TPTP Problem File: SEV629+1.p
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%------------------------------------------------------------------------------
% File : SEV629+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnSets set subset refl
% 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 : HahnSets.set.subset.refl.p [Kal26]
% Status : Theorem
% Rating : 0.57 v9.3.0
% Syntax : Number of formulae : 2963 (1234 unt; 0 def)
% Number of atoms : 9939 (2577 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 7080 ( 104 ~; 754 |;1744 &)
% (1170 <=>;3308 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 633 ( 632 usr; 0 prp; 1-23 aty)
% Number of functors : 1692 (1692 usr;1131 con; 0-22 aty)
% Number of variables : 9575 (8869 !; 706 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.list$19559',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2419646___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419559___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__19563] :
( t(Vvar__1___24Anonymous__19563,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__19564] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__19564)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419646___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19563,Vvar__2___24Anonymous__19564)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419559___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19563,c_24__fix__19691__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__19564,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$19646',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419646___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__19650] :
( t(Vvar__1___24Anonymous__19650,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__19651] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__19651)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19650,Vvar__2___24Anonymous__19651)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2419646___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19650,c_24__fix__19691__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__19651,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$29196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2429196___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29197] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29197)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29197)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2429196___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__29197)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$29218',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29219] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29219)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29219)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__29219)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$24453',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__24466___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__24458] :
( t(Vvar__2___24Anonymous__24458,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__24459] :
( t(Vvar__3___24Anonymous__24459,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__24458,Vvar__3___24Anonymous__24459)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2424453___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__24458)),Vvar__3___24Anonymous__24459)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$29213',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2429213___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29214)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29214)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2429213___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29214) )
| ? [Vvar__0___24Anonymous__29215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29215)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29215)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2429213___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29215) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$32314',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__32315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32315)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32315)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2432314___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__32330__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__32315)) )
| ? [Vvar__0___24Anonymous__32322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32322)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32322)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2432314___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32322) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2432314___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_$_let_var_6_p_12650_12653',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12649] : c_24__let__var__6__p__12650__12653___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12649) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12649) ).
fof('$_def_$_let_var_6_p_12652_12654',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12651] : c_24__let__var__6__p__12652__12654___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12651) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12651) ).
fof('$_def_Coq.Arith.Between.in_int',axiom,
! [V0__p,V1__q,V2__r] :
( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
<=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r)
& cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q) ) ) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__30887] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30887)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30887)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__30888] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30888)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30888)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30891] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30891)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30891)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__30888,Vvar__0___24Anonymous__30891) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
& V1__y = cCoq_2eInit_2eNat_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eq',axiom,
cCoq_2eArith_2ePeanoNat_2eNat_2eeq = c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.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__35184___24a1(V0__A)) ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__33737] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33737)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33737)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__33737,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Arith.Wf_nat.gtof',axiom,
! [V0__A,V1__f,V2__a,V3__b] :
( cCoq_2eArith_2eWf__nat_2egtof___24a4(V0__A,V1__f,V2__a,V3__b)
<=> cCoq_2eInit_2ePeano_2egt___24a2(happ(V1__f,V3__b),happ(V1__f,V2__a)) ) ).
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.Bool.Zerob.zerob',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__25946] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25946)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25946)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__10413] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__10413)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__10413) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26405] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__26405)
& ? [Vvar__1___24Anonymous__26406] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__26406)
& ? [Vvar__2___24Anonymous__26407] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__26407)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__26405,Vvar__1___24Anonymous__26406,Vvar__2___24Anonymous__26407)
& ( ? [Vvar__0___24Anonymous__26420] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26420)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26420)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__26420,Vvar__2___24Anonymous__26407) )
| ? [Vvar__0___24Anonymous__26421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26421)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26421)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__26421,Vvar__0___24Anonymous__26405) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__26406 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__10414] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__10414)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__10414) ) ).
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('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__30859] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__30859)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__30859,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_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__10527] :
( t(Vvar__1___24Anonymous__10527,V0__A)
& ? [Vvar__2___24Anonymous__10528] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10528)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10527,Vvar__2___24Anonymous__10528)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10527,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__10528,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__32766] :
( t(Vvar__2___24Anonymous__32766,V0__A)
& ? [Vvar__3___24Anonymous__32767] :
( t(Vvar__3___24Anonymous__32767,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__32766,Vvar__3___24Anonymous__32767)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__32766 ) ) ) ) ) ).
fof('$_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.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__10517] :
( t(Vvar__1___24Anonymous__10517,V0__A)
& ? [Vvar__2___24Anonymous__10518] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10518)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10517,Vvar__2___24Anonymous__10518)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__10518)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__32732___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__32730] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32730)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32730)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__32730),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__32730)) ) ) ) ) ).
fof('$_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__14691] :
( t(Vvar__2___24Anonymous__14691,V0__A)
& ? [Vvar__3___24Anonymous__14692] :
( t(Vvar__3___24Anonymous__14692,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__14691,Vvar__3___24Anonymous__14692)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__14692 ) ) ) ) ) ).
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.int_of_int',axiom,
! [V0__i] : cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V0__i) = V0__i ).
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__32781] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32781)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__32781)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__32781) )
| ? [Vvar__0___24Anonymous__32782] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32782)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__32782)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32783] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32783)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__32783)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32784] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32784)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__32784)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32785] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32785)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__32785)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32786] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32786)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__32786)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32787] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32787)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__32787)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32788] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32788)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__32788)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32789] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32789)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__32789)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__32790] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__32790)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__32790)
& 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__11144] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11144)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11144)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__11144,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__33111] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33111)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33111)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__33112] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33112)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33112)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__33115] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33115)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33115)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__33112,Vvar__0___24Anonymous__33115) ) ) ) ) ) ) ) ).
fof('$_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__33153] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33153)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33153)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33153)
& ( ( Vvar__0___24Anonymous__33153 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__33156] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33156)
& Vvar__0___24Anonymous__33153 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33156)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__33156)) ) ) ) ) ) ) ) ).
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__33098] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33098)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33098)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__33099] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33099)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33099)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__33102] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33102)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33102)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__33099,Vvar__0___24Anonymous__33102) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.even',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__19034] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19034)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19034)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19034)
& ( ( Vvar__0___24Anonymous__19034 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__19037] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19037)
& Vvar__0___24Anonymous__19034 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19037)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__19037) ) ) ) ) ) ) ) ).
fof('$_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__33105] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33105)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33105)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__33108] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33108)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33108)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__33105,Vvar__0___24Anonymous__33108) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__33142] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33142)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33142)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__33142,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__33145] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33145)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33145)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__33142,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__33145) ) ) ) ) ) ) ) ).
fof('$_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__19028] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19028)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19028)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__19031] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19031)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19031)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__19028,Vvar__0___24Anonymous__19031)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__33120] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33120)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33120)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__33123] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33123)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33123)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__33120,Vvar__0___24Anonymous__33123)) ) ) ) ) ) ) ) ).
fof('$_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__11149] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__11149)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__11149)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__11149,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.one',axiom,
cCoq_2eInit_2eNat_2eone = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_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__19041] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19041)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19041)
& 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__19041)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__19020] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19020)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19020)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__19020 ) ) ) ).
fof('$_def_Coq.Init.Nat.square',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esquare___24a1(V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V0__n,V0__n) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__19022] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19022)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19022)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__19025] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19025)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19025)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__19022,Vvar__0___24Anonymous__19025) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__30956] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__30956)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__30956) ) ).
fof('$_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__33126] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__33126)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__33126)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__33126,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__19064] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__19064)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__19064)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__19064) ) ) ) ).
fof('$_def_Coq.Init.Nat.zero',axiom,
cCoq_2eInit_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).
fof('$_def_Coq.Init.Peano.IsSucc',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__30957] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30957)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30957)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Specif.Exc',axiom,
! [V0__A] : cCoq_2eInit_2eSpecif_2eExc___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A) ).
fof('$_def_Coq.Init.Specif.except',axiom,
cCoq_2eInit_2eSpecif_2eexcept = cCoq_2eInit_2eLogic_2eFalse__rec ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__34810___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__34804] :
( t(Vvar__2__x__34804,V0__A)
& p(happ(V1__P,Vvar__2__x__34804))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__34804)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__34804 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__24947___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__24941] :
( t(Vvar__2__x__24941,V0__A)
& ? [Vvar__3___24Anonymous__24942] :
( t(Vvar__3___24Anonymous__24942,happ(V1__P,Vvar__2__x__24941))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__24941,Vvar__3___24Anonymous__24942)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__24941 ) ) ) ) ) ).
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__18807] :
( t(Vvar__1___24Anonymous__18807,V0__A)
& ? [Vvar__2___24Anonymous__18808] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__18808)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__18807,Vvar__2___24Anonymous__18808)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__18807 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__18808) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__18819] :
( t(Vvar__1___24Anonymous__18819,V1__B)
& ? [Vvar__2___24Anonymous__18820] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__18820)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__18819,Vvar__2___24Anonymous__18820)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__18820,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__18819)) ) ) ) ) ) ) ).
fof('$_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__1944] :
( t(Vvar__1___24Anonymous__1944,V1__B)
& ? [Vvar__2___24Anonymous__1945] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__1945)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__1944,Vvar__2___24Anonymous__1945)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__1944),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__1945)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.hd',axiom,
! [V0__A,V1__default,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
| ? [Vvar__1___24Anonymous__32904] :
( t(Vvar__1___24Anonymous__32904,V0__A)
& ? [Vvar__2___24Anonymous__32905] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32905)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32904,Vvar__2___24Anonymous__32905)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__32904 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__32948] :
( t(Vvar__1___24Anonymous__32948,V0__A)
& ? [Vvar__2___24Anonymous__32949] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32949)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32949)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32948,Vvar__2___24Anonymous__32949)
& ( ( Vvar__2___24Anonymous__32949 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__32948 )
| ? [Vvar__1___24Anonymous__32960] :
( t(Vvar__1___24Anonymous__32960,V0__A)
& ? [Vvar__2___24Anonymous__32961] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32961)
& Vvar__2___24Anonymous__32949 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32960,Vvar__2___24Anonymous__32961)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__32949,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__32923] :
( t(Vvar__1___24Anonymous__32923,V0__A)
& ? [Vvar__2___24Anonymous__32924] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32924)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32923,Vvar__2___24Anonymous__32924)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__32923 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__32926] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32926)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32926)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__32933] :
( t(Vvar__1___24Anonymous__32933,V0__A)
& ? [Vvar__2___24Anonymous__32934] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32934)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32933,Vvar__2___24Anonymous__32934)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__32926,Vvar__2___24Anonymous__32934,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__32915] :
( t(Vvar__1___24Anonymous__32915,V0__A)
& ? [Vvar__2___24Anonymous__32916] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__32916)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__32915,Vvar__2___24Anonymous__32916)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__32916 ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_op',axiom,
! [V0__A,V1__B,V2__eqA,V3__eqB,V4__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V0__A,V1__B,V2__eqA,V3__eqB,V4__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__29920___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__7308___24a2(V0__A,V1__B),V2__eqA,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V1__B,V1__B,V3__eqB,V3__eqB)),V4__f) ) ).
fof('$_def_Coq.Lists.SetoidList.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__32559___24a1(V0__A) ).
fof('$_def_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__30745___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,happ(V1__B,V3__x))
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__30752___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle)
<=> ! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__14575___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__27503___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_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__27503___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('$_def_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__30762___24t(V0__A,V1__R)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__R,V2__n),V3__y)) ) )
=> ? [V3__f] :
( c_24__type__30767___24t(V0__A,V3__f)
& ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> p(happ(happ(V1__R,V4__n),happ(V3__f,V4__n))) ) ) ) ) ) ).
fof('$_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__7284___24t(V0__A,V2__R)
=> ! [V3__S] :
( c_24__type__32516___24t(V0__A,V1__B,V3__S)
=> ! [V4__T] :
( c_24__type__14575___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__27503___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('$_def_Coq.Logic.ChoiceFacts.GuardedFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eGuardedFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__P] :
( c_24__type__36___24t(V0__A,V2__P)
=> ! [V3__R] :
( c_24__type__14575___24t(V0__A,V1__B,V3__R)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(V1__B)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( p(happ(V2__P,V5__x))
=> ? [V7__y] :
( t(V7__y,V1__B)
& p(happ(happ(V3__R,V5__x),V7__y)) ) ) )
=> ? [V6__f] :
( c_24__type__27503___24t(V0__A,V1__B,V6__f)
& ! [V7__x] :
( t(V7__x,V0__A)
=> ( p(happ(V2__P,V7__x))
=> p(happ(happ(V3__R,V7__x),happ(V6__f,V7__x))) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.IndependenceOfGeneralPremises',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eIndependenceOfGeneralPremises)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ! [V2__Q] :
( cProp___24t(V2__Q)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(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('$_def_Coq.Logic.ChoiceFacts.OmniscientFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eOmniscientFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__14575___24t(V0__A,V1__B,V2__R)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(V1__B)
=> ? [V4__f] :
( c_24__type__27503___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> ( ? [V6__y] :
( t(V6__y,V1__B)
& p(happ(happ(V2__R,V5__x),V6__y)) )
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Logic.ChoiceFacts.RepresentativeFunctionalChoice_on',axiom,
! [V0__A] :
( cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on___24a1(V0__A)
<=> ! [V1__R] :
( c_24__type__7284___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R)
=> ? [V3__f] :
( c_24__type__7279___24t(V0__A,V3__f)
& ! [V4__x] :
( t(V4__x,V0__A)
=> ( p(happ(happ(V1__R,V4__x),happ(V3__f,V4__x)))
& ! [V5__x_27] :
( t(V5__x_27,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__x_27))
=> happ(V3__f,V4__x) = happ(V3__f,V5__x_27) ) ) ) ) ) ) ) ) ).
fof('$_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__7284___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__14575___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__27503___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('$_def_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__7284___24t(V0__A,V2__R)
=> ! [V3__T] :
( c_24__type__14575___24t(V0__A,V1__B,V3__T)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V2__R)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ? [V6__y] :
( t(V6__y,V1__B)
& ! [V7__x_27] :
( t(V7__x_27,V0__A)
=> ( p(happ(happ(V2__R,V5__x),V7__x_27))
=> p(happ(happ(V3__T,V7__x_27),V6__y)) ) ) ) )
=> ? [V6__f] :
( c_24__type__27503___24t(V0__A,V1__B,V6__f)
& ! [V7__x] :
( t(V7__x,V0__A)
=> ( p(happ(happ(V3__T,V7__x),happ(V6__f,V7__x)))
& ! [V8__x_27] :
( t(V8__x_27,V0__A)
=> ( p(happ(happ(V2__R,V7__x),V8__x_27))
=> happ(V6__f,V7__x) = happ(V6__f,V8__x_27) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.SmallDrinker\'sParadox',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eSmallDrinker_27sParadox)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___24t(V0__A,V1__P)
=> ( cCoq_2eInit_2eLogic_2einhabited___24a1(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('$_def_Coq.Logic.ClassicalFacts.BoolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eBoolP)
<=> ! [V0__C] :
( cProp___24t(V0__C)
=> ( p(V0__C)
=> ( p(V0__C)
=> p(V0__C) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.DrinkerParadox',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__36___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__36___24t(V0__A,V1__P)
=> ! [V2__Q] :
( cProp___24t(V2__Q)
=> ! [V3___24Anonymous] :
( t(V3___24Anonymous,V0__A)
=> ( ( p(V2__Q)
=> ? [V5__x] :
( t(V5__x,V0__A)
& p(happ(V1__P,V5__x)) ) )
=> ? [V5__x] :
( t(V5__x,V0__A)
& ( p(V2__Q)
=> p(happ(V1__P,V5__x)) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.Minimal',axiom,
! [V0__P,V1__n] :
( cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V0__P,V1__n)
<=> ( p(happ(V0__P,V1__n))
& ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( p(happ(V0__P,V2__k))
=> cCoq_2eInit_2ePeano_2ele___24a2(V1__n,V2__k) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__C] :
( cProp___24t(V2__C)
=> ( ( p(V2__C)
=> ( p(V0__A)
| p(V1__B) ) )
=> ( ( p(V2__C)
=> p(V0__A) )
| ( p(V2__C)
=> p(V1__B) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V0__A)
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.provable_prop_extensionality',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprovable__prop__extensionality)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> V0__A = c_24True ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.weak_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( ~ ~ p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(V1__B) )
| ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
! [V0__U,V1__P,V2__p,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V0__U,V1__P,V2__p,V3__x)
<=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_def_Coq.NArith.BinNat.N.divide',axiom,
! [V0__p,V1__q] :
( cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__p,V1__q)
<=> ? [V2__r] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__r)
& V1__q = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__r,V0__p) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.eq',axiom,
cCoq_2eNArith_2eBinNat_2eN_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__26198___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__13636] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13636)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13636)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__13639] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13639)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13639)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__13636,Vvar__0___24Anonymous__13639)) ) ) ) ) ) ) ) ).
fof('$_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__26101] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26101)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26101)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26101)
& ( ? [Vvar__0___24Anonymous__26105] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26105)
& Vvar__0___24Anonymous__26101 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26105)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26105) )
| ? [Vvar__0___24Anonymous__26106] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26106)
& Vvar__0___24Anonymous__26101 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26106)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26106) )
| ( Vvar__0___24Anonymous__26101 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__35170] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35170)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35170)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35170)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__26095] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26095)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26095)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__26096] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26096)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26096)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26099] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26099)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26099)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__26096,Vvar__0___24Anonymous__26099) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__26107] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26107)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26107)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26107)
& ( ? [Vvar__0___24Anonymous__26111] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26111)
& Vvar__0___24Anonymous__26107 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26111)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__26112] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26112)
& Vvar__0___24Anonymous__26107 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26112)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__26107 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__35175] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35175)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35175)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__35178] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35178)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35178)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__35175,Vvar__0___24Anonymous__35178) ) ) ) ) ) ) ) ).
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('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__13641] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13641)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13641)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__13644] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13644)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13644)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__13641,Vvar__0___24Anonymous__13644)) ) ) ) ) ) ) ) ).
fof('$_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__26083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26083)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26083)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__26083) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__13635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13635)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13635)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__13635)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_pos',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__35171] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35171)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35171)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__35171) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__32273] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__32273)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__32273) ) ).
fof('$_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__10399] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10399)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__10399)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__10399,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__13717] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13717)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13717)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__13717) ) ) ) ).
fof('$_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('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__35211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35211)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35211)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__35211 )
| ? [Vvar__0___24Anonymous__35212] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35212)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35212)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__35212 )
| ( 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__35224] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35224)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35224)
& ( ? [Vvar__0___24Anonymous__35228] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35228)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35228)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__35224,Vvar__0___24Anonymous__35228) )
| ? [Vvar__0___24Anonymous__35229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35229)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35229)
& 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__35230] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35230)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35230)
& ( ? [Vvar__0___24Anonymous__35234] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35234)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35234)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35235] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35235)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35235)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__35230,Vvar__0___24Anonymous__35235) )
| ( 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__35236] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35236)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35236)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35237] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35237)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35237)
& 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__30615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30615)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30615)
& 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__30615),Vvar__0___24Anonymous__30615)) )
| ? [Vvar__0___24Anonymous__30616] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30616)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30616)
& 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__30616),Vvar__0___24Anonymous__30616) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__13747] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13747)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13747)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__13747,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__13748] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13748)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__13748)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__13748,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.max',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V1__p_27 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V0__p,V1__p_27) = V0__p ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.min',axiom,
! [V0__p,V1__p_27] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p_27)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V0__p )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__p,V1__p_27) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V0__p,V1__p_27) = V1__p_27 ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__26328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26328)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__26328)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__y,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26328,V2__y))) )
| ? [Vvar__0___24Anonymous__26329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26329)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__26329)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__26329,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__35272] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35272)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35272)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35272)
& ( ( Vvar__0___24Anonymous__35272 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__35275] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35275)
& Vvar__0___24Anonymous__35272 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35275)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__35272)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__35279] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35279)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35279)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__35279)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35217)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35217)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__35217)) )
| ? [Vvar__0___24Anonymous__35218] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35218)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35218)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__35218)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35214)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35214)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__35214)) )
| ? [Vvar__0___24Anonymous__35215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35215)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35215)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__35215)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__26325] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26325)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__26325)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__26325 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__13744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13744)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13744)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__13744)) )
| ? [Vvar__0___24Anonymous__13745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13745)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__13745)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__13745) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__32275] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__32275)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__32275) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__35242] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35242)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35242)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__35255___24a1(Vvar__0___24Anonymous__35242) )
| ? [Vvar__0___24Anonymous__35246] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35246)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35246)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__35262___24a1(Vvar__0___24Anonymous__35246) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__35266 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__19163] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__19163)
& ? [Vvar__1__Qden__19164] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__19164)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19163,Vvar__1__Qden__19164)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__19164 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__19158] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__19158)
& ? [Vvar__1__Qden__19159] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__19159)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19158,Vvar__1__Qden__19159)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__19158 ) ) ) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
| ? [Vvar__0___24Anonymous__12262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12262)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__12262)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__12262) )
| ? [Vvar__0___24Anonymous__12263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12263)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__12263)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__12263)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.equiv',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V0__A,V1__R)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__7284___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__7284___24a1(V0__U) ).
fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__32862___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('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__32862___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).
fof('$_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__30612] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__30612)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__30612) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__30613] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__30613)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__30613) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__32258] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32258)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32258)
& ( ? [Vvar__0___24Anonymous__32262] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32262)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32262)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__32258,Vvar__0___24Anonymous__32262) ) )
| ? [Vvar__0___24Anonymous__32263] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32263)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32263)
& ( 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__32264] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32264)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32264)
& ( ? [Vvar__0___24Anonymous__32268] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32268)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32268)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__32269] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32269)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32269)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__32264,Vvar__0___24Anonymous__32269) ) )
| ( 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__32270] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32270)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32270)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__32271] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32271)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32271)
& ( 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('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__30564] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__30564)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__30564) ) ).
fof('$_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__30627] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__30627)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__30627) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__32348] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__32348)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__32348) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__30629] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__30629)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__30629) ) ).
fof('$_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.b2z',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
<=> ? [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
& V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__35316] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35316)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35316)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35316) )
| ? [Vvar__0___24Anonymous__35317] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35317)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35317)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35317) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__35320] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35320)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35320)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35320) )
| ? [Vvar__0___24Anonymous__35321] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35321)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35321)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35321) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__35318] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35318)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35318)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__35318) )
| ? [Vvar__0___24Anonymous__35319] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35319)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35319)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__35319) ) ) ) ).
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__1730] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1730)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1730)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__1734] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1734)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1734)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__1730,Vvar__0___24Anonymous__1734)) )
| ? [Vvar__0___24Anonymous__1735] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1735)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1735)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__1730,Vvar__0___24Anonymous__1735) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1736] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1736)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1736)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__1740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1740)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1740)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__1740,Vvar__0___24Anonymous__1736) )
| ? [Vvar__0___24Anonymous__1741] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1741)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1741)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__1736,Vvar__0___24Anonymous__1741)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.compare',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__10434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10434)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10434)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__10435] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10435)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10435)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__10436] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10436)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10436)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__10440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10440)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10440)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__10436,Vvar__0___24Anonymous__10440) )
| ? [Vvar__0___24Anonymous__10441] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10441)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10441)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__10442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10442)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10442)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__10446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10446)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__10446)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__10447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__10447)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10447)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__10442,Vvar__0___24Anonymous__10447)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__26688] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__26688)
& ? [Vvar__3___24Anonymous__26689] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__26689)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__26688,Vvar__3___24Anonymous__26689)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__26688 ) ) ) ) ).
fof('$_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__35322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35322)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35322)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35322)
& ( ? [Vvar__0___24Anonymous__35326] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35326)
& Vvar__0___24Anonymous__35322 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35326)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35327] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35327)
& Vvar__0___24Anonymous__35322 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35327)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__35322 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__35328] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35328)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35328)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35328)
& ( ? [Vvar__0___24Anonymous__35332] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35332)
& Vvar__0___24Anonymous__35328 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35332)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35333] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35333)
& Vvar__0___24Anonymous__35328 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35333)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__35328 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__26696] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__26696)
& ? [Vvar__3___24Anonymous__26697] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__26697)
& 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__26696,Vvar__3___24Anonymous__26697)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__26697 ) ) ) ) ).
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__1747] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1747)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1747)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1751)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1751)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1747,Vvar__0___24Anonymous__1751)) )
| ? [Vvar__0___24Anonymous__1752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1752)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1752)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1747,Vvar__0___24Anonymous__1752)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1753] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1753)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1753)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1757)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1757)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1753,Vvar__0___24Anonymous__1757)) )
| ? [Vvar__0___24Anonymous__1758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1758)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1758)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1753,Vvar__0___24Anonymous__1758)) ) ) ) ) ) ) ) ).
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__35334] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35334)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35334)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__35334)
& ( ? [Vvar__0___24Anonymous__35338] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35338)
& Vvar__0___24Anonymous__35334 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35338)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35339] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35339)
& Vvar__0___24Anonymous__35334 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35339)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__35334 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__35340] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35340)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35340)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__35340)
& ( ? [Vvar__0___24Anonymous__35344] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35344)
& Vvar__0___24Anonymous__35340 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35344)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35345] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35345)
& Vvar__0___24Anonymous__35340 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35345)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__35340 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__13795] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13795)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__13795)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13795) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__26681] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__26681)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__26681)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__26681)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1743] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1743)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1743)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1743) )
| ? [Vvar__0___24Anonymous__1744] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1744)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1744)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1744) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__26665] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26665)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26665)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__26665) )
| ? [Vvar__0___24Anonymous__26666] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26666)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26666)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__30628] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__30628)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__30628) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__26677] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26677)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26677)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__26677) )
| ? [Vvar__0___24Anonymous__26678] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26678)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26678)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__26673] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26673)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26673)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__26673) )
| ? [Vvar__0___24Anonymous__26674] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26674)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26674)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__32349] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32349)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32349)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__32349 )
| ? [Vvar__0___24Anonymous__32350] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32350)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32350)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_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__32192] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32192)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32192)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32192)
& ( ? [Vvar__0___24Anonymous__32196] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32196)
& Vvar__0___24Anonymous__32192 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32196)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__32197] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32197)
& Vvar__0___24Anonymous__32192 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32197)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__32192 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__32198] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32198)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32198)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32198)
& ( ? [Vvar__0___24Anonymous__32202] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32202)
& Vvar__0___24Anonymous__32198 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32202)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__32203] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32203)
& Vvar__0___24Anonymous__32198 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32203)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__32198 = 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__32204] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32204)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32204)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32204)
& ( ? [Vvar__0___24Anonymous__32208] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32208)
& Vvar__0___24Anonymous__32204 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32208)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__32209] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32209)
& Vvar__0___24Anonymous__32204 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32209)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__32204 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__32210] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32210)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32210)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32210)
& ( ? [Vvar__0___24Anonymous__32214] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32214)
& Vvar__0___24Anonymous__32210 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32214)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__32215] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32215)
& Vvar__0___24Anonymous__32210 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32215)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__32210 = 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__32217] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32217)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32217)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__32218] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32218)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32218)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__32218) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.log_inf',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__25948] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25948)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25948)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__25948)) )
| ? [Vvar__0___24Anonymous__25949] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25949)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25949)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__25949)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__14732___24a1(V0__D) ).
fof('$_def_Coq.micromega.Refl.make_conj',axiom,
! [V1__A,V2__eval,V3__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__33786] :
( t(Vvar__1___24Anonymous__33786,V1__A)
& ? [Vvar__2___24Anonymous__33787] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__33787)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__33787)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__33786,Vvar__2___24Anonymous__33787)
& ( ( Vvar__2___24Anonymous__33787 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> p(happ(V2__eval,Vvar__1___24Anonymous__33786)) ) )
| ? [Vvar__1___24Anonymous__33798] :
( t(Vvar__1___24Anonymous__33798,V1__A)
& ? [Vvar__2___24Anonymous__33799] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__33799)
& Vvar__2___24Anonymous__33787 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__33798,Vvar__2___24Anonymous__33799)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__33786))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__33787) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__33767] :
( t(Vvar__1___24Anonymous__33767,V1__A)
& ? [Vvar__2___24Anonymous__33768] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__33768)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__33767,Vvar__2___24Anonymous__33768)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__33767))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__33768,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('$_def_Coq.micromega.RingMicromega.cneqb',axiom,
! [V0__C,V1__ceqb,V2__x,V3__y] : cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V2__x,V3__y) = cCoq_2eInit_2eDatatypes_2enegb___24a1(happ(happ(V1__ceqb,V2__x),V3__y)) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__19996___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20004___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20012___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__20020___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34433] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34433)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34433)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__34434] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34434)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34434)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__34437] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34437)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__34437)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__34434,Vvar__0___24Anonymous__34437) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.TFormula',axiom,
! [V0__Term,V1__Annot,V2__TX,V3__AF] : cCoq_2emicromega_2eTauto_2eTFormula___24a4(V0__Term,V1__Annot,V2__TX,V3__AF) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V0__Term,V2__TX,V1__Annot,V3__AF) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
! [V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp] : cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__ropp) ).
fof('$_def_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd = cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eAdd ).
fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
! [Vvar__25873] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__25873)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__25873) ) ).
fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
! [Vvar__35162] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__35162)
<=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__35162) ) ).
fof('$_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.ArithRing.protected_to_nat',axiom,
cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.NotConstant',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNotConstant = cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
! [Vvar__32897] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__32897)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__32897) ) ).
fof('$_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__30915] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30915)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30915)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30915)
& ( ? [Vvar__0___24Anonymous__30919] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30919)
& Vvar__0___24Anonymous__30915 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30919)
& 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__30915))) )
| ? [Vvar__0___24Anonymous__30920] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30920)
& Vvar__0___24Anonymous__30915 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30920)
& 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__30915))) )
| ( Vvar__0___24Anonymous__30915 = 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__30921] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30921)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30921)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30921)
& ( ? [Vvar__0___24Anonymous__30925] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30925)
& Vvar__0___24Anonymous__30921 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30925)
& 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__30921)) )
| ? [Vvar__0___24Anonymous__30926] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30926)
& Vvar__0___24Anonymous__30921 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30926)
& 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__30921)) )
| ( Vvar__0___24Anonymous__30921 = 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('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__28797] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28797)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__28797)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__28797))) )
| ? [Vvar__0___24Anonymous__28798] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__28798)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__28798)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__28798)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__11049] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11049)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__11049)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__11049) )
| ? [Vvar__0___24Anonymous__11050] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11050)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11050)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__11050)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
! [V0__C,V1__ceqb,V3__P,V4__P_27] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
=> ( ? [Vvar__1___24Anonymous__20728] :
( t(Vvar__1___24Anonymous__20728,V0__C)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20728)
& ( ? [Vvar__1___24Anonymous__20738] :
( t(Vvar__1___24Anonymous__20738,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20738)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__20728),Vvar__1___24Anonymous__20738) )
| ? [Vvar__1___24Anonymous__20740] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20740)
& ? [Vvar__2___24Anonymous__20741] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20741)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20740,Vvar__2___24Anonymous__20741)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__20744] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20744)
& ? [Vvar__2___24Anonymous__20745] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20745)
& ? [Vvar__3___24Anonymous__20746] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20746)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20744,Vvar__2___24Anonymous__20745,Vvar__3___24Anonymous__20746)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__20751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20751)
& ? [Vvar__2___24Anonymous__20752] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20752)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20751,Vvar__2___24Anonymous__20752)
& ( ? [Vvar__1___24Anonymous__20772] :
( t(Vvar__1___24Anonymous__20772,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20772)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__20774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20774)
& ? [Vvar__2___24Anonymous__20775] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20775)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20751)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20774)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20774,Vvar__2___24Anonymous__20775)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__20751,Vvar__1___24Anonymous__20774) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__2___24Anonymous__20752,Vvar__2___24Anonymous__20775) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__20751,Vvar__1___24Anonymous__20774) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__20751,Vvar__1___24Anonymous__20774) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__20780] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20780)
& ? [Vvar__2___24Anonymous__20781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20781)
& ? [Vvar__3___24Anonymous__20782] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20782)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20780,Vvar__2___24Anonymous__20781,Vvar__3___24Anonymous__20782)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__20787] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20787)
& ? [Vvar__2___24Anonymous__20788] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20788)
& ? [Vvar__3___24Anonymous__20789] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20789)
& ( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V4__P_27)
=> ( V3__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20787,Vvar__2___24Anonymous__20788,Vvar__3___24Anonymous__20789)
& ( ? [Vvar__1___24Anonymous__20822] :
( t(Vvar__1___24Anonymous__20822,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__20822)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__20824] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20824)
& ? [Vvar__2___24Anonymous__20825] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__20825)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__20824,Vvar__2___24Anonymous__20825)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__20828] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20828)
& ? [Vvar__2___24Anonymous__20829] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20829)
& ? [Vvar__3___24Anonymous__20830] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__20830)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20788)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20829)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__20828,Vvar__2___24Anonymous__20829,Vvar__3___24Anonymous__20830)
& ( ( cType___24t(V0__C)
=> ( c_24__type__10937___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20787)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__20828)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__20788,Vvar__2___24Anonymous__20829) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__20787,Vvar__1___24Anonymous__20828) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__3___24Anonymous__20789,Vvar__3___24Anonymous__20830) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__20787,Vvar__1___24Anonymous__20828) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__20788,Vvar__2___24Anonymous__20829) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__20788,Vvar__2___24Anonymous__20829) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__30999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30999)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30999)
& 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__30999),V4__x,Vvar__0___24Anonymous__30999) )
| ? [Vvar__0___24Anonymous__31000] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31000)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31000)
& 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__31000),V4__x,Vvar__0___24Anonymous__31000) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_def_Coq.setoid_ring.Ring_theory.IDphi',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRopp',axiom,
! [V0__R,V1__x] : cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V1__x) = V1__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.SRsub',axiom,
! [V0__R,V1__radd,V2__x,V3__y] : cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V0__R,V1__radd,V2__x,V3__y) = happ(happ(V1__radd,V2__x),cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V0__R,V3__y)) ).
fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__23613] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23613)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__23613)
& 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__23613) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__12649] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12649)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12649)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__12650__12653___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12649)),c_24__let__var__6__p__12650__12653___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12649))) )
| ? [Vvar__0___24Anonymous__12651] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12651)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12651)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__12652__12654___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12651)),c_24__let__var__6__p__12652__12654___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__12651)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_HahnSets.set_bunion',axiom,
! [V0__A,V1__B,V2__s,V3__ss,V4__x] :
( cHahnSets_2eset__bunion___24a5(V0__A,V1__B,V2__s,V3__ss,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V2__s,V5__y))
& p(happ(happ(V3__ss,V5__y),V4__x)) ) ) ).
fof('$_def_HahnSets.set_collect',axiom,
! [V0__A,V1__B,V2__f,V3__s,V4__x] :
( cHahnSets_2eset__collect___24a5(V0__A,V1__B,V2__f,V3__s,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V3__s,V5__y))
& happ(V2__f,V5__y) = V4__x ) ) ).
fof('$_def_HahnSets.set_compl',axiom,
! [V0__A,V1__s,V2__x] :
( cHahnSets_2eset__compl___24a3(V0__A,V1__s,V2__x)
<=> ~ p(happ(V1__s,V2__x)) ) ).
fof('$_def_HahnSets.set_disjoint',axiom,
! [V0__A,V1__s,V2__s_27] :
( cHahnSets_2eset__disjoint___24a3(V0__A,V1__s,V2__s_27)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> ( p(happ(V2__s_27,V3__x))
=> p(c_24False) ) ) ) ) ).
fof('$_def_HahnSets.set_empty',axiom,
! [V0__A,V1__x] :
( cHahnSets_2eset__empty___24a2(V0__A,V1__x)
<=> p(c_24False) ) ).
fof('$_def_HahnSets.set_equiv',axiom,
! [V0__A,V1__s,V2__s_27] :
( cHahnSets_2eset__equiv___24a3(V0__A,V1__s,V2__s_27)
<=> ( cHahnSets_2eset__subset___24a3(V0__A,V1__s,V2__s_27)
& cHahnSets_2eset__subset___24a3(V0__A,V2__s_27,V1__s) ) ) ).
fof('$_def_HahnSets.set_full',axiom,
! [V0__A,V1__x] :
( cHahnSets_2eset__full___24a2(V0__A,V1__x)
<=> p(c_24True) ) ).
fof('$_def_HahnSets.set_inter',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( cHahnSets_2eset__inter___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
& p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_def_HahnSets.set_minus',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( cHahnSets_2eset__minus___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
& ~ p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_def_HahnSets.set_subset',axiom,
! [V0__A,V1__s,V2__s_27] :
( cHahnSets_2eset__subset___24a3(V0__A,V1__s,V2__s_27)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> p(happ(V2__s_27,V3__x)) ) ) ) ).
fof('$_def_HahnSets.set_union',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( cHahnSets_2eset__union___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
| p(happ(V2__s_27,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('$_def_hahn.HahnBase.eqn_rec',axiom,
! [V1__x,V2__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> ( V1__x = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__y = cCoq_2eInit_2eDatatypes_2eO
& chahn_2eHahnBase_2eeqn__rec___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__32891] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32891)
& V2__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32891)
& chahn_2eHahnBase_2eeqn__rec___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__32892] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32892)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__y)
=> ( V1__x = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32892)
& ( ( V2__y = cCoq_2eInit_2eDatatypes_2eO
& chahn_2eHahnBase_2eeqn__rec___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__32895] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32895)
& V2__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32895)
& chahn_2eHahnBase_2eeqn__rec___24a2(V1__x,V2__y) = chahn_2eHahnBase_2eeqn__rec___24a2(Vvar__0___24Anonymous__32892,Vvar__0___24Anonymous__32895) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnBase.is_true',axiom,
! [V0__b] :
( chahn_2eHahnBase_2eis__true___24a1(V0__b)
<=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__13909,Vvar__1___24Anonymous__13910,Vvar__0__P__13911,Vvar__1___24Anonymous__13912] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__13909) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__13911) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__27485,Vvar__1___24Anonymous__27486,Vvar__2___24Anonymous__27487] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__27485,Vvar__1___24Anonymous__27486,Vvar__2___24Anonymous__27487) ).
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__30827,Vvar__1__Plt__30828,Vvar__2__Pgt__30829,Vvar__3___24Anonymous__30830,Vvar__0__Peq__30831,Vvar__1__Plt__30832,Vvar__2__Pgt__30833,Vvar__3___24Anonymous__30834] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__30827,Vvar__1__Plt__30828,Vvar__2__Pgt__30829) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__30831,Vvar__1__Plt__30832,Vvar__2__Pgt__30833) ).
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__1779] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1779) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__10478,Vvar__1___24Anonymous__10479,Vvar__0__A__10480] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__10478,Vvar__1___24Anonymous__10479) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__10480) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__27568,Vvar__1__B__27569,Vvar__2___24Anonymous__27570,Vvar__0__A__27571,Vvar__1__B__27572,Vvar__2___24Anonymous__27573] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__27568,Vvar__1__B__27569,Vvar__2___24Anonymous__27570) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__27571,Vvar__1__B__27572,Vvar__2___24Anonymous__27573) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__1792,Vvar__0__A__1793,Vvar__1___24Anonymous__1794,Vvar__2___24Anonymous__1795] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1792) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1793,Vvar__1___24Anonymous__1794,Vvar__2___24Anonymous__1795) ).
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__30866,Vvar__1__f__30867,Vvar__0__i__30868,Vvar__1__f__30869,Vvar__2__e__30870] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30866,Vvar__1__f__30867) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30868,Vvar__1__f__30869,Vvar__2__e__30870) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__26912] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__26912) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__27595,Vvar__0__d__27596] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__27595) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__27596) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__27457,Vvar__1__B__27458,Vvar__2___24Anonymous__27459,Vvar__0__A__27460,Vvar__1__B__27461,Vvar__2___24Anonymous__27462] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__27457,Vvar__1__B__27458,Vvar__2___24Anonymous__27459) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__27460,Vvar__1__B__27461) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__68,Vvar__1__B__69,Vvar__2___24Anonymous__70,Vvar__0__A__71,Vvar__1__B__72,Vvar__2___24Anonymous__73] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__68,Vvar__1__B__69) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__71,Vvar__1__B__72) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__49] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__49) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__7] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1765,Vvar__0___24Anonymous__1766] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1765) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1766) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__32333,Vvar__1___24Anonymous__32334] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__32333,Vvar__1___24Anonymous__32334) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__27478] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__27478) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__29238,Vvar__1___24Anonymous__29239,Vvar__0__x__29240,Vvar__1__n__29241,Vvar__2___24Anonymous__29242] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__29238) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__29240,Vvar__1__n__29241) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__25494,Vvar__1___24Anonymous__25495] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25494,Vvar__1___24Anonymous__25495) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__28973,Vvar__1__lt__28974,Vvar__2__eq__28975,Vvar__3__x__28976,Vvar__4__y__28977,Vvar__5___24Anonymous__28978,Vvar__0__X__28979,Vvar__1__lt__28980,Vvar__2__eq__28981,Vvar__3__x__28982,Vvar__4__y__28983,Vvar__5___24Anonymous__28984] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__28973,Vvar__1__lt__28974,Vvar__2__eq__28975,Vvar__3__x__28976,Vvar__4__y__28977) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__28979,Vvar__1__lt__28980,Vvar__2__eq__28981,Vvar__3__x__28982,Vvar__4__y__28983) ).
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__1871,Vvar__0__n__1872,Vvar__1___24Anonymous__1873] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1871) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1872,Vvar__1___24Anonymous__1873) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__25709,Vvar__0__A__25710,Vvar__1__h__25711,Vvar__2__n__25712,Vvar__3___24Anonymous__25713] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25709) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25710,Vvar__1__h__25711,Vvar__2__n__25712,Vvar__3___24Anonymous__25713) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__14874,Vvar__1___24Anonymous__14875,Vvar__0__C__14876,Vvar__1___24Anonymous__14877] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14874,Vvar__1___24Anonymous__14875) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14876,Vvar__1___24Anonymous__14877) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__14938,Vvar__1___24Anonymous__14939,Vvar__0__C__14940,Vvar__1___24Anonymous__14941,Vvar__2___24Anonymous__14942] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14938,Vvar__1___24Anonymous__14939) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14940,Vvar__1___24Anonymous__14941,Vvar__2___24Anonymous__14942) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__27617,Vvar__1___24Anonymous__27618] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27617,Vvar__1___24Anonymous__27618) ).
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__29369,Vvar__1___24Anonymous__29370,Vvar__0__C__29371,Vvar__1___24Anonymous__29372] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__29369,Vvar__1___24Anonymous__29370) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__29371,Vvar__1___24Anonymous__29372) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__30383,Vvar__1__TX__30384,Vvar__2__AA__30385,Vvar__3__AF__30386,Vvar__0__TA__30387,Vvar__1__TX__30388,Vvar__2__AA__30389,Vvar__3__AF__30390] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30383,Vvar__1__TX__30384,Vvar__2__AA__30385,Vvar__3__AF__30386) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30387,Vvar__1__TX__30388,Vvar__2__AA__30389,Vvar__3__AF__30390) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__25520,Vvar__0__A__25521,Vvar__1___24Anonymous__25522] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25520) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25521,Vvar__1___24Anonymous__25522) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__25901,Vvar__1___24Anonymous__25902] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25901,Vvar__1___24Anonymous__25902) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__17797,Vvar__0__C__17798] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17797) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17798) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__12451,Vvar__0__C__12452] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12451) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12452) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__20699,Vvar__1___24Anonymous__20700,Vvar__0__C__20701,Vvar__1___24Anonymous__20702,Vvar__2___24Anonymous__20703] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20699,Vvar__1___24Anonymous__20700) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20701,Vvar__1___24Anonymous__20702,Vvar__2___24Anonymