop__37354___24a2(Vvar__0___24Anonymous__37324,Vvar__0__P__37346))
<=> ~ p(Vvar__0__P__37346) ) ).
fof('$_prop_37368',axiom,
! [Vvar__0___24Anonymous__37355,Vvar__0__s__37359] :
( p(c_24__prop__37368___24a2(Vvar__0___24Anonymous__37355,Vvar__0__s__37359))
<=> ! [Vvar__1__a__37360] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__37360)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__37360,Vvar__0__s__37359) ) ) ).
fof('$_prop_37369',axiom,
! [Vvar__0___24Anonymous__37355,Vvar__0__s1__37361,Vvar__1__s2__37362] :
( p(c_24__prop__37369___24a3(Vvar__0___24Anonymous__37355,Vvar__0__s1__37361,Vvar__1__s2__37362))
<=> ! [Vvar__2__a__37363] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__37363)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__37363,Vvar__0__s1__37361)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__37363,Vvar__1__s2__37362) ) ) ) ).
fof('$_prop_37370',axiom,
! [Vvar__0___24Anonymous__37355,Vvar__0__s1__37365,Vvar__1__s2__37366] :
( p(c_24__prop__37370___24a3(Vvar__0___24Anonymous__37355,Vvar__0__s1__37365,Vvar__1__s2__37366))
<=> ! [Vvar__2__a__37367] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__37367)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__37367,Vvar__0__s1__37365)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__37367,Vvar__1__s2__37366) ) ) ) ).
fof('$_type_10096',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__10097] :
( c_24__type__10096___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__10097)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10097,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__102] :
( c_24__type__101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__102)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,happ(Vvar__102,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10309',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__10310] :
( c_24__type__10309___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__10310)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__10310,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1036',axiom,
! [Vvar__1037] :
( c_24__type__1036___24t(Vvar__1037)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1037,Vv__CANONICAL__0)) ) ) ).
fof('$_type_104',axiom,
! [Vvar__105] :
( c_24__type__104___24t(Vvar__105)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__105,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10504',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__10505] :
( c_24__type__10504___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__10505)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__10505,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_1052',axiom,
! [Vvar__1053] :
( c_24__type__1052___24t(Vvar__1053)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1053,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1057',axiom,
! [Vvar__1058] :
( c_24__type__1057___24t(Vvar__1058)
<=> ! [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)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1058,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__10718] :
( c_24__type__10717___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__10718)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__10718,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_10930',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__10931] :
( c_24__type__10930___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__10931)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__10931,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_11143',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__11144] :
( c_24__type__11143___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__11144)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__11144,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_1124',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1125] :
( c_24__type__1124___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1125)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__1125,Vv__CANONICAL__2)) ) ) ).
fof('$_type_11356',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__11357] :
( c_24__type__11356___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__11357)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__11357,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_11551',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__11552] :
( c_24__type__11551___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__11552)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__11552,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_1165',axiom,
! [Vvar__1166] :
( c_24__type__1165___24t(Vvar__1166)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__1166,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11764',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__11765] :
( c_24__type__11764___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__11765)
<=> ! [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__11765,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_1180',axiom,
! [Vvar__1181] :
( c_24__type__1180___24t(Vvar__1181)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__1181,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1183',axiom,
! [Vvar__1184] :
( c_24__type__1183___24t(Vvar__1184)
<=> ! [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__1184,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1189',axiom,
! [Vv__CANONICAL__0,Vvar__1190] :
( c_24__type__1189___24t(Vv__CANONICAL__0,Vvar__1190)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1190,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11959',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__11960] :
( c_24__type__11959___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__11960)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__11960,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_120',axiom,
! [Vvar__121] :
( c_24__type__120___24t(Vvar__121)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(Vv__CANONICAL__1,Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__121,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12093',axiom,
! [Vvar__12094] :
( c_24__type__12093___24t(Vvar__12094)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12094,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12235] :
( c_24__type__12234___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12235)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12235,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_12275',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12276] :
( c_24__type__12275___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12276)
<=> ! [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__12276,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_12318',axiom,
! [Vvar__12319] :
( c_24__type__12318___24t(Vvar__12319)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1189___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__12328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__12319,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1232',axiom,
! [Vvar__1233] :
( c_24__type__1232___24t(Vvar__1233)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__147___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ! [Vv__CANONICAL__2] :
( cZornsLemma_2eFamilies_2eFamily___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2,Vv__CANONICAL__3)
=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ) )
=> p(happ(Vv__CANONICAL__1,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2))) ) )
=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__4))
=> p(happ(Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) )
=> ( p(happ(Vv__CANONICAL__1,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(Vv__CANONICAL__0)))
=> cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(happ(happ(Vvar__1233,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ) ).
fof('$_type_12328',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12329] :
( c_24__type__12328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12329)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__12329,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_12338',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12339] :
( c_24__type__12338___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12339)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12339,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_12445',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12446] :
( c_24__type__12445___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12446)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12446,Vv__CANONICAL__2)) ) ) ).
fof('$_type_12449',axiom,
! [Vvar__12450] :
( c_24__type__12449___24t(Vvar__12450)
<=> ! [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__12450,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12467',axiom,
! [Vvar__12468] :
( c_24__type__12467___24t(Vvar__12468)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__12468,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_12494',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12495] :
( c_24__type__12494___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12495)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12495,Vv__CANONICAL__3)) ) ) ).
fof('$_type_12502',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12503] :
( c_24__type__12502___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12503)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12503,Vv__CANONICAL__3)) ) ) ).
fof('$_type_12510',axiom,
! [Vvar__12511] :
( c_24__type__12510___24t(Vvar__12511)
<=> ! [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__12511,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12540',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12541] :
( c_24__type__12540___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12541)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__12541,Vv__CANONICAL__2)) ) ) ).
fof('$_type_12544',axiom,
! [Vvar__12545] :
( c_24__type__12544___24t(Vvar__12545)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__12545,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12547',axiom,
! [Vv__CANONICAL__0,Vvar__12548] :
( c_24__type__12547___24t(Vv__CANONICAL__0,Vvar__12548)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__12548,Vv__CANONICAL__1)) ) ) ).
fof('$_type_12571',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12572] :
( c_24__type__12571___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__12572)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12572,Vv__CANONICAL__2)) ) ) ).
fof('$_type_12577',axiom,
! [Vvar__12578] :
( c_24__type__12577___24t(Vvar__12578)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__12578,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_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('$_type_147',axiom,
! [Vv__CANONICAL__0,Vvar__148] :
( c_24__type__147___24t(Vv__CANONICAL__0,Vvar__148)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__148,Vv__CANONICAL__1)) ) ) ).
fof('$_type_150750',axiom,
! [Vvar__150751] :
( c_24__type__150750___24t(Vvar__150751)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),happ(happ(Vvar__150751,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_150887',axiom,
! [Vvar__150888] :
( c_24__type__150887___24t(Vvar__150888)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4737___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__150888,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_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('$_type_20118',axiom,
! [Vvar__20119] :
( c_24__type__20118___24t(Vvar__20119)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__20119,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20141',axiom,
! [Vvar__20142] :
( c_24__type__20141___24t(Vvar__20142)
<=> ! [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__20142,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_20146',axiom,
! [Vvar__20147] :
( c_24__type__20146___24t(Vvar__20147)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__20147,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_20311',axiom,
! [Vvar__20312] :
( c_24__type__20311___24t(Vvar__20312)
<=> ! [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__20312,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21705',axiom,
! [Vvar__21706] :
( c_24__type__21705___24t(Vvar__21706)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__21706,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22239',axiom,
! [Vvar__22240] :
( c_24__type__22239___24t(Vvar__22240)
<=> ! [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__22240,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22242',axiom,
! [Vvar__22243] :
( c_24__type__22242___24t(Vvar__22243)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22243,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22305',axiom,
! [Vvar__22306] :
( c_24__type__22305___24t(Vvar__22306)
<=> ! [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__22306,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22309',axiom,
! [Vvar__22310] :
( c_24__type__22309___24t(Vvar__22310)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__22310,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22318',axiom,
! [Vvar__22319] :
( c_24__type__22318___24t(Vvar__22319)
<=> ! [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__22319,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22419',axiom,
! [Vvar__22420] :
( c_24__type__22419___24t(Vvar__22420)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__22420,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22425',axiom,
! [Vvar__22426] :
( c_24__type__22425___24t(Vvar__22426)
<=> ! [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__22426,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22468',axiom,
! [Vvar__22469] :
( c_24__type__22468___24t(Vvar__22469)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__22469,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22511',axiom,
! [Vvar__22512] :
( c_24__type__22511___24t(Vvar__22512)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__22512,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22553',axiom,
! [Vvar__22554] :
( c_24__type__22553___24t(Vvar__22554)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__22554,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22558',axiom,
! [Vvar__22559] :
( c_24__type__22558___24t(Vvar__22559)
<=> ! [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__22559,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22916',axiom,
! [Vvar__22917] :
( c_24__type__22916___24t(Vvar__22917)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__22917,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23012',axiom,
! [Vvar__23013] :
( c_24__type__23012___24t(Vvar__23013)
<=> ! [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__23013,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23015',axiom,
! [Vvar__23016] :
( c_24__type__23015___24t(Vvar__23016)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__23016,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23050',axiom,
! [Vvar__23051] :
( c_24__type__23050___24t(Vvar__23051)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23051,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23093',axiom,
! [Vvar__23094] :
( c_24__type__23093___24t(Vvar__23094)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__23094,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23096',axiom,
! [Vvar__23097] :
( c_24__type__23096___24t(Vvar__23097)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23097,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23099',axiom,
! [Vvar__23100] :
( c_24__type__23099___24t(Vvar__23100)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__23100,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23103',axiom,
! [Vvar__23104] :
( c_24__type__23103___24t(Vvar__23104)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__23104,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23281',axiom,
! [Vvar__23282] :
( c_24__type__23281___24t(Vvar__23282)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__23282,Vv__CANONICAL__0)) ) ) ).
fof('$_type_234',axiom,
! [Vvar__235] :
( c_24__type__234___24t(Vvar__235)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__235,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23447',axiom,
! [Vvar__23448] :
( c_24__type__23447___24t(Vvar__23448)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__23448,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_23466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23467] :
( c_24__type__23466___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23467)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__23467,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23488] :
( c_24__type__23487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__23488)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__23488,Vv__CANONICAL__3)) ) ) ).
fof('$_type_23522',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23523] :
( c_24__type__23522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23523)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__23523,Vv__CANONICAL__5)) ) ) ).
fof('$_type_23530',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23531] :
( c_24__type__23530___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23531)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__23531,Vv__CANONICAL__5)) ) ) ).
fof('$_type_23533',axiom,
! [Vvar__23534] :
( c_24__type__23533___24t(Vvar__23534)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23534,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23538',axiom,
! [Vvar__23539] :
( c_24__type__23538___24t(Vvar__23539)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__23539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23548',axiom,
! [Vvar__23549] :
( c_24__type__23548___24t(Vvar__23549)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__23549,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23562',axiom,
! [Vvar__23563] :
( c_24__type__23562___24t(Vvar__23563)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__23563,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23576',axiom,
! [Vvar__23577] :
( c_24__type__23576___24t(Vvar__23577)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__23577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23589',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23590] :
( c_24__type__23589___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23590)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(Vvar__23590,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_23596',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23597] :
( c_24__type__23596___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__23597)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__23597,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_23600',axiom,
! [Vvar__23601] :
( c_24__type__23600___24t(Vvar__23601)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23601,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23606',axiom,
! [Vv__CANONICAL__0,Vvar__23607] :
( c_24__type__23606___24t(Vv__CANONICAL__0,Vvar__23607)
<=> ! [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__23607,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_23611',axiom,
! [Vv__CANONICAL__0,Vvar__23612] :
( c_24__type__23611___24t(Vv__CANONICAL__0,Vvar__23612)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__23612,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_23684',axiom,
! [Vv__CANONICAL__0,Vvar__23685] :
( c_24__type__23684___24t(Vv__CANONICAL__0,Vvar__23685)
<=> ! [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,c_24__lam__23691___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__23685,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23753',axiom,
! [Vvar__23754] :
( c_24__type__23753___24t(Vvar__23754)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__4323___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__23754,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23823',axiom,
! [Vvar__23824] :
( c_24__type__23823___24t(Vvar__23824)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__23824,Vv__CANONICAL__0)) ) ) ).
fof('$_type_23848',axiom,
! [Vvar__23849] :
( c_24__type__23848___24t(Vvar__23849)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__23849,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_23905',axiom,
! [Vvar__23906] :
( c_24__type__23905___24t(Vvar__23906)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__23906,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24119',axiom,
! [Vvar__24120] :
( c_24__type__24119___24t(Vvar__24120)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24169',axiom,
! [Vvar__24170] :
( c_24__type__24169___24t(Vvar__24170)
<=> ! [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__24170,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24201] :
( c_24__type__24200___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24201)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24201,Vv__CANONICAL__6)) ) ) ).
fof('$_type_24228',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24229] :
( c_24__type__24228___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__24229)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24229,Vv__CANONICAL__6)) ) ) ).
fof('$_type_24432',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24433] :
( c_24__type__24432___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24433)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24433,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24525',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__24526] :
( c_24__type__24525___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__24526)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24526,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24618',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24619] :
( c_24__type__24618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24619)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24619,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24700',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__24701] :
( c_24__type__24700___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__24701)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__24701,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_24793',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24794] :
( c_24__type__24793___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24794)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24794,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24875',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__24876] :
( c_24__type__24875___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__24876)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__24876,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_24968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24969] :
( c_24__type__24968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__24969)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24969,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_25302',axiom,
! [Vvar__25303] :
( c_24__type__25302___24t(Vvar__25303)
<=> ! [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__25303,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25305',axiom,
! [Vvar__25306] :
( c_24__type__25305___24t(Vvar__25306)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__25306,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25529',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__25530] :
( c_24__type__25529___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__25530)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25530,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25622',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__25623] :
( c_24__type__25622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__25623)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25623,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25715',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__25716] :
( c_24__type__25715___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__25716)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25716,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25797',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__25798] :
( c_24__type__25797___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__25798)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__25798,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_25890',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__25891] :
( c_24__type__25890___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__25891)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25891,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__25973] :
( c_24__type__25972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__25973)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__25973,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_26065',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__26066] :
( c_24__type__26065___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__26066)
<=> ! [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__26066,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_26219',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26220] :
( c_24__type__26219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26220)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26220,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26282',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__26283] :
( c_24__type__26282___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__26283)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26283,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26345',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26346] :
( c_24__type__26345___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26346)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26346,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26399',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__26400] :
( c_24__type__26399___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__26400)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__26400,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_26462',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26463] :
( c_24__type__26462___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__26463)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26463,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_26495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26496] :
( c_24__type__26495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26496)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__26496,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26501] :
( c_24__type__26500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26501)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__26501,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26506',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26507] :
( c_24__type__26506___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26507)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__26507,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26511',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26512] :
( c_24__type__26511___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26512)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__26512,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26523',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26524] :
( c_24__type__26523___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26524)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__26524,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26543',axiom,
! [Vv__CANONICAL__0,Vvar__26544] :
( c_24__type__26543___24t(Vv__CANONICAL__0,Vvar__26544)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__26544,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_26554',axiom,
! [Vvar__26555] :
( c_24__type__26554___24t(Vvar__26555)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__26543___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__26555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_26596',axiom,
! [Vvar__26597] :
( c_24__type__26596___24t(Vvar__26597)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__26597,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_26648',axiom,
! [Vvar__26649] :
( c_24__type__26648___24t(Vvar__26649)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(happ(happ(Vvar__26649,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26659',axiom,
! [Vvar__26660] :
( c_24__type__26659___24t(Vvar__26660)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__26660,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_26683',axiom,
! [Vvar__26684] :
( c_24__type__26683___24t(Vvar__26684)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__26690___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__26684,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_26690',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26691] :
( c_24__type__26690___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26691)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__26691,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26715] :
( c_24__type__26714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26715)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__26715,Vv__CANONICAL__3)) ) ) ).
fof('$_type_26749',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26750] :
( c_24__type__26749___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26750)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26750,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_26765',axiom,
! [Vvar__26766] :
( c_24__type__26765___24t(Vvar__26766)
<=> ! [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__26766,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26780',axiom,
! [Vvar__26781] :
( c_24__type__26780___24t(Vvar__26781)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__26781,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26793',axiom,
! [Vvar__26794] :
( c_24__type__26793___24t(Vvar__26794)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__26794,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26809',axiom,
! [Vvar__26810] :
( c_24__type__26809___24t(Vvar__26810)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__26810,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_26818',axiom,
! [Vvar__26819] :
( c_24__type__26818___24t(Vvar__26819)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__26793___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__26793___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__26819,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2695',axiom,
! [Vvar__2696] :
( c_24__type__2695___24t(Vvar__2696)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__2696,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2740',axiom,
! [Vvar__2741] :
( c_24__type__2740___24t(Vvar__2741)
<=> ! [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_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2741,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_27463',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27464] :
( c_24__type__27463___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27464)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27464,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_27482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27483] :
( c_24__type__27482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27483)
<=> ! [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__27483,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_27502',axiom,
! [Vvar__27503] :
( c_24__type__27502___24t(Vvar__27503)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1189___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__27503,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_27595',axiom,
! [Vvar__27596] :
( c_24__type__27595___24t(Vvar__27596)
<=> ! [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__27596,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27600',axiom,
! [Vvar__27601] :
( c_24__type__27600___24t(Vvar__27601)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__27601,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27605',axiom,
! [Vvar__27606] :
( c_24__type__27605___24t(Vvar__27606)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__27606,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27607',axiom,
! [Vvar__27608] :
( c_24__type__27607___24t(Vvar__27608)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__27608,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27789',axiom,
! [Vvar__27790] :
( c_24__type__27789___24t(Vvar__27790)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__27790,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27792',axiom,
! [Vvar__27793] :
( c_24__type__27792___24t(Vvar__27793)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__27793,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27796',axiom,
! [Vvar__27797] :
( c_24__type__27796___24t(Vvar__27797)
<=> ! [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__27797,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27798',axiom,
! [Vvar__27799] :
( c_24__type__27798___24t(Vvar__27799)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__27799,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27804',axiom,
! [Vvar__27805] :
( c_24__type__27804___24t(Vvar__27805)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27805,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2783] :
( c_24__type__2782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2783)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2783,Vv__CANONICAL__3)) ) ) ).
fof('$_type_27822',axiom,
! [Vvar__27823] :
( c_24__type__27822___24t(Vvar__27823)
<=> ! [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__27823,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27848',axiom,
! [Vvar__27849] :
( c_24__type__27848___24t(Vvar__27849)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__27849,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2791',axiom,
! [Vvar__2792] :
( c_24__type__2791___24t(Vvar__2792)
<=> ! [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__2792,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27943] :
( c_24__type__27942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27943)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27943,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_27967',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27968] :
( c_24__type__27967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27968)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__27968,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_28009',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28010] :
( c_24__type__28009___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28010)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28010,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28060',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28061] :
( c_24__type__28060___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28061)
<=> ! [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__28061,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28158',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28159] :
( c_24__type__28158___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28159)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28159,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_2829',axiom,
! [Vvar__2830] :
( c_24__type__2829___24t(Vvar__2830)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__2830,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2831',axiom,
! [Vvar__2832] :
( c_24__type__2831___24t(Vvar__2832)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2832,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2842',axiom,
! [Vvar__2843] :
( c_24__type__2842___24t(Vvar__2843)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__2843,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2855',axiom,
! [Vvar__2856] :
( c_24__type__2855___24t(Vvar__2856)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2856,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2857',axiom,
! [Vvar__2858] :
( c_24__type__2857___24t(Vvar__2858)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2858,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2862',axiom,
! [Vvar__2863] :
( c_24__type__2862___24t(Vvar__2863)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2863,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28636',axiom,
! [Vvar__28637] :
( c_24__type__28636___24t(Vvar__28637)
<=> ! [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__28637,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2864',axiom,
! [Vvar__2865] :
( c_24__type__2864___24t(Vvar__2865)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2865,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29203',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__29204] :
( c_24__type__29203___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__29204)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29204,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29549',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29550] :
( c_24__type__29549___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__29550)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29550,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29895',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__29896] :
( c_24__type__29895___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__29896)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29896,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_302',axiom,
! [Vvar__303] :
( c_24__type__302___24t(Vvar__303)
<=> ! [Vv__CANONICAL__0] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__303,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30218',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__30219] :
( c_24__type__30218___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__30219)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__30219,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_30564',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30565] :
( c_24__type__30564___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__30565)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30565,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_30910',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__30911] :
( c_24__type__30910___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__30911)
<=> ! [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__30911,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_31256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31257] :
( c_24__type__31256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31257)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__31257,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_31602',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__31603] :
( c_24__type__31602___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__31603)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__31603,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_31948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31949] :
( c_24__type__31948___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__31949)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__31949,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_32271',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__32272] :
( c_24__type__32271___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__32272)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__32272,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_324',axiom,
! [Vvar__325] :
( c_24__type__324___24t(Vvar__325)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__325,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_326',axiom,
! [Vvar__327] :
( c_24__type__326___24t(Vvar__327)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__327,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32617',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32618] :
( c_24__type__32617___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__32618)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__32618,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_32963',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__32964] :
( c_24__type__32963___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__32964)
<=> ! [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__32964,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_33286',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33287] :
( c_24__type__33286___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33287)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__33287,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_33609',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__33610] :
( c_24__type__33609___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__33610)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__33610,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_33955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33956] :
( c_24__type__33955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__33956)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__33956,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34125',axiom,
! [Vvar__34126] :
( c_24__type__34125___24t(Vvar__34126)
<=> ! [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__34126,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34127',axiom,
! [Vvar__34128] :
( c_24__type__34127___24t(Vvar__34128)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__34128,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34130',axiom,
! [Vvar__34131] :
( c_24__type__34130___24t(Vvar__34131)
<=> ! [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__34131,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34133',axiom,
! [Vvar__34134] :
( c_24__type__34133___24t(Vvar__34134)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__34134,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34142',axiom,
! [Vvar__34143] :
( c_24__type__34142___24t(Vvar__34143)
<=> ! [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__34143,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34160',axiom,
! [Vvar__34161] :
( c_24__type__34160___24t(Vvar__34161)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__34161,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_34181',axiom,
! [Vvar__34182] :
( c_24__type__34181___24t(Vvar__34182)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4728___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__34182,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_34202',axiom,
! [Vvar__34203] :
( c_24__type__34202___24t(Vvar__34203)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__34203,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_34375',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34376] :
( c_24__type__34375___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34376)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34376,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34414',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34415] :
( c_24__type__34414___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34415)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34415,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34453',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34454] :
( c_24__type__34453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34454)
<=> ! [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__34454,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34609',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34610] :
( c_24__type__34609___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34610)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34610,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34632',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34633] :
( c_24__type__34632___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34633)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34633,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34655',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34656] :
( c_24__type__34655___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34656)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34656,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34678',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34679] :
( c_24__type__34678___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34679)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34679,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34697] :
( c_24__type__34696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34697)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__34697,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_347',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__348] :
( c_24__type__347___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__348)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__348,Vv__CANONICAL__3)) ) ) ).
fof('$_type_34722',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34723] :
( c_24__type__34722___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34723)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34723,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34740',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34741] :
( c_24__type__34740___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34741)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__34741,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_34998',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__34999] :
( c_24__type__34998___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__34999)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__34999,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35123',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__35124] :
( c_24__type__35123___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__35124)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35124,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3519',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3520] :
( c_24__type__3519___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3520)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3520,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_352',axiom,
! [Vvar__353] :
( c_24__type__352___24t(Vvar__353)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__353,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35249] :
( c_24__type__35248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35249)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35249,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_3526',axiom,
! [Vvar__3527] :
( c_24__type__3526___24t(Vvar__3527)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3527,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35374] :
( c_24__type__35373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35374)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__35374,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_35498',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__35499] :
( c_24__type__35498___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__35499)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__35499,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_35623',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35624] :
( c_24__type__35623___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__35624)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__35624,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_35734',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__35735] :
( c_24__type__35734___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__35735)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__35735,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_35883',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35884] :
( c_24__type__35883___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35884)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35884,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_35933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35934] :
( c_24__type__35933___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35934)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__35934,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_35983',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35984] :
( c_24__type__35983___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__35984)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__35984,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_36025',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36026] :
( c_24__type__36025___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36026)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__36026,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_36075',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36076] :
( c_24__type__36075___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36076)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__36076,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_36151',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36152] :
( c_24__type__36151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36152)
<=> ! [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__36152,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_36260',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36261] :
( c_24__type__36260___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36261)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36261,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36304',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36305] :
( c_24__type__36304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36305)
<=> ! [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__36305,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_36340',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36341] :
( c_24__type__36340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36341)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__36341,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_36384',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36385] :
( c_24__type__36384___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__36385)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__36385,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36598',axiom,
! [Vvar__36599] :
( c_24__type__36598___24t(Vvar__36599)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__36599,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36638',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36639] :
( c_24__type__36638___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36639)
<=> ! [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__36639,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_36689',axiom,
! [Vvar__36690] :
( c_24__type__36689___24t(Vvar__36690)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1189___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__36699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__12328___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__36690,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_36699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36700] :
( c_24__type__36699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__36700)
<=> ! [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__36700,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_36778',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36779] :
( c_24__type__36778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36779)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__36779,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_36817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36818] :
( c_24__type__36817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36818)
<=> ! [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__36818,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_36852',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36853] :
( c_24__type__36852___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36853)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__36853,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_36887',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36888] :
( c_24__type__36887___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36888)
<=> ! [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__36888,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_36896',axiom,
! [Vvar__36897] :
( c_24__type__36896___24t(Vvar__36897)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__36897,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36923',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36924] :
( c_24__type__36923___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36924)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__36924,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36931',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36932] :
( c_24__type__36931___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36932)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__36932,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36939',axiom,
! [Vvar__36940] :
( c_24__type__36939___24t(Vvar__36940)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__12547___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__36940,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36965',axiom,
! [Vvar__36966] :
( c_24__type__36965___24t(Vvar__36966)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__36966,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36986',axiom,
! [Vvar__36987] :
( c_24__type__36986___24t(Vvar__36987)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__36987,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_37061',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37062] :
( c_24__type__37061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__37062)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__37062,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_37069',axiom,
! [Vvar__37070] :
( c_24__type__37069___24t(Vvar__37070)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__37070,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37081',axiom,
! [Vvar__37082] :
( c_24__type__37081___24t(Vvar__37082)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__37084___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__37082,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_37084',axiom,
! [Vv__CANONICAL__0,Vvar__37085] :
( c_24__type__37084___24t(Vv__CANONICAL__0,Vvar__37085)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__37085,Vv__CANONICAL__1)) ) ) ).
fof('$_type_37177',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37178] :
( c_24__type__37177___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37178)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37178,Vv__CANONICAL__4)) ) ) ).
fof('$_type_37186',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37187] :
( c_24__type__37186___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__37187)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__37187,Vv__CANONICAL__4)) ) ) ).
fof('$_type_37290',axiom,
! [Vvar__37291] :
( c_24__type__37290___24t(Vvar__37291)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__37291,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37387',axiom,
! [Vvar__37388] :
( c_24__type__37387___24t(Vvar__37388)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__37388,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37392',axiom,
! [Vvar__37393] :
( c_24__type__37392___24t(Vvar__37393)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__37387___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__37387___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__37393,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_37410',axiom,
! [Vvar__37411] :
( c_24__type__37410___24t(Vvar__37411)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__37415___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__37411,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_37415',axiom,
! [Vv__CANONICAL__0,Vvar__37416] :
( c_24__type__37415___24t(Vv__CANONICAL__0,Vvar__37416)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__37416,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_37436',axiom,
! [Vvar__37437] :
( c_24__type__37436___24t(Vvar__37437)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4737___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__37437,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_37469',axiom,
! [Vvar__37470] :
( c_24__type__37469___24t(Vvar__37470)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__37470,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_37532',axiom,
! [Vvar__37533] :
( c_24__type__37532___24t(Vvar__37533)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__37533,Vv__CANONICAL__0)) ) ) ).
fof('$_type_37573',axiom,
! [Vvar__37574] :
( c_24__type__37573___24t(Vvar__37574)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__23281___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__23281___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__37574,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_389',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__390] :
( c_24__type__389___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__390)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__390,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_391',axiom,
! [Vvar__392] :
( c_24__type__391___24t(Vvar__392)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__392,Vv__CANONICAL__0)) ) ) ).
fof('$_type_398',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__399] :
( c_24__type__398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__399)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__399,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
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_4311',axiom,
! [Vvar__4312] :
( c_24__type__4311___24t(Vvar__4312)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__4312,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4323',axiom,
! [Vvar__4324] :
( c_24__type__4323___24t(Vvar__4324)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__4324,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4367',axiom,
! [Vvar__4368] :
( c_24__type__4367___24t(Vvar__4368)
<=> ! [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__4368,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4379',axiom,
! [Vvar__4380] :
( c_24__type__4379___24t(Vvar__4380)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__4380,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_438',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__439] :
( c_24__type__438___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__439)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__439,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_4391',axiom,
! [Vvar__4392] :
( c_24__type__4391___24t(Vvar__4392)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__4392,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_4411',axiom,
! [Vvar__4412] :
( c_24__type__4411___24t(Vvar__4412)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__4412,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4416',axiom,
! [Vvar__4417] :
( c_24__type__4416___24t(Vvar__4417)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__4417,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4434',axiom,
! [Vvar__4435] :
( c_24__type__4434___24t(Vvar__4435)
<=> ! [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__4435,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_445',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__446] :
( c_24__type__445___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__446)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__446,Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ).
fof('$_type_4460',axiom,
! [Vvar__4461] :
( c_24__type__4460___24t(Vvar__4461)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( ~ ( p(Vv__CANONICAL__0)
& p(Vv__CANONICAL__1) )
=> ( ( p(Vv__CANONICAL__0)
| p(Vv__CANONICAL__1) )
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__4461,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ) ).
fof('$_type_4593',axiom,
! [Vvar__4594] :
( c_24__type__4593___24t(Vvar__4594)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__4594,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4710',axiom,
! [Vv__CANONICAL__0,Vvar__4711] :
( c_24__type__4710___24t(Vv__CANONICAL__0,Vvar__4711)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__4711,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_4728',axiom,
! [Vv__CANONICAL__0,Vvar__4729] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vvar__4729)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4729,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4737',axiom,
! [Vv__CANONICAL__0,Vvar__4738] :
( c_24__type__4737___24t(Vv__CANONICAL__0,Vvar__4738)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__4738,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_4812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4813] :
( c_24__type__4812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4813)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__4813,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_4842',axiom,
! [Vvar__4843] :
( c_24__type__4842___24t(Vvar__4843)
<=> ! [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__4843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4867',axiom,
! [Vvar__4868] :
( c_24__type__4867___24t(Vvar__4868)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__4868,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_4917',axiom,
! [Vvar__4918] :
( c_24__type__4917___24t(Vvar__4918)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4924___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__4918,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_4924',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4925] :
( c_24__type__4924___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4925)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4925,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5038',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5039] :
( c_24__type__5038___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__5039)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5039,Vv__CANONICAL__3)) ) ) ).
fof('$_type_5086',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__5087] :
( c_24__type__5086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__5087)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5087,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_5096',axiom,
! [Vvar__5097] :
( c_24__type__5096___24t(Vvar__5097)
<=> ! [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__5097,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5119',axiom,
! [Vvar__5120] :
( c_24__type__5119___24t(Vvar__5120)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5558',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__5559] :
( c_24__type__5558___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__5559)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5559,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5660] :
( c_24__type__5659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5660)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5660,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5760',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__5761] :
( c_24__type__5760___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__5761)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5761,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5850',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5851] :
( c_24__type__5850___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5851)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5851,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_59',axiom,
! [Vvar__60] :
( c_24__type__59___24t(Vvar__60)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__60,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5951',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5952] :
( c_24__type__5951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5952)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5952,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_6052',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__6053] :
( c_24__type__6052___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__6053)
<=> ! [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__6053,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_6153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6154] :
( c_24__type__6153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6154)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__6154,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_6225',axiom,
! [Vvar__6226] :
( c_24__type__6225___24t(Vvar__6226)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2ePartial__Order_2eRel___24t(Vv__CANONICAL__0,happ(happ(Vvar__6226,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6303',axiom,
! [Vvar__6304] :
( c_24__type__6303___24t(Vvar__6304)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__6304,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6619',axiom,
! [Vv__CANONICAL__0,Vvar__6620] :
( c_24__type__6619___24t(Vv__CANONICAL__0,Vvar__6620)
<=> ! [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__6620,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_6674',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6675] :
( c_24__type__6674___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6675)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__6675,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_6688',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6689] :
( c_24__type__6688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6689)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__6689,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_6695',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6696] :
( c_24__type__6695___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6696)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6696,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_6924',axiom,
! [Vvar__6925] :
( c_24__type__6924___24t(Vvar__6925)
<=> ! [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__6925,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_8346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8347] :
( c_24__type__8346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8347)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8347,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8409',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__8410] :
( c_24__type__8409___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__8410)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8410,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8472',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8473] :
( c_24__type__8472___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8473)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8473,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8526',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__8527] :
( c_24__type__8526___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__8527)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__8527,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_8589',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8590] :
( c_24__type__8589___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8590)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8590,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_8863',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__8864] :
( c_24__type__8863___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__8864)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8864,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8926',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8927] :
( c_24__type__8926___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8927)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8927,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8989',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__8990] :
( c_24__type__8989___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__8990)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8990,Vv__CANONICAL__8),Vv__CANONICAL__9),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_9043',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__9044] :
( c_24__type__9043___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__9044)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__9044,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_9106',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__9107] :
( c_24__type__9106___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__9107)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9107,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_9262',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9263] :
( c_24__type__9262___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9263)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9263,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9292',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9293] :
( c_24__type__9292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9293)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9293,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9317] :
( c_24__type__9316___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9317)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9317,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9347] :
( c_24__type__9346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9347)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9347,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_9376',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9377] :
( c_24__type__9376___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9377)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9377,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9401] :
( c_24__type__9400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9401)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9401,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9433',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9434] :
( c_24__type__9433___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9434)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9434,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9457',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9458] :
( c_24__type__9457___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9458)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9458,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9484',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9485] :
( c_24__type__9484___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9485)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9485,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_97',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__98] :
( c_24__type__97___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__98)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__98,Vv__CANONICAL__5),Vv__CANONICAL__1) ) ) ).
fof('$_type_9883',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__9884] :
( c_24__type__9883___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__9884)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9884,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__1183___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__1183___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__26818___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__1183___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__1183___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__37410___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__5096___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__37081___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__23533___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__2862___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__23538___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__23548___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__2864___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__22916___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_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__23012___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
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.byte_of_byte',axiom,
c_24__type__23562___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).
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('$_typeof_Coq.Init.Byte.x80',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).
fof('$_typeof_Coq.Init.Byte.x81',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).
fof('$_typeof_Coq.Init.Byte.x82',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).
fof('$_typeof_Coq.Init.Byte.x83',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).
fof('$_typeof_Coq.Init.Byte.x84',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).
fof('$_typeof_Coq.Init.Byte.x85',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).
fof('$_typeof_Coq.Init.Byte.x86',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).
fof('$_typeof_Coq.Init.Byte.x87',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).
fof('$_typeof_Coq.Init.Byte.x88',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).
fof('$_typeof_Coq.Init.Byte.x89',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).
fof('$_typeof_Coq.Init.Byte.x8a',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).
fof('$_typeof_Coq.Init.Byte.x8b',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).
fof('$_typeof_Coq.Init.Byte.x8c',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).
fof('$_typeof_Coq.Init.Byte.x8d',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).
fof('$_typeof_Coq.Init.Byte.x8e',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).
fof('$_typeof_Coq.Init.Byte.x8f',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).
fof('$_typeof_Coq.Init.Byte.x90',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).
fof('$_typeof_Coq.Init.Byte.x91',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).
fof('$_typeof_Coq.Init.Byte.x92',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).
fof('$_typeof_Coq.Init.Byte.x93',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).
fof('$_typeof_Coq.Init.Byte.x94',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).
fof('$_typeof_Coq.Init.Byte.x95',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).
fof('$_typeof_Coq.Init.Byte.x96',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).
fof('$_typeof_Coq.Init.Byte.x97',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).
fof('$_typeof_Coq.Init.Byte.x98',axiom,
cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__23823___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__23848___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('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__326___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__1036___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__324___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__2862___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__4434___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__4416___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__4379___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__2862___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_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.negb',axiom,
c_24__type__4311___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__4411___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__4___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__2862___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__4367___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__104___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__4391___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__104___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__2862___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.D1',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD1) ).
fof('$_typeof_Coq.Init.Decimal.D2',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD2) ).
fof('$_typeof_Coq.Init.Decimal.D3',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD3) ).
fof('$_typeof_Coq.Init.Decimal.D4',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD4) ).
fof('$_typeof_Coq.Init.Decimal.D5',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD5) ).
fof('$_typeof_Coq.Init.Decimal.D6',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD6) ).
fof('$_typeof_Coq.Init.Decimal.D7',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD7) ).
fof('$_typeof_Coq.Init.Decimal.D8',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD8) ).
fof('$_typeof_Coq.Init.Decimal.D9',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2eD9) ).
fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).
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('$_typeof_Coq.Init.Decimal.nzhead',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2enzhead) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
c_24__type__4593___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__391___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__26780___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__1036___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__1036___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__26765___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__26793___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__26765___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__26809___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__1036___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__1036___24t(cCoq_2eInit_2eNat_2esucc) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__5096___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).
fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
c_24__type__4323___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__1183___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__1183___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__1183___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__36986___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__12467___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__36896___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__20141___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__12577___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__20146___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__12449___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__12510___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__12544___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__36939___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__20118___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__36965___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__37069___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__4842___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__26683___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__4917___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__26659___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__4867___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__12318___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__12318___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__36689___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__36689___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on',axiom,
c_24__type__4___24t(cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
c_24__type__23600___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__3526___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
c_24__type__23576___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
c_24__type__391___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
c_24__type__3526___24t(cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ProofIrrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
c_24__type__391___24t(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
c_24__type__3526___24t(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
c_24__type__3526___24t(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on) ).
fof('$_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__23753___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.weak_generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__23905___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__22425___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__37392___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__22425___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__22425___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__22318___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__22309___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__37387___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__22318___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__22318___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__22318___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__22309___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__22309___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__5119___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__22419___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__26818___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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__2842___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__2855___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__2855___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__2829___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__2829___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__37532___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__22305___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_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__22511___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__22553___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__2829___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__22558___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__37436___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__37469___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__22468___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__22468___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__2829___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
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__27605___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__27595___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__27600___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__27607___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_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('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_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.Rgt',axiom,
c_24__type__27796___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__27607___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__27796___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__27796___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__27792___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__27607___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__27792___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__27798___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__28636___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__4___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__36598___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('$_typeof_Coq.Sets.Ensembles.Add',axiom,
c_24__type__1052___24t(cCoq_2eSets_2eEnsembles_2eAdd) ).
fof('$_typeof_Coq.Sets.Ensembles.Complement',axiom,
c_24__type__59___24t(cCoq_2eSets_2eEnsembles_2eComplement) ).
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.Ensembles.Same_set',axiom,
c_24__type__14___24t(cCoq_2eSets_2eEnsembles_2eSame__set) ).
fof('$_typeof_Coq.Sets.Ensembles.Setminus',axiom,
c_24__type__1057___24t(cCoq_2eSets_2eEnsembles_2eSetminus) ).
fof('$_typeof_Coq.Sets.Ensembles.Strict_Included',axiom,
c_24__type__14___24t(cCoq_2eSets_2eEnsembles_2eStrict__Included) ).
fof('$_typeof_Coq.Sets.Ensembles.Subtract',axiom,
c_24__type__1052___24t(cCoq_2eSets_2eEnsembles_2eSubtract) ).
fof('$_typeof_Coq.Sets.Image.injective',axiom,
c_24__type__2695___24t(cCoq_2eSets_2eImage_2einjective) ).
fof('$_typeof_Coq.Sets.Partial_Order.Carrier',axiom,
c_24__type__4___24t(cCoq_2eSets_2ePartial__Order_2eCarrier) ).
fof('$_typeof_Coq.Sets.Partial_Order.Carrier_of',axiom,
c_24__type__1165___24t(cCoq_2eSets_2ePartial__Order_2eCarrier__of) ).
fof('$_typeof_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
c_24__type__2740___24t(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO) ).
fof('$_typeof_Coq.Sets.Partial_Order.PO',axiom,
c_24__type__4___24t(cCoq_2eSets_2ePartial__Order_2ePO) ).
fof('$_typeof_Coq.Sets.Partial_Order.Rel_of',axiom,
c_24__type__1180___24t(cCoq_2eSets_2ePartial__Order_2eRel__of) ).
fof('$_typeof_Coq.Sets.Partial_Order.Strict_Rel_of',axiom,
c_24__type__6225___24t(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of) ).
fof('$_typeof_Coq.Sets.Relations_1.Antisymmetric',axiom,
c_24__type__2791___24t(cCoq_2eSets_2eRelations__1_2eAntisymmetric) ).
fof('$_typeof_Coq.Sets.Relations_1.Reflexive',axiom,
c_24__type__2791___24t(cCoq_2eSets_2eRelations__1_2eReflexive) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__4___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__2791___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Sets.Relations_1.contains',axiom,
c_24__type__6303___24t(cCoq_2eSets_2eRelations__1_2econtains) ).
fof('$_typeof_Coq.Sets.Relations_1.same_relation',axiom,
c_24__type__6303___24t(cCoq_2eSets_2eRelations__1_2esame__relation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__23447___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_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,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
c_24__type__26554___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
c_24__type__26554___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__27502___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__22425___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__22425___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__1183___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__1183___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__22305___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__22305___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__22305___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__22305___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__22305___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__22242___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__22242___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_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('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__2864___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__21705___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__22242___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__22242___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__37573___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__22242___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__22242___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__22242___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__23050___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__23281___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__23281___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__23099___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__23050___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__23015___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__23050___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
c_24__type__23093___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__23103___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ezero) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__22239___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__2857___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__2857___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__2831___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__28636___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__37290___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_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.PEc',axiom,
c_24__type__24119___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.Pc',axiom,
c_24__type__24169___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
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('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__27789___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__27848___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__27822___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('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).
fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_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('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__20311___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__4___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.coneMember',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
c_24__type__23099___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__23096___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__2855___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__2855___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__25305___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__25302___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_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('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__26596___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__26596___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.InitialRing.mkhypo',axiom,
c_24__type__26648___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).
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__34127___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__34127___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__34133___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__6924___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__34130___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__6924___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__34142___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__6924___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__34125___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__4___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__34160___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_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('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__12093___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__12093___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__22309___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__34202___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__34181___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).
fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__27804___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__27804___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_InteriorsClosures.closure',axiom,
c_24__type__150750___24t(cInteriorsClosures_2eclosure) ).
fof('$_typeof_InteriorsClosures.interior',axiom,
c_24__type__150750___24t(cInteriorsClosures_2einterior) ).
fof('$_typeof_InteriorsClosures.interior_closure_relations.idempotent',axiom,
c_24__type__150887___24t(cInteriorsClosures_2einterior__closure__relations_2eidempotent) ).
fof('$_typeof_Topology.TopologicalSpaces.Build_TopologicalSpace',axiom,
c_24__type__1232___24t(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace) ).
fof('$_typeof_Topology.TopologicalSpaces.TopologicalSpace',axiom,
cType___24t(cTopology_2eTopologicalSpaces_2eTopologicalSpace) ).
fof('$_typeof_Topology.TopologicalSpaces.closed',axiom,
c_24__type__302___24t(cTopology_2eTopologicalSpaces_2eclosed) ).
fof('$_typeof_Topology.TopologicalSpaces.open',axiom,
c_24__type__302___24t(cTopology_2eTopologicalSpaces_2eopen) ).
fof('$_typeof_Topology.TopologicalSpaces.point_set',axiom,
c_24__type__234___24t(cTopology_2eTopologicalSpaces_2epoint__set) ).
fof('$_typeof_X',axiom,
cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(cX) ).
fof('$_typeof_ZornsLemma.DecidableDec.exclusive_dec',axiom,
c_24__type__4460___24t(cZornsLemma_2eDecidableDec_2eexclusive__dec) ).
fof('$_typeof_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
c_24__type__352___24t(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble) ).
fof('$_typeof_ZornsLemma.Families.Family',axiom,
c_24__type__4___24t(cZornsLemma_2eFamilies_2eFamily) ).
fof('$_typeof_ZornsLemma.FunctionProperties.injective',axiom,
c_24__type__2695___24t(cZornsLemma_2eFunctionProperties_2einjective) ).
fof('$_typeof_ZornsLemma.FunctionProperties.surjective',axiom,
c_24__type__2695___24t(cZornsLemma_2eFunctionProperties_2esurjective) ).
fof('$_typeof_ZornsLemma.IndexedFamilies.ImageFamily',axiom,
c_24__type__120___24t(cZornsLemma_2eIndexedFamilies_2eImageFamily) ).
fof('$_typeof_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
c_24__type__104___24t(cZornsLemma_2eIndexedFamilies_2eIndexedFamily) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
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_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_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_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_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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
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_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_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_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.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_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.Wf_nat.lt_wf_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__4323___24t(V1__P)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__m,V2__n)
=> p(happ(V1__P,V3__m)) ) )
=> p(happ(V1__P,V2__n)) ) )
=> p(happ(V1__P,V0__n)) ) ) ) ).
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.Init.Datatypes.idProp',axiom,
p(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__4323___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.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.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.FalseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.TrueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.falseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
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.trueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
fof('Coq.Logic.Classical_Pred_Type.ex_not_not_all',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_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_Pred_Type.not_all_not_ex',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.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
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.imply_to_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ~ p(V0__P)
| p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ~ p(V1__Q) ) ) ) ).
fof('Coq.Logic.Classical_Prop.or_to_imply',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
| p(V1__Q) )
=> ( p(V0__P)
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.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.FunctionalExtensionality.equal_f',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__398___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__398___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__12547___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__26495___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__26500___24t(V0__A,V1__B,V3__g)
=> ( V2__f = V3__g
=> ! [V5__x] :
( t(V5__x,V0__A)
=> happ(V2__f,V5__x) = happ(V3__g,V5__x) ) ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__398___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__26539___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.eta_expansion_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__12547___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__26523___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__26531___24a3(V0__A,V1__B,V2__f) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__398___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__398___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.functional_extensionality_dep',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( c_24__type__12547___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__26506___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__26511___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> happ(V2__f,V4__x) = happ(V3__g,V4__x) )
=> V2__f = V3__g ) ) ) ) ) ).
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.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_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_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_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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
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_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_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).
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.Sets.Classical_sets.Complement_Complement',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,V1__A)) = V1__A ) ) ).
fof('Coq.Sets.Classical_sets.Included_Strict_Included',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y)
| V1__X = V2__Y ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Strict_Included_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Subtract_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
=> ( V2__x != V3__y
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__A,V2__x),V3__y) ) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Subtract_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__A,V2__x),V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
& V2__x != V3__y ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_intro1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_intro2',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V2__x) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
| V2__x = V3__y ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_not_Empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x) != cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Extension',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ( V1__B = V2__C
=> cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__B,V2__C) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Included_Empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__A) ) ) ).
fof('Coq.Sets.Constructive_sets.Inhabited_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x)) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Inhabited_not_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__X)
=> V1__X != cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Noone_in_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Constructive_sets.Setminus_intro',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)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V1__A,V2__B),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Singleton_intro',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
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Singleton_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V2__y)
=> V1__x = V2__y ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Strict_Included_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
& V1__X != V2__Y )
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Strict_Included_strict',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ~ cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V1__X) ) ) ).
fof('Coq.Sets.Constructive_sets.not_Empty_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) != cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__P] :
( c_24__type__2___24t(V0__U,V3__P)
=> ( p(happ(V3__P,V1__x))
=> ( p(happ(V3__P,V2__y))
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(V0__U,V1__x,V2__y,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),V1__x) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),V2__y) ) ) ) ).
fof('Coq.Sets.Ensembles.Empty_set_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__2___24t(V0__U,V1__P)
=> ! [V2__u] :
( t(V2__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eEmpty__set___24a2(V0__U,V2__u)
=> p(happ(V1__P,V2__u)) ) ) ) ) ).
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.Ensembles.In_singleton',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V1__x) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__2___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V4__x)
=> p(happ(V3__P,V4__x)) ) ) )
=> ! [V5__u] :
( t(V5__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V0__U,V1__B,V2__C,V5__u)
=> p(happ(V3__P,V5__u)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,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)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__2___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V4__x)
=> p(happ(V3__P,V4__x)) ) ) )
=> ! [V5__u] :
( t(V5__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V0__U,V1__B,V2__C,V5__u)
=> p(happ(V3__P,V5__u)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Singleton_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__2___24t(V0__U,V2__P)
=> ( p(happ(V2__P,V1__x))
=> ! [V4__u] :
( t(V4__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V0__U,V1__x,V4__u)
=> p(happ(V2__P,V4__u)) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> ! [V4__P] :
( c_24__type__2___24t(V0__U,V4__P)
=> ( p(happ(V4__P,V1__x))
=> ( p(happ(V4__P,V2__y))
=> ( p(happ(V4__P,V3__z))
=> ! [V8__u] :
( t(V8__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eTriple___24a5(V0__U,V1__x,V2__y,V3__z,V8__u)
=> p(happ(V4__P,V8__u)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z),V1__x) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_m',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z),V2__y) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z),V3__z) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__2___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> p(happ(V3__P,V4__x)) ) )
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V5__x)
=> p(happ(V3__P,V5__x)) ) )
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(V0__U,V1__B,V2__C,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_introl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,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,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_intror',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__2___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> p(happ(V3__P,V4__x)) ) )
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V5__x)
=> p(happ(V3__P,V5__x)) ) )
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(V0__U,V1__B,V2__C,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.Empty_is_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) ) ).
fof('Coq.Sets.Finite_sets.Union_is_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_elim',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__p)
=> c_24__case__Coq_2eInit_2eDatatypes_2enat_242680___24a3(V0__U,V1__X,V2__p) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Finite_downward_closed',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__X) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.G_aux',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__147___24t(V0__U,V1__P)
=> ( ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V2__X)
=> ( ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V4__Y,V2__X)
=> p(happ(V1__P,V4__Y)) ) )
=> p(happ(V1__P,V2__X)) ) ) )
=> p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Generalized_induction_on_finite_sets',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__147___24t(V0__U,V1__P)
=> ( ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V2__X)
=> ( ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V4__Y,V2__X)
=> p(happ(V1__P,V4__Y)) ) )
=> p(happ(V1__P,V2__X)) ) ) )
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__X)
=> p(happ(V1__P,V3__X)) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinalO_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,cCoq_2eInit_2eDatatypes_2eO)
=> V1__X = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__n)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__X) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_is_functional',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__c1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__c1)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__c1)
=> ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ! [V5__c2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__c2)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__Y,V5__c2)
=> ( V1__X = V4__Y
=> V2__c1 = V5__c2 ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_unicity',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V4__m)
=> V2__n = V4__m ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.finite_cardinal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__X)
=> ? [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V3__n) ) ) ) ) ).
fof('Coq.Sets.Image.Im_add',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__x] :
( t(V3__x,V0__U)
=> ! [V4__f] :
( c_24__type__398___24t(V0__U,V1__V,V4__f)
=> cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__X,V3__x),V4__f) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V1__V,cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,V2__X,V4__f),happ(V4__f,V3__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__398___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_ind',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__398___24t(V0__U,V1__V,V3__f)
=> ! [V4__P] :
( c_24__type__1124___24t(V0__U,V1__V,V4__P)
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V5__x)
=> ! [V7__y] :
( t(V7__y,V1__V)
=> ( V7__y = happ(V3__f,V5__x)
=> p(happ(V4__P,V7__y)) ) ) ) )
=> ! [V6__v] :
( t(V6__v,V1__V)
=> ( cCoq_2eSets_2eImage_2eIm___24a5(V0__U,V1__V,V2__X,V3__f,V6__v)
=> p(happ(V4__P,V6__v)) ) ) ) ) ) ) ) ) ).
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__398___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.Sets.Image.Im_sind',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__398___24t(V0__U,V1__V,V3__f)
=> ! [V4__P] :
( c_24__type__1124___24t(V0__U,V1__V,V4__P)
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X,V5__x)
=> ! [V7__y] :
( t(V7__y,V1__V)
=> ( V7__y = happ(V3__f,V5__x)
=> p(happ(V4__P,V7__y)) ) ) ) )
=> ! [V6__v] :
( t(V6__v,V1__V)
=> ( cCoq_2eSets_2eImage_2eIm___24a5(V0__U,V1__V,V2__X,V3__f,V6__v)
=> p(happ(V4__P,V6__v)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Image.image_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__V] :
( cType___24t(V1__V)
=> ! [V2__f] :
( c_24__type__398___24t(V0__U,V1__V,V2__f)
=> cCoq_2eSets_2eImage_2eIm___24a4(V0__U,V1__V,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V2__f) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V1__V) ) ) ) ).
fof('Coq.Sets.Partial_Order.Strict_Rel_Transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a2(V0__U,V1__D)) ) ) ).
fof('Coq.Sets.Powerset.Definition_of_Power_set',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,V1__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__A),V2__X) ) ) ) ) ).
fof('Coq.Sets.Powerset.Empty_set_minimal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__X) ) ) ).
fof('Coq.Sets.Powerset.Inclusion_is_an_order',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Inclusion_is_transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_l',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_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V1__a) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_r',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_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V2__b) ) ) ) ).
fof('Coq.Sets.Powerset.Power_set_Inhabited',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__X)) ) ) ).
fof('Coq.Sets.Powerset.Power_set_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__P] :
( c_24__type__147___24t(V0__U,V2__P)
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> p(happ(V2__P,V3__X)) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(V0__U,V1__A,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Power_set_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__P] :
( c_24__type__147___24t(V0__U,V2__P)
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> p(happ(V2__P,V3__X)) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(V0__U,V1__A,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eStrict__Included___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive_with_inclusion',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__x)
=> ! [V2__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__y)
=> ! [V3__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__z)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V2__y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__y,V3__z)
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V3__z) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Union_increases_l',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_2eIncluded___24a3(V0__U,V1__a,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b)) ) ) ) ).
fof('Coq.Sets.Powerset.Union_increases_r',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_2eIncluded___24a3(V0__U,V2__b,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b)) ) ) ) ).
fof('Coq.Sets.Powerset.Union_minimal',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)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__a,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__b,V3__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b),V3__X) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Included_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__A)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__A,V3__x))
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__A)
| ? [V5__A_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__A_27)
& V1__X = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V5__A_27,V3__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V5__A_27,V2__A) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Simplify_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__X0] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X0)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V3__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X0,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V3__x) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__X0,V3__x)
=> V1__X = V2__X0 ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_add_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V2__x),V1__X) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Add_commutative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__y),V2__x) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Add_commutative\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y),V4__z) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V4__z),V2__x),V3__y) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Empty_set_zero',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__X) = V1__X ) ) ).
fof('Coq.Sets.Powerset_facts.Empty_set_zero\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__x) = cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x) ) ) ).
fof('Coq.Sets.Powerset_facts.Empty_set_zero_right',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) = V1__X ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_Empty_set_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A),V1__s) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_Empty_set_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__A,V1__s,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A)) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_commutative',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_2eIntersection___24a3(V0__U,V1__A,V2__B) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__B,V1__A) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Non_disjoint_union',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x) = V1__X ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Non_disjoint_union\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x) = V1__X ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Seminus_Empty_set_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A),V1__s) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ).
fof('Coq.Sets.Powerset_facts.Seminus_Empty_set_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A)) = V1__s ) ) ).
fof('Coq.Sets.Powerset_facts.Setminus_Included_empty',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__A,V1__s1,V2__s2)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,V2__s2) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Triple_as_Couple',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y) = cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V1__x,V2__y) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_absorbs',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_2eIncluded___24a3(V0__U,V2__B,V1__A)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B) = V1__A ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_add',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)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__x) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_associative',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)
=> ! [V3__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__C)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__C) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V3__C)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_commutative',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_2eUnion___24a3(V0__U,V1__A,V2__B) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V1__A) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_idempotent',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V1__A) = V1__A ) ) ).
fof('Coq.Sets.Powerset_facts.incl_add',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)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.less_than_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))
=> V1__X = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Relations_1_facts.cong_transitive_same_relation',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__R] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,V1__R)
=> ! [V2__R_27] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,V2__R_27)
=> ( cCoq_2eSets_2eRelations__1_2esame__relation___24a3(V0__U,V1__R,V2__R_27)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V2__R_27) ) ) ) ) ) ).
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)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x)
=> 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)
=> ( ~ 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_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_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)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
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_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
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)
| 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.lt_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_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)
=> ( 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_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_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
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.OrderedRing.Rle_antisymm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V11__n))
=> p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_gt_cases',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_lt_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_refl',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V11__n),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rle_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V8__rle,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_0_1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> p(happ(happ(V9__rlt,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_le_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_lt_succ',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_succ_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V12__m),V13__p))
=> p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trichotomy',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V1__rO),V11__n)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V1__rO)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V12__m)),happ(happ(V3__rplus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_le_lt_mono',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_le_mono',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V8__rle,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V13__p),V14__q))
=> p(happ(happ(V8__rle,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_lt_le_mono',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V8__rle,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_lt_mono',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ( p(happ(happ(V9__rlt,V13__p),V14__q))
=> p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_nonneg_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_nonneg_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_pos_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rplus_pos_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V1__rO),V11__n)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V1__rO))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_nonneg_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V8__rle,V1__rO),V11__n))
=> ( p(happ(happ(V8__rle,V1__rO),V12__m))
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_refl',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,V11__x),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_sym',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ( p(happ(happ(V7__req,V11__x),V12__y))
=> p(happ(happ(V7__req,V12__y),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZCoeff.req_trans',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__4728___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__4728___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__4728___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1189___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1189___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> ( p(happ(happ(V7__req,V11__x),V12__y))
=> ( p(happ(happ(V7__req,V12__y),V13__z))
=> p(happ(happ(V7__req,V11__x),V13__z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__4728___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4728___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4728___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___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_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__4728___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4728___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4728___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___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__4728___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4728___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4728___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4728___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4728___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4728___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4728___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4728___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4728___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___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__4728___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4728___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4728___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4737___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1189___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('InteriorsClosures.closure_closed',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('InteriorsClosures.closure_fixes_closed',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__S)
=> cInteriorsClosures_2eclosure___24a2(V0__X,V1__S) = V1__S ) ) ) ).
fof('InteriorsClosures.closure_inflationary',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,cInteriorsClosures_2eclosure___24a2(V0__X,V1__S)) ) ) ).
fof('InteriorsClosures.closure_minimal',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__F)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S,V2__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cInteriorsClosures_2eclosure___24a2(V0__X,V1__S),V2__F) ) ) ) ) ) ).
fof('InteriorsClosures.interior_closure_relations.closure_complement',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> cInteriorsClosures_2eclosure___24a2(cX,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2einterior___24a2(cX,V0__S)) ) ).
fof('InteriorsClosures.interior_closure_relations.closure_idempotent',axiom,
cInteriorsClosures_2einterior__closure__relations_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)),cInteriorsClosures_2eclosure___24a1(cX)) ).
fof('InteriorsClosures.interior_closure_relations.closure_increasing',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> ! [V1__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V1__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S,V1__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2eclosure___24a2(cX,V0__S),cInteriorsClosures_2eclosure___24a2(cX,V1__T)) ) ) ) ).
fof('InteriorsClosures.interior_closure_relations.closure_interior_idempotent',axiom,
cInteriorsClosures_2einterior__closure__relations_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)),c_24__lam__157541) ).
fof('InteriorsClosures.interior_closure_relations.closure_intersection',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> ! [V1__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V1__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2eclosure___24a2(cX,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S,V1__T)),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2eclosure___24a2(cX,V0__S),cInteriorsClosures_2eclosure___24a2(cX,V1__T))) ) ) ).
fof('InteriorsClosures.interior_closure_relations.closure_union',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> ! [V1__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V1__T)
=> cInteriorsClosures_2eclosure___24a2(cX,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S,V1__T)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2eclosure___24a2(cX,V0__S),cInteriorsClosures_2eclosure___24a2(cX,V1__T)) ) ) ).
fof('InteriorsClosures.interior_closure_relations.complement_inclusion',axiom,
! [V0__Y] :
( cType___24t(V0__Y)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__Y,V1__S)
=> ! [V2__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__Y,V2__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__Y,V1__S,V2__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__Y,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__Y,V2__T),cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__Y,V1__S)) ) ) ) ) ).
fof('InteriorsClosures.interior_closure_relations.interior_complement',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> cInteriorsClosures_2einterior___24a2(cX,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2eclosure___24a2(cX,V0__S)) ) ).
fof('InteriorsClosures.interior_closure_relations.interior_idempotent',axiom,
cInteriorsClosures_2einterior__closure__relations_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)),cInteriorsClosures_2einterior___24a1(cX)) ).
fof('InteriorsClosures.interior_closure_relations.interior_increasing',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> ! [V1__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V1__T)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S,V1__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2einterior___24a2(cX,V0__S),cInteriorsClosures_2einterior___24a2(cX,V1__T)) ) ) ) ).
fof('InteriorsClosures.interior_closure_relations.interior_intersection',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> ! [V1__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V1__T)
=> cInteriorsClosures_2einterior___24a2(cX,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S,V1__T)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2einterior___24a2(cX,V0__S),cInteriorsClosures_2einterior___24a2(cX,V1__T)) ) ) ).
fof('InteriorsClosures.interior_closure_relations.interior_union',axiom,
! [V0__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S)
=> ! [V1__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V1__T)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),cInteriorsClosures_2einterior___24a2(cX,V0__S),cInteriorsClosures_2einterior___24a2(cX,V1__T)),cInteriorsClosures_2einterior___24a2(cX,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX),V0__S,V1__T))) ) ) ).
fof('InteriorsClosures.interior_deflationary',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),cInteriorsClosures_2einterior___24a2(V0__X,V1__S),V1__S) ) ) ).
fof('InteriorsClosures.interior_fixes_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__S)
=> cInteriorsClosures_2einterior___24a2(V0__X,V1__S) = V1__S ) ) ) ).
fof('InteriorsClosures.interior_maximal',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> ! [V2__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U,V1__S)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__U,cInteriorsClosures_2einterior___24a2(V0__X,V1__S)) ) ) ) ) ) ).
fof('InteriorsClosures.interior_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__S)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cInteriorsClosures_2einterior___24a2(V0__X,V1__S)) ) ) ).
fof('Topology.TopologicalSpaces.closed_complement_open',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eComplement___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U))
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__U) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_family_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X)),V1__F,V2__S)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__S) ) )
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_finite_indexed_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V1__A)
=> ( ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,happ(V2__F,V4__a)) )
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_indexed_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( ! [V3__a] :
( t(V3__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,happ(V2__F,V3__a)) )
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_intersection2',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__G)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F,V2__G)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.closed_union2',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__F] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F)
=> ! [V2__G] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__G)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V1__F)
=> ( cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,V2__G)
=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__F,V2__G)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_empty',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X))) ) ).
fof('Topology.TopologicalSpaces.open_family_union',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__F)
=> ( ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t)),V1__F,V2__S)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V2__S) ) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__F)) ) ) ) ).
fof('Topology.TopologicalSpaces.open_finite_indexed_intersection',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V1__A)
=> ( ! [V4__a] :
( t(V4__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,happ(V2__F,V4__a)) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_full',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t))) ) ).
fof('Topology.TopologicalSpaces.open_indexed_union',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)
=> ( ! [V3__a] :
( t(V3__a,V1__A)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,happ(V2__F,V3__a)) )
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__F)) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_intersection2',axiom,
! [V0__t] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__t)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__U)
=> ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V2__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V1__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,V2__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__t,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__t),V1__U,V2__V)) ) ) ) ) ) ).
fof('Topology.TopologicalSpaces.open_union2',axiom,
! [V0__X] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V0__X)
=> ! [V1__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U)
=> ! [V2__V] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V2__V)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V1__U)
=> ( cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,V2__V)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(V0__X,cCoq_2eSets_2eEnsembles_2eUnion___24a3(cTopology_2eTopologicalSpaces_2epoint__set___24a1(V0__X),V1__U,V2__V)) ) ) ) ) ) ).
fof('ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble_is_identity',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( c_24__type__2___24t(V0__X,V1__P)
=> cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__4708___24a2(V0__X,V1__P)) = V1__P ) ) ).
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.Families.empty_family_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T))) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__T) ) ).
fof('ZornsLemma.Families.family_intersection_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__x] :
( t(V2__x,V0__T)
=> ( ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V3__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V3__S,V2__x) ) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V1__F),V2__x) ) ) ) ) ).
fof('ZornsLemma.Families.family_union_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V2__S)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V2__S,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V1__F),V3__x) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.FiniteT_ind',axiom,
! [V0__P] :
( c_24__type__391___24t(V0__P)
=> ( p(happ(V0__P,c_24False))
=> ( ! [V2__T] :
( cType___24t(V2__T)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V2__T)
=> ( p(happ(V0__P,V2__T))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eoption___24a1(V2__T))) ) ) )
=> ( ! [V3__X] :
( cType___24t(V3__X)
=> ! [V4__Y] :
( cType___24t(V4__Y)
=> ! [V5__f] :
( c_24__type__398___24t(V3__X,V4__Y,V5__f)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V3__X)
=> ( p(happ(V0__P,V3__X))
=> ( cZornsLemma_2eFunctionProperties_2einvertible___24a3(V3__X,V4__Y,V5__f)
=> p(happ(V0__P,V4__Y)) ) ) ) ) ) )
=> ! [V4__T] :
( cType___24t(V4__T)
=> ( cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V4__T)
=> p(happ(V0__P,V4__T)) ) ) ) ) ) ) ).
fof('ZornsLemma.FiniteTypes.empty_finite',axiom,
cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(c_24False) ).
fof('ZornsLemma.FunctionProperties.intro_invertible',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__398___24t(V0__X,V1__Y,V2__f)
=> ! [V3__g] :
( c_24__type__4812___24t(V0__X,V1__Y,V3__g)
=> ( ! [V4__x] :
( t(V4__x,V0__X)
=> happ(V3__g,happ(V2__f,V4__x)) = V4__x )
=> ( ! [V5__y] :
( t(V5__y,V1__Y)
=> happ(V2__f,happ(V3__g,V5__y)) = V5__y )
=> cZornsLemma_2eFunctionProperties_2einvertible___24a3(V0__X,V1__Y,V2__f) ) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.empty_indexed_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(c_24False,V0__T,V1__F)
=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(c_24False,V0__T,V1__F) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__T) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_intersection_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V0__A,V1__T,V2__F)
=> ! [V3__x] :
( t(V3__x,V1__T)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,happ(V2__F,V4__a),V3__x) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V0__A,V1__T,V2__F),V3__x) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_to_family_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,V0__T,V2__F)
=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__A,V0__T,V2__F) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V0__T,V1__A,V2__F)) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_to_family_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__A,V0__T,V2__F)
=> cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__A,V0__T,V2__F) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V0__T,V1__A,V2__F)) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.indexed_union_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__T] :
( cType___24t(V1__T)
=> ! [V2__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V0__A,V1__T,V2__F)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__x] :
( t(V4__x,V1__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,happ(V2__F,V3__a),V4__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__T,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V0__A,V1__T,V2__F),V4__x) ) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.sub_indexed_intersection',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__T] :
( cType___24t(V2__T)
=> ! [V3__f] :
( c_24__type__398___24t(V0__A,V1__B,V3__f)
=> ! [V4__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__B,V2__T,V4__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V2__T,cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V1__B,V2__T,V4__F),cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V0__A,V2__T,c_24__let__5__subF__4825___24a5(V0__A,V1__B,V2__T,V3__f,V4__F))) ) ) ) ) ) ).
fof('ZornsLemma.IndexedFamilies.sub_indexed_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__T] :
( cType___24t(V2__T)
=> ! [V3__f] :
( c_24__type__398___24t(V0__A,V1__B,V3__f)
=> ! [V4__F] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V1__B,V2__T,V4__F)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V2__T,cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V0__A,V2__T,c_24__let__5__subF__4822___24a5(V0__A,V1__B,V2__T,V3__f,V4__F)),cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V1__B,V2__T,V4__F)) ) ) ) ) ) ).
fof('$adef_$_fix_37529_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__37529__v__CANONICAL__0,V_24X1) = c_24__fix__37529__v__CANONICAL__0___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('$adef_Coq.Arith.PeanoNat.Nat.eqf_$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('$adef_Coq.NArith.Ndigits.eqf_$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('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$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('$adef_ZornsLemma.Families.FamilyUnion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Empty_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eEmpty__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$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('$adef_Coq.Reals.Rfunctions.ZintPos_$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('$adef_Coq.Init.Datatypes.implb_$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('$adef_Coq.Sets.Cpo.Upper_Bound_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eUpper__Bound,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.setoid_ring.Ring_polynom.Pc_$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('$adef_Coq.micromega.RMicromega.CMult_$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('$adef_$_case_Coq.Numbers.BinNums.positive$37513_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2437513,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2437513___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('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ZornsLemma.FiniteTypes.FiniteT_$a1',axiom,
! [V_24X1] :
( p(happ(cZornsLemma_2eFiniteTypes_2eFiniteT,V_24X1))
<=> cZornsLemma_2eFiniteTypes_2eFiniteT___24a1(V_24X1) ) ).
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('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_4708_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__4708,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__4708___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Sets.Relations_1.same_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eRelations__1_2esame__relation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eRelations__1_2esame__relation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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_ZornsLemma.Families.FamilyIntersection_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.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.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_$_lam_23691_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__23691,V_24X1),V_24X2) = c_24__lam__23691___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.In_$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('$adef_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on_$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('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Datatypes.app_$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('$adef_Coq.Init.Specif.existT_$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('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_$_lam_157542_$a1',axiom,
! [V_24X1] : happ(c_24__lam__157542,V_24X1) = c_24__lam__157542___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.IndexedFamilies.ImageFamily_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eImageFamily,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eImageFamily___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Topology.TopologicalSpaces.open_$a1',axiom,
! [V_24X1] : happ(cTopology_2eTopologicalSpaces_2eopen,V_24X1) = cTopology_2eTopologicalSpaces_2eopen___24a1(V_24X1) ).
fof('$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.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.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.Relations.Relation_Operators.symprod_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Sets.Cpo.Directed_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eDirected,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eDirected___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Topology.TopologicalSpaces.closed_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eTopologicalSpaces_2eclosed,V_24X1),V_24X2))
<=> cTopology_2eTopologicalSpaces_2eclosed___24a2(V_24X1,V_24X2) ) ).
fof('$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.Subtract_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSubtract,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_Coq.Sets.Ensembles.Complement_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_26531_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__26531,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__26531___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_case_Coq.Numbers.BinNums.Z$28624_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428624,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2428624___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Specif.proj1_sig_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).
fof('$adef_$_lam_150754_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__150754,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__150754___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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.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.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.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.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.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.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eComplement___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.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.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_5_subF_4825_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__5__subF__4825,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__5__subF__4825___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Sets.Partial_Order.Rel_of_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eRel__of,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Strict_Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eStrict__Included,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Init.Datatypes.identity_$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('$adef_Coq.Init.Datatypes.id_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.EnvRing.zmon_$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('$adef_Coq.Init.Nat.eqb_$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('$adef_Hammer.Tactics.Reconstr.rdone_$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('$adef_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on,V_24X1) = cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on___24a1(V_24X1) ).
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('$adef_Coq.Lists.SetoidList.transpose2_$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('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$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('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Forall2_$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('$adef_ZornsLemma.Families.FamilyUnion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyUnion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$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('$adef_InteriorsClosures.closure_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cInteriorsClosures_2eclosure,V_24X1),V_24X2) = cInteriorsClosures_2eclosure___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('$adef_Coq.Reals.Rdefinitions.Rmult_$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('$adef_Coq.Sets.Ensembles.Couple_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eCouple,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eCouple___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$28443_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2428443,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2428443___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.ZArith.Znumtheory.Bezout_$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('$adef_Coq.setoid_ring.Ring_theory.Morphism_$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('$adef_Coq.setoid_ring.Ring_theory.IDphi_$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('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
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('$adef_Topology.TopologicalSpaces.open_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cTopology_2eTopologicalSpaces_2eopen,V_24X1),V_24X2))
<=> cTopology_2eTopologicalSpaces_2eopen___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('$adef_Coq.Sets.Ensembles.Setminus_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSetminus,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eSetminus___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_InteriorsClosures.interior_closure_relations.idempotent_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cInteriorsClosures_2einterior__closure__relations_2eidempotent,V_24X1),V_24X2))
<=> cInteriorsClosures_2einterior__closure__relations_2eidempotent___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___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('$adef_Coq.micromega.RMicromega.CPlus_$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('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___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('$adef_Coq.Sets.Cpo.Complete_$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('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).
fof('$adef_$_prop_37370_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37370,V_24X1),V_24X2),V_24X3) = c_24__prop__37370___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.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.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.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.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.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.Sets.Cpo.Lower_Bound_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLower__Bound,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.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.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_ZornsLemma.IndexedFamilies.IndexedUnion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedUnion,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_let_5_subF_4825_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__5__subF__4825,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__5__subF__4825___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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_157541_$a1',axiom,
! [V_24X1] : happ(c_24__lam__157541,V_24X1) = c_24__lam__157541___24a1(V_24X1) ).
fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_ZornsLemma.IndexedFamilies.IndexedUnion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedUnion,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eIndexedUnion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_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_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_$_let_5_subF_4822_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__let__5__subF__4822,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__let__5__subF__4822___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_prop_37352_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37352,V_24X1),V_24X2),V_24X3) = c_24__prop__37352___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_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.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_$_fix_28488_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__28488__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__28488__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Included_$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('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_InteriorsClosures.interior_$a1',axiom,
! [V_24X1] : happ(cInteriorsClosures_2einterior,V_24X1) = cInteriorsClosures_2einterior___24a1(V_24X1) ).
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('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic.eq_rect_$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('$adef_Coq.setoid_ring.Ring_polynom.PEO_$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('$adef_Coq.Numbers.BinNums.xO_$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('$adef_ZornsLemma.Families.Family_$a1',axiom,
! [V_24X1] : happ(cZornsLemma_2eFamilies_2eFamily,V_24X1) = cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1) ).
fof('$adef_InteriorsClosures.closure_$a1',axiom,
! [V_24X1] : happ(cInteriorsClosures_2eclosure,V_24X1) = cInteriorsClosures_2eclosure___24a1(V_24X1) ).
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('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$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('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_Coq.micromega.OrderedRing.SOR_$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('$adef_InteriorsClosures.interior_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cInteriorsClosures_2einterior,V_24X1),V_24X2) = cInteriorsClosures_2einterior___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.NArith.BinNatDef.N.min_$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('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$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('$adef_Coq.Sets.Ensembles.Intersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Cpo.Lub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLub,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eLub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_ZornsLemma.FunctionProperties.surjective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2esurjective,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2esurjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.In_$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('$adef_ZornsLemma.IndexedFamilies.IndexedIntersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Partial_Order.Strict_Rel_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_4708_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__4708,V_24X1),V_24X2) = c_24__lam__4708___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_Coq.Structures.GenericMinMax.gmin_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmin,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.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.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$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.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$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.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_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.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_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_Topology.TopologicalSpaces.point_set_$a1',axiom,
! [V_24X1] : happ(cTopology_2eTopologicalSpaces_2epoint__set,V_24X1) = cTopology_2eTopologicalSpaces_2epoint__set___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Partial_Order.Carrier_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePartial__Order_2eCarrier,V_24X1) = cCoq_2eSets_2ePartial__Order_2eCarrier___24a1(V_24X1) ).
fof('$adef_$_lam_150754_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__150754,V_24X1),V_24X2) = c_24__lam__150754___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Bottom_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eBottom,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eBottom___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Lists.SetoidList.transpose_$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('$adef_Coq.Init.Datatypes.nat_rect_$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('$adef_Coq.Init.Datatypes.inr_$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('$adef_$_let_var_6_p_34169_34171_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__34169__34171,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__34169__34171___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.Sets.Ensembles.Setminus_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSetminus,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.Sets.Relations_1.contains_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eRelations__1_2econtains,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eRelations__1_2econtains___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_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_Topology.TopologicalSpaces.Build_TopologicalSpace_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace,V_24X1),V_24X2) = cTopology_2eTopologicalSpaces_2eBuild__TopologicalSpace___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$36138_$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_2436138,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_2436138___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Operators_2eDesc___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('$adef_Coq.Sets.Ensembles.Triple_$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('$adef_Coq.Sets.Partial_Order.Strict_Rel_of_$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('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$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('$adef_$_prop_37368_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37368,V_24X1),V_24X2) = c_24__prop__37368___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.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.Init.Peano.IsSucc_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
<=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).
fof('$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_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.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_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.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Powerset.Power_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$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.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$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_$_prop_37348_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__37348,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__37348___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_37398_$a1',axiom,
! [V_24X1] : happ(c_24__lam__37398,V_24X1) = c_24__lam__37398___24a1(V_24X1) ).
fof('$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_ZornsLemma.IndexedFamilies.IndexedIntersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedIntersection,V_24X1),V_24X2),V_24X3) = cZornsLemma_2eIndexedFamilies_2eIndexedIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Sets.Relations_1.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_37350_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37350,V_24X1),V_24X2),V_24X3) = c_24__prop__37350___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Sets.Finite_sets.Finite_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eFinite__sets_2eFinite,V_24X1),V_24X2))
<=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on___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('$adef_$_prop_37369_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37369,V_24X1),V_24X2),V_24X3) = c_24__prop__37369___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_ZornsLemma.FunctionProperties.injective_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2einjective,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2einjective___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_lam_26539_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__26539,V_24X1),V_24X2),V_24X3) = c_24__lam__26539___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Powerset.Power_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2ePowerset_2ePower__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2ePowerset_2ePower__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.setoid_ring.Field_theory.FEopp_$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('$adef_Coq.Init.Specif.exist2_$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('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.xorb_$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('$adef_$_prop_37353_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37353,V_24X1),V_24X2),V_24X3) = c_24__prop__37353___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Sets.Ensembles.Triple_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eTriple,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eEnsembles_2eTriple___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).
fof('$adef_Coq.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.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_ZornsLemma.Families.FamilyIntersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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_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_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.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_$_lam_26539_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__26539,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__26539___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_150748_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__150748,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__150748___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_ZornsLemma.FunctionProperties.invertible_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFunctionProperties_2einvertible,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFunctionProperties_2einvertible___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_ZornsLemma.IndexedFamilies.IndexedFamily_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eIndexedFamilies_2eIndexedFamily,V_24X1),V_24X2) = cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V_24X1,V_24X2) ).
fof('$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.Init.Byte.byte_of_byte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).
fof('$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.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.Arith.Wf_nat.ltof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.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.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Relations_1.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$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.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_$_lam_26531_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__26531,V_24X1),V_24X2),V_24X3) = c_24__lam__26531___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Specif.exist_$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('$adef_Coq.ZArith.BinInt.Z.le_$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('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$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('$adef_$_let_5_subF_4822_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__let__5__subF__4822,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__let__5__subF__4822___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$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.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.Cpo.Glb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eGlb,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eGlb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_37354_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__37354,V_24X1),V_24X2) = c_24__prop__37354___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.list$28356_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2428356,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2428356___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.Sets.Ensembles.Add_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eAdd,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_37349_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37349,V_24X1),V_24X2),V_24X3) = c_24__prop__37349___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_prop_37351_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__37351,V_24X1),V_24X2),V_24X3) = c_24__prop__37351___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Partial_Order.Rel_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eRel__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eRel__of___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('$adef_$_lam_150748_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__150748,V_24X1),V_24X2) = c_24__lam__150748___24a2(V_24X1,V_24X2) ).
fof('$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.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.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.Sets.Cpo.Conditionally_complete_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete,V_24X1),V_24X2))
<=> cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.nat$28629_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2428629___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$28607_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2428607,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2428607___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
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('$adef_Coq.Sets.Ensembles.Strict_Included_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eStrict__Included,V_24X1) = cCoq_2eSets_2eEnsembles_2eStrict__Included___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Included_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1) = cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V_24X1) ).
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('$adef_Coq.Init.Datatypes.fst_$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('$adef_$_let_var_6_p_34167_34170_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__34167__34170,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__34167__34170___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_23691_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__23691,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__23691___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Logic.ClassicalFacts.Minimal_$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('$adef_Coq.PArith.BinPos.Pos.PeanoView_$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('$adef_$_lam_37398_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__37398,V_24X1),V_24X2) = c_24__lam__37398___24a2(V_24X1,V_24X2) ).
fof('$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.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_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.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$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.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_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.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_$_case_Coq.Init.Datatypes.nat$2680_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_242680,V_24X1),V_24X2),V_24X3))
<=> c_24__case__Coq_2eInit_2eDatatypes_2enat_242680___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Image.Im_$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('$adef_Coq.Init.Specif.sig2_$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('$adef_Coq.setoid_ring.Field_theory.FEpow_$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('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$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('$adef_Coq.NArith.BinNat.N.le_$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('$adef_Coq.Sets.Ensembles.Ensemble_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEnsemble,V_24X1) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1) ).
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('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).
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_4379',axiom,
! [V_24Y] :
( c_24__type__4379___24t(V_24Y)
<=> t(V_24Y,c_24__type__4379) ) ).
fof('$tdef_$_type_34655',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34655___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34655___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_37081',axiom,
! [V_24Y] :
( c_24__type__37081___24t(V_24Y)
<=> t(V_24Y,c_24__type__37081) ) ).
fof('$tdef_$_type_37061',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__37061___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__37061___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_12571',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12571___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12571___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26523',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26523___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26523___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9292',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9292___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9292___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35983',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35983___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35983___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_24875',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__24875___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__24875___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_8526',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8526___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8526___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23530',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23530___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23530___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_9457',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9457___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9457___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22916',axiom,
! [V_24Y] :
( c_24__type__22916___24t(V_24Y)
<=> t(V_24Y,c_24__type__22916) ) ).
fof('$tdef_$_type_4434',axiom,
! [V_24Y] :
( c_24__type__4434___24t(V_24Y)
<=> t(V_24Y,c_24__type__4434) ) ).
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_27822',axiom,
! [V_24Y] :
( c_24__type__27822___24t(V_24Y)
<=> t(V_24Y,c_24__type__27822) ) ).
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_$_type_4728',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4728___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4728___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12540',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12540___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12540___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4460',axiom,
! [V_24Y] :
( c_24__type__4460___24t(V_24Y)
<=> t(V_24Y,c_24__type__4460) ) ).
fof('$tdef_$_type_23015',axiom,
! [V_24Y] :
( c_24__type__23015___24t(V_24Y)
<=> t(V_24Y,c_24__type__23015) ) ).
fof('$tdef_$_type_9346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9346___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_26282',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26282___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26282___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2855',axiom,
! [V_24Y] :
( c_24__type__2855___24t(V_24Y)
<=> t(V_24Y,c_24__type__2855) ) ).
fof('$tdef_$_type_4367',axiom,
! [V_24Y] :
( c_24__type__4367___24t(V_24Y)
<=> t(V_24Y,c_24__type__4367) ) ).
fof('$tdef_$_type_2740',axiom,
! [V_24Y] :
( c_24__type__2740___24t(V_24Y)
<=> t(V_24Y,c_24__type__2740) ) ).
fof('$tdef_$_type_9316',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9316___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9316___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_326',axiom,
! [V_24Y] :
( c_24__type__326___24t(V_24Y)
<=> t(V_24Y,c_24__type__326) ) ).
fof('$tdef_$_type_36151',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__36151___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__36151___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2862',axiom,
! [V_24Y] :
( c_24__type__2862___24t(V_24Y)
<=> t(V_24Y,c_24__type__2862) ) ).
fof('$tdef_$_type_33609',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__33609___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__33609___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_26683',axiom,
! [V_24Y] :
( c_24__type__26683___24t(V_24Y)
<=> t(V_24Y,c_24__type__26683) ) ).
fof('$tdef_$_type_104',axiom,
! [V_24Y] :
( c_24__type__104___24t(V_24Y)
<=> t(V_24Y,c_24__type__104) ) ).
fof('$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_36986',axiom,
! [V_24Y] :
( c_24__type__36986___24t(V_24Y)
<=> t(V_24Y,c_24__type__36986) ) ).
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_$_type_4867',axiom,
! [V_24Y] :
( c_24__type__4867___24t(V_24Y)
<=> t(V_24Y,c_24__type__4867) ) ).
fof('$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_4411',axiom,
! [V_24Y] :
( c_24__type__4411___24t(V_24Y)
<=> t(V_24Y,c_24__type__4411) ) ).
fof('$tdef_$_type_26345',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26345___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__26345___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23611',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23611___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23611___24a1(V_24X1)) ) ).
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_23093',axiom,
! [V_24Y] :
( c_24__type__23093___24t(V_24Y)
<=> t(V_24Y,c_24__type__23093) ) ).
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_$_type_23589',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23589___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23589___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23753',axiom,
! [V_24Y] :
( c_24__type__23753___24t(V_24Y)
<=> t(V_24Y,c_24__type__23753) ) ).
fof('$tdef_$_type_29203',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__29203___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__29203___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_23522',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23522___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23522___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_26399',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26399___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__26399___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_4917',axiom,
! [V_24Y] :
( c_24__type__4917___24t(V_24Y)
<=> t(V_24Y,c_24__type__4917) ) ).
fof('$tdef_$_type_12328',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12328___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12328___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2695',axiom,
! [V_24Y] :
( c_24__type__2695___24t(V_24Y)
<=> t(V_24Y,c_24__type__2695) ) ).
fof('$tdef_$_type_22425',axiom,
! [V_24Y] :
( c_24__type__22425___24t(V_24Y)
<=> t(V_24Y,c_24__type__22425) ) ).
fof('$tdef_$_type_4',axiom,
! [V_24Y] :
( c_24__type__4___24t(V_24Y)
<=> t(V_24Y,c_24__type__4) ) ).
fof('$tdef_$_type_23096',axiom,
! [V_24Y] :
( c_24__type__23096___24t(V_24Y)
<=> t(V_24Y,c_24__type__23096) ) ).
fof('$tdef_$_type_27595',axiom,
! [V_24Y] :
( c_24__type__27595___24t(V_24Y)
<=> t(V_24Y,c_24__type__27595) ) ).
fof('$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('$tdef_$_type_34740',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34740___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34740___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_26749',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26749___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26749___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_24793',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__24793___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__24793___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_36852',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36852___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36852___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_5119',axiom,
! [V_24Y] :
( c_24__type__5119___24t(V_24Y)
<=> t(V_24Y,c_24__type__5119) ) ).
fof('$tdef_$_type_37177',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__37177___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__37177___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_9',axiom,
! [V_24Y] :
( c_24__type__9___24t(V_24Y)
<=> t(V_24Y,c_24__type__9) ) ).
fof('$tdef_$_type_9262',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9262___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9262___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5096',axiom,
! [V_24Y] :
( c_24__type__5096___24t(V_24Y)
<=> t(V_24Y,c_24__type__5096) ) ).
fof('$tdef_$_type_1183',axiom,
! [V_24Y] :
( c_24__type__1183___24t(V_24Y)
<=> t(V_24Y,c_24__type__1183) ) ).
fof('$tdef_$_type_36778',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36778___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36778___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_$_type_12445',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12445___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12445___24a2(V_24X1,V_24X2)) ) ).
fof('$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_26511',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26511___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26511___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23562',axiom,
! [V_24Y] :
( c_24__type__23562___24t(V_24Y)
<=> t(V_24Y,c_24__type__23562) ) ).
fof('$tdef_$_type_37436',axiom,
! [V_24Y] :
( c_24__type__37436___24t(V_24Y)
<=> t(V_24Y,c_24__type__37436) ) ).
fof('$tdef_$_type_23099',axiom,
! [V_24Y] :
( c_24__type__23099___24t(V_24Y)
<=> t(V_24Y,c_24__type__23099) ) ).
fof('$tdef_$_type_24200',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__24200___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__24200___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_1036',axiom,
! [V_24Y] :
( c_24__type__1036___24t(V_24Y)
<=> t(V_24Y,c_24__type__1036) ) ).
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_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_$_type_31256',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__31256___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__31256___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.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('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$tdef_$_type_12275',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12275___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12275___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_23012',axiom,
! [V_24Y] :
( c_24__type__23012___24t(V_24Y)
<=> t(V_24Y,c_24__type__23012) ) ).
fof('$tdef_$_type_9376',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9376___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9376___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_12449',axiom,
! [V_24Y] :
( c_24__type__12449___24t(V_24Y)
<=> t(V_24Y,c_24__type__12449) ) ).
fof('$tdef_$_type_6225',axiom,
! [V_24Y] :
( c_24__type__6225___24t(V_24Y)
<=> t(V_24Y,c_24__type__6225) ) ).
fof('$tdef_$_type_391',axiom,
! [V_24Y] :
( c_24__type__391___24t(V_24Y)
<=> t(V_24Y,c_24__type__391) ) ).
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_$_type_26793',axiom,
! [V_24Y] :
( c_24__type__26793___24t(V_24Y)
<=> t(V_24Y,c_24__type__26793) ) ).
fof('$tdef_$_type_26596',axiom,
! [V_24Y] :
( c_24__type__26596___24t(V_24Y)
<=> t(V_24Y,c_24__type__26596) ) ).
fof('$tdef_$_type_35498',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__35498___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__35498___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_101',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__101___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__101___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4710',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4710___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4710___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23538',axiom,
! [V_24Y] :
( c_24__type__23538___24t(V_24Y)
<=> t(V_24Y,c_24__type__23538) ) ).
fof('$tdef_$_type_14',axiom,
! [V_24Y] :
( c_24__type__14___24t(V_24Y)
<=> t(V_24Y,c_24__type__14) ) ).
fof('$tdef_$_type_31602',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__31602___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__31602___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_27848',axiom,
! [V_24Y] :
( c_24__type__27848___24t(V_24Y)
<=> t(V_24Y,c_24__type__27848) ) ).
fof('$tdef_$_type_23684',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23684___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23684___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34375',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34375___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34375___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_37415',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37415___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37415___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12544',axiom,
! [V_24Y] :
( c_24__type__12544___24t(V_24Y)
<=> t(V_24Y,c_24__type__12544) ) ).
fof('$tdef_$_type_23447',axiom,
! [V_24Y] :
( c_24__type__23447___24t(V_24Y)
<=> t(V_24Y,c_24__type__23447) ) ).
fof('$tdef_$_type_36075',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__36075___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__36075___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_35933',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35933___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35933___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_24968',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__24968___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__24968___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5850',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__5850___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__5850___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_37532',axiom,
! [V_24Y] :
( c_24__type__37532___24t(V_24Y)
<=> t(V_24Y,c_24__type__37532) ) ).
fof('$tdef_$_type_36939',axiom,
! [V_24Y] :
( c_24__type__36939___24t(V_24Y)
<=> t(V_24Y,c_24__type__36939) ) ).
fof('$tdef_$_type_3526',axiom,
! [V_24Y] :
( c_24__type__3526___24t(V_24Y)
<=> t(V_24Y,c_24__type__3526) ) ).
fof('$tdef_$_type_23606',axiom,
! [V_24X1,V_24Y] :
( c_24__type__23606___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__23606___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1124',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1124___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1124___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36384',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__36384___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__36384___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_5951',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__5951___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__5951___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4924',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4924___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4924___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26065',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__26065___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__26065___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_5086',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__5086___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__5086___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_10096',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__10096___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__10096___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Topology.TopologicalSpaces.TopologicalSpace',axiom,
! [V_24Y] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(V_24Y)
<=> t(V_24Y,cTopology_2eTopologicalSpaces_2eTopologicalSpace) ) ).
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_$_type_33955',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__33955___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__33955___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_29895',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__29895___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__29895___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_34722',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34722___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34722___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_20141',axiom,
! [V_24Y] :
( c_24__type__20141___24t(V_24Y)
<=> t(V_24Y,c_24__type__20141) ) ).
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_$_type_4416',axiom,
! [V_24Y] :
( c_24__type__4416___24t(V_24Y)
<=> t(V_24Y,c_24__type__4416) ) ).
fof('$tdef_$_type_2831',axiom,
! [V_24Y] :
( c_24__type__2831___24t(V_24Y)
<=> t(V_24Y,c_24__type__2831) ) ).
fof('$tdef_$_type_389',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__389___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__389___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6619',axiom,
! [V_24X1,V_24Y] :
( c_24__type__6619___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__6619___24a1(V_24X1)) ) ).
fof('$tdef_$_type_25972',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__25972___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__25972___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30564',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__30564___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__30564___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_23576',axiom,
! [V_24Y] :
( c_24__type__23576___24t(V_24Y)
<=> t(V_24Y,c_24__type__23576) ) ).
fof('$tdef_$_type_23281',axiom,
! [V_24Y] :
( c_24__type__23281___24t(V_24Y)
<=> t(V_24Y,c_24__type__23281) ) ).
fof('$tdef_$_type_3519',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3519___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3519___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34125',axiom,
! [V_24Y] :
( c_24__type__34125___24t(V_24Y)
<=> t(V_24Y,c_24__type__34125) ) ).
fof('$tdef_$_type_1165',axiom,
! [V_24Y] :
( c_24__type__1165___24t(V_24Y)
<=> t(V_24Y,c_24__type__1165) ) ).
fof('$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_150750',axiom,
! [V_24Y] :
( c_24__type__150750___24t(V_24Y)
<=> t(V_24Y,c_24__type__150750) ) ).
fof('$tdef_$_type_34414',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34414___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34414___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_24618',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__24618___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__24618___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27607',axiom,
! [V_24Y] :
( c_24__type__27607___24t(V_24Y)
<=> t(V_24Y,c_24__type__27607) ) ).
fof('$tdef_$_type_26765',axiom,
! [V_24Y] :
( c_24__type__26765___24t(V_24Y)
<=> t(V_24Y,c_24__type__26765) ) ).
fof('$tdef_$_type_26500',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26500___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26500___24a2(V_24X1,V_24X2)) ) ).
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_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('$tdef_$_type_2857',axiom,
! [V_24Y] :
( c_24__type__2857___24t(V_24Y)
<=> t(V_24Y,c_24__type__2857) ) ).
fof('$tdef_$_type_10930',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__10930___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__10930___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_147',axiom,
! [V_24X1,V_24Y] :
( c_24__type__147___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__147___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35248',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__35248___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__35248___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('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_36887',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36887___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36887___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_398',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__398___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__398___24a2(V_24X1,V_24X2)) ) ).
fof('$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_34130',axiom,
! [V_24Y] :
( c_24__type__34130___24t(V_24Y)
<=> t(V_24Y,c_24__type__34130) ) ).
fof('$tdef_$_type_2782',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2782___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2782___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_2864',axiom,
! [V_24Y] :
( c_24__type__2864___24t(V_24Y)
<=> t(V_24Y,c_24__type__2864) ) ).
fof('$tdef_$_type_35734',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__35734___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__35734___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_30910',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__30910___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__30910___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_22468',axiom,
! [V_24Y] :
( c_24__type__22468___24t(V_24Y)
<=> t(V_24Y,c_24__type__22468) ) ).
fof('$tdef_$_type_1057',axiom,
! [V_24Y] :
( c_24__type__1057___24t(V_24Y)
<=> t(V_24Y,c_24__type__1057) ) ).
fof('$tdef_$_type_26690',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26690___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26690___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8863',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8863___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__8863___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_324',axiom,
! [V_24Y] :
( c_24__type__324___24t(V_24Y)
<=> t(V_24Y,c_24__type__324) ) ).
fof('$tdef_$_type_26818',axiom,
! [V_24Y] :
( c_24__type__26818___24t(V_24Y)
<=> t(V_24Y,c_24__type__26818) ) ).
fof('$tdef_$_type_27804',axiom,
! [V_24Y] :
( c_24__type__27804___24t(V_24Y)
<=> t(V_24Y,c_24__type__27804) ) ).
fof('$tdef_$_type_27798',axiom,
! [V_24Y] :
( c_24__type__27798___24t(V_24Y)
<=> t(V_24Y,c_24__type__27798) ) ).
fof('$tdef_$_type_9106',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__9106___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__9106___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_33286',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__33286___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__33286___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_2829',axiom,
! [V_24Y] :
( c_24__type__2829___24t(V_24Y)
<=> t(V_24Y,c_24__type__2829) ) ).
fof('$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_$_type_36817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36817___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22318',axiom,
! [V_24Y] :
( c_24__type__22318___24t(V_24Y)
<=> t(V_24Y,c_24__type__22318) ) ).
fof('$tdef_$_type_24525',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__24525___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__24525___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_9484',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9484___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9484___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9400___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22558',axiom,
! [V_24Y] :
( c_24__type__22558___24t(V_24Y)
<=> t(V_24Y,c_24__type__22558) ) ).
fof('$tdef_$_type_36260',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__36260___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__36260___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_8409',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8409___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8409___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_5558',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5558___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5558___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20118',axiom,
! [V_24Y] :
( c_24__type__20118___24t(V_24Y)
<=> t(V_24Y,c_24__type__20118) ) ).
fof('$tdef_$_type_445',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__445___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__445___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_352',axiom,
! [V_24Y] :
( c_24__type__352___24t(V_24Y)
<=> t(V_24Y,c_24__type__352) ) ).
fof('$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_34678',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34678___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34678___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22419',axiom,
! [V_24Y] :
( c_24__type__22419___24t(V_24Y)
<=> t(V_24Y,c_24__type__22419) ) ).
fof('$tdef_$_type_37084',axiom,
! [V_24X1,V_24Y] :
( c_24__type__37084___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__37084___24a1(V_24X1)) ) ).
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_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_5038',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__5038___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__5038___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_37387',axiom,
! [V_24Y] :
( c_24__type__37387___24t(V_24Y)
<=> t(V_24Y,c_24__type__37387) ) ).
fof('$tdef_$_type_11764',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__11764___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__11764___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('$tdef_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2)) ) ).
fof('$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_25529',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__25529___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__25529___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34127',axiom,
! [V_24Y] :
( c_24__type__34127___24t(V_24Y)
<=> t(V_24Y,c_24__type__34127) ) ).
fof('$tdef_$_type_37573',axiom,
! [V_24Y] :
( c_24__type__37573___24t(V_24Y)
<=> t(V_24Y,c_24__type__37573) ) ).
fof('$tdef_$_type_36304',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__36304___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__36304___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_12502',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12502___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12502___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4391',axiom,
! [V_24Y] :
( c_24__type__4391___24t(V_24Y)
<=> t(V_24Y,c_24__type__4391) ) ).
fof('$tdef_$_type_26554',axiom,
! [V_24Y] :
( c_24__type__26554___24t(V_24Y)
<=> t(V_24Y,c_24__type__26554) ) ).
fof('$tdef_$_type_27792',axiom,
! [V_24Y] :
( c_24__type__27792___24t(V_24Y)
<=> t(V_24Y,c_24__type__27792) ) ).
fof('$tdef_$_type_26780',axiom,
! [V_24Y] :
( c_24__type__26780___24t(V_24Y)
<=> t(V_24Y,c_24__type__26780) ) ).
fof('$tdef_$_type_27600',axiom,
! [V_24Y] :
( c_24__type__27600___24t(V_24Y)
<=> t(V_24Y,c_24__type__27600) ) ).
fof('$tdef_$_type_34160',axiom,
! [V_24Y] :
( c_24__type__34160___24t(V_24Y)
<=> t(V_24Y,c_24__type__34160) ) ).
fof('$tdef_$_type_27605',axiom,
! [V_24Y] :
( c_24__type__27605___24t(V_24Y)
<=> t(V_24Y,c_24__type__27605) ) ).
fof('$tdef_$_type_23848',axiom,
! [V_24Y] :
( c_24__type__23848___24t(V_24Y)
<=> t(V_24Y,c_24__type__23848) ) ).
fof('$tdef_$_type_22553',axiom,
! [V_24Y] :
( c_24__type__22553___24t(V_24Y)
<=> t(V_24Y,c_24__type__22553) ) ).
fof('$tdef_$_type_12093',axiom,
! [V_24Y] :
( c_24__type__12093___24t(V_24Y)
<=> t(V_24Y,c_24__type__12093) ) ).
fof('$tdef_$_type_20311',axiom,
! [V_24Y] :
( c_24__type__20311___24t(V_24Y)
<=> t(V_24Y,c_24__type__20311) ) ).
fof('$tdef_$_type_6052',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__6052___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__6052___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('$tdef_$_type_34142',axiom,
! [V_24Y] :
( c_24__type__34142___24t(V_24Y)
<=> t(V_24Y,c_24__type__34142) ) ).
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_Coq.micromega.ZMicromega.coneMember',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).
fof('$tdef_$_type_11356',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__11356___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__11356___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_6688',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6688___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6688___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_25715',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__25715___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__25715___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_10309',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__10309___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__10309___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_35623',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__35623___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__35623___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_26543',axiom,
! [V_24X1,V_24Y] :
( c_24__type__26543___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__26543___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8926',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8926___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__8926___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_27482',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__27482___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__27482___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6303',axiom,
! [V_24Y] :
( c_24__type__6303___24t(V_24Y)
<=> t(V_24Y,c_24__type__6303) ) ).
fof('$tdef_$_type_1232',axiom,
! [V_24Y] :
( c_24__type__1232___24t(V_24Y)
<=> t(V_24Y,c_24__type__1232) ) ).
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_$_type_2791',axiom,
! [V_24Y] :
( c_24__type__2791___24t(V_24Y)
<=> t(V_24Y,c_24__type__2791) ) ).
fof('$tdef_$_type_23103',axiom,
! [V_24Y] :
( c_24__type__23103___24t(V_24Y)
<=> t(V_24Y,c_24__type__23103) ) ).
fof('$tdef_$_type_22305',axiom,
! [V_24Y] :
( c_24__type__22305___24t(V_24Y)
<=> t(V_24Y,c_24__type__22305) ) ).
fof('$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_36965',axiom,
! [V_24Y] :
( c_24__type__36965___24t(V_24Y)
<=> t(V_24Y,c_24__type__36965) ) ).
fof('$tdef_$_type_4812',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4812___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4812___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26809',axiom,
! [V_24Y] :
( c_24__type__26809___24t(V_24Y)
<=> t(V_24Y,c_24__type__26809) ) ).
fof('$tdef_$_type_25622',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__25622___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__25622___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_24228',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__24228___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__24228___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_36699',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__36699___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__36699___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36931',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36931___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36931___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_2842',axiom,
! [V_24Y] :
( c_24__type__2842___24t(V_24Y)
<=> t(V_24Y,c_24__type__2842) ) ).
fof('$tdef_$_type_234',axiom,
! [V_24Y] :
( c_24__type__234___24t(V_24Y)
<=> t(V_24Y,c_24__type__234) ) ).
fof('$tdef_$_type_36025',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__36025___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__36025___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_35123',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__35123___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__35123___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_1189',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1189___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1189___24a1(V_24X1)) ) ).
fof('$tdef_$_type_37290',axiom,
! [V_24Y] :
( c_24__type__37290___24t(V_24Y)
<=> t(V_24Y,c_24__type__37290) ) ).
fof('$tdef_$_type_8346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8346___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__8346___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4311',axiom,
! [V_24Y] :
( c_24__type__4311___24t(V_24Y)
<=> t(V_24Y,c_24__type__4311) ) ).
fof('$tdef_$_type_347',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__347___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__347___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34133',axiom,
! [V_24Y] :
( c_24__type__34133___24t(V_24Y)
<=> t(V_24Y,c_24__type__34133) ) ).
fof('$tdef_$_type_21705',axiom,
! [V_24Y] :
( c_24__type__21705___24t(V_24Y)
<=> t(V_24Y,c_24__type__21705) ) ).
fof('$tdef_$_type_11143',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__11143___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__11143___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_26648',axiom,
! [V_24Y] :
( c_24__type__26648___24t(V_24Y)
<=> t(V_24Y,c_24__type__26648) ) ).
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_$_type_27942',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__27942___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__27942___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_12467',axiom,
! [V_24Y] :
( c_24__type__12467___24t(V_24Y)
<=> t(V_24Y,c_24__type__12467) ) ).
fof('$tdef_$_type_12494',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12494___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12494___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_36923',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36923___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36923___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_4323',axiom,
! [V_24Y] :
( c_24__type__4323___24t(V_24Y)
<=> t(V_24Y,c_24__type__4323) ) ).
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_$_type_23533',axiom,
! [V_24Y] :
( c_24__type__23533___24t(V_24Y)
<=> t(V_24Y,c_24__type__23533) ) ).
fof('$tdef_$_type_10717',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__10717___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__10717___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_12547',axiom,
! [V_24X1,V_24Y] :
( c_24__type__12547___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__12547___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24700',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__24700___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__24700___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23823',axiom,
! [V_24Y] :
( c_24__type__23823___24t(V_24Y)
<=> t(V_24Y,c_24__type__23823) ) ).
fof('$tdef_$_type_28636',axiom,
! [V_24Y] :
( c_24__type__28636___24t(V_24Y)
<=> t(V_24Y,c_24__type__28636) ) ).
fof('$tdef_ZornsLemma.Families.Family',axiom,
! [V_24X1,V_24Y] :
( cZornsLemma_2eFamilies_2eFamily___24t(V_24X1,V_24Y)
<=> t(V_24Y,cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26506',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26506___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26506___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12577',axiom,
! [V_24Y] :
( c_24__type__12577___24t(V_24Y)
<=> t(V_24Y,c_24__type__12577) ) ).
fof('$tdef_$_type_438',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__438___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__438___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_26495',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26495___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26495___24a2(V_24X1,V_24X2)) ) ).
fof('$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_27789',axiom,
! [V_24Y] :
( c_24__type__27789___24t(V_24Y)
<=> t(V_24Y,c_24__type__27789) ) ).
fof('$tdef_$_type_25890',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__25890___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__25890___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_37186',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__37186___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__37186___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_31948',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__31948___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__31948___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_34696',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34696___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34696___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_26219',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26219___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__26219___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_37392',axiom,
! [V_24Y] :
( c_24__type__37392___24t(V_24Y)
<=> t(V_24Y,c_24__type__37392) ) ).
fof('$tdef_$_type_23596',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__23596___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__23596___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Sets.Partial_Order.Rel',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2ePartial__Order_2eRel___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2ePartial__Order_2eRel___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22309',axiom,
! [V_24Y] :
( c_24__type__22309___24t(V_24Y)
<=> t(V_24Y,c_24__type__22309) ) ).
fof('$tdef_$_type_1052',axiom,
! [V_24Y] :
( c_24__type__1052___24t(V_24Y)
<=> t(V_24Y,c_24__type__1052) ) ).
fof('$tdef_$_type_26462',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__26462___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__26462___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_32963',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__32963___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__32963___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_28009',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28009___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28009___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11959',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__11959___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__11959___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_5760',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5760___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5760___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_28158',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28158___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28158___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_27967',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__27967___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__27967___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_4593',axiom,
! [V_24Y] :
( c_24__type__4593___24t(V_24Y)
<=> t(V_24Y,c_24__type__4593) ) ).
fof('$tdef_$_type_25302',axiom,
! [V_24Y] :
( c_24__type__25302___24t(V_24Y)
<=> t(V_24Y,c_24__type__25302) ) ).
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_$_type_22242',axiom,
! [V_24Y] :
( c_24__type__22242___24t(V_24Y)
<=> t(V_24Y,c_24__type__22242) ) ).
fof('$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_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_25797',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__25797___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__25797___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_302',axiom,
! [V_24Y] :
( c_24__type__302___24t(V_24Y)
<=> t(V_24Y,c_24__type__302) ) ).
fof('$tdef_$_type_35373',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__35373___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__35373___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('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_23905',axiom,
! [V_24Y] :
( c_24__type__23905___24t(V_24Y)
<=> t(V_24Y,c_24__type__23905) ) ).
fof('$tdef_$_type_34632',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34632___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34632___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_26659',axiom,
! [V_24Y] :
( c_24__type__26659___24t(V_24Y)
<=> t(V_24Y,c_24__type__26659) ) ).
fof('$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_30218',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__30218___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__30218___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_23466',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23466___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23466___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_36689',axiom,
! [V_24Y] :
( c_24__type__36689___24t(V_24Y)
<=> t(V_24Y,c_24__type__36689) ) ).
fof('$tdef_$_type_9043',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__9043___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__9043___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_ZornsLemma.IndexedFamilies.IndexedFamily',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cZornsLemma_2eIndexedFamilies_2eIndexedFamily___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34202',axiom,
! [V_24Y] :
( c_24__type__34202___24t(V_24Y)
<=> t(V_24Y,c_24__type__34202) ) ).
fof('$tdef_$_type_8589',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8589___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__8589___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_34181',axiom,
! [V_24Y] :
( c_24__type__34181___24t(V_24Y)
<=> t(V_24Y,c_24__type__34181) ) ).
fof('$tdef_$_type_4737',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4737___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4737___24a1(V_24X1)) ) ).
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_$_type_28060',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28060___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28060___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_6924',axiom,
! [V_24Y] :
( c_24__type__6924___24t(V_24Y)
<=> t(V_24Y,c_24__type__6924) ) ).
fof('$tdef_$_type_11551',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__11551___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__11551___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_26714',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26714___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26714___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_23548',axiom,
! [V_24Y] :
( c_24__type__23548___24t(V_24Y)
<=> t(V_24Y,c_24__type__23548) ) ).
fof('$tdef_$_type_32271',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__32271___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__32271___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_5659',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5659___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5659___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_36638',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__36638___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__36638___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_23487',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__23487___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__23487___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6674',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6674___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6674___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8472',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8472___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8472___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_36598',axiom,
! [V_24Y] :
( c_24__type__36598___24t(V_24Y)
<=> t(V_24Y,c_24__type__36598) ) ).
fof('$tdef_$_type_35883',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__35883___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__35883___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_12234',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12234___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12234___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_36896',axiom,
! [V_24Y] :
( c_24__type__36896___24t(V_24Y)
<=> t(V_24Y,c_24__type__36896) ) ).
fof('$tdef_$_type_24169',axiom,
! [V_24Y] :
( c_24__type__24169___24t(V_24Y)
<=> t(V_24Y,c_24__type__24169) ) ).
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_$_type_27463',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__27463___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__27463___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22239',axiom,
! [V_24Y] :
( c_24__type__22239___24t(V_24Y)
<=> t(V_24Y,c_24__type__22239) ) ).
fof('$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_10504',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__10504___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__10504___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_23600',axiom,
! [V_24Y] :
( c_24__type__23600___24t(V_24Y)
<=> t(V_24Y,c_24__type__23600) ) ).
fof('$tdef_$_type_36340',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__36340___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__36340___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_12510',axiom,
! [V_24Y] :
( c_24__type__12510___24t(V_24Y)
<=> t(V_24Y,c_24__type__12510) ) ).
fof('$tdef_$_type_12318',axiom,
! [V_24Y] :
( c_24__type__12318___24t(V_24Y)
<=> t(V_24Y,c_24__type__12318) ) ).
fof('$tdef_$_type_1180',axiom,
! [V_24Y] :
( c_24__type__1180___24t(V_24Y)
<=> t(V_24Y,c_24__type__1180) ) ).
fof('$tdef_$_type_97',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__97___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__97___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32617',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__32617___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__32617___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('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_37410',axiom,
! [V_24Y] :
( c_24__type__37410___24t(V_24Y)
<=> t(V_24Y,c_24__type__37410) ) ).
fof('$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_8989',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8989___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__8989___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_150887',axiom,
! [V_24Y] :
( c_24__type__150887___24t(V_24Y)
<=> t(V_24Y,c_24__type__150887) ) ).
fof('$tdef_$_type_34453',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34453___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34453___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_20146',axiom,
! [V_24Y] :
( c_24__type__20146___24t(V_24Y)
<=> t(V_24Y,c_24__type__20146) ) ).
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_$_type_24432',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__24432___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__24432___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Vectors.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_$_type_59',axiom,
! [V_24Y] :
( c_24__type__59___24t(V_24Y)
<=> t(V_24Y,c_24__type__59) ) ).
fof('$tdef_$_type_120',axiom,
! [V_24Y] :
( c_24__type__120___24t(V_24Y)
<=> t(V_24Y,c_24__type__120) ) ).
fof('$tdef_$_type_27502',axiom,
! [V_24Y] :
( c_24__type__27502___24t(V_24Y)
<=> t(V_24Y,c_24__type__27502) ) ).
fof('$tdef_$_type_9433',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9433___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9433___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27796',axiom,
! [V_24Y] :
( c_24__type__27796___24t(V_24Y)
<=> t(V_24Y,c_24__type__27796) ) ).
fof('$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_$_type_22511',axiom,
! [V_24Y] :
( c_24__type__22511___24t(V_24Y)
<=> t(V_24Y,c_24__type__22511) ) ).
fof('$tdef_$_type_29549',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__29549___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__29549___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_23050',axiom,
! [V_24Y] :
( c_24__type__23050___24t(V_24Y)
<=> t(V_24Y,c_24__type__23050) ) ).
fof('$tdef_$_type_34609',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34609___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34609___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).
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_$_type_37469',axiom,
! [V_24Y] :
( c_24__type__37469___24t(V_24Y)
<=> t(V_24Y,c_24__type__37469) ) ).
fof('$tdef_$_type_25305',axiom,
! [V_24Y] :
( c_24__type__25305___24t(V_24Y)
<=> t(V_24Y,c_24__type__25305) ) ).
fof('$tdef_$_type_9883',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__9883___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__9883___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_12338',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__12338___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__12338___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6695',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6695___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6695___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6153',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6153___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6153___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4842',axiom,
! [V_24Y] :
( c_24__type__4842___24t(V_24Y)
<=> t(V_24Y,c_24__type__4842) ) ).
fof('$tdef_$_type_34998',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__34998___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__34998___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_37069',axiom,
! [V_24Y] :
( c_24__type__37069___24t(V_24Y)
<=> t(V_24Y,c_24__type__37069) ) ).
fof('$tdef_$_type_24119',axiom,
! [V_24Y] :
( c_24__type__24119___24t(V_24Y)
<=> t(V_24Y,c_24__type__24119) ) ).
fof('_HAMMER_GOAL',conjecture,
cInteriorsClosures_2einterior__closure__relations_2eidempotent___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)),c_24__lam__157542) ).
%------------------------------------------------------------------------------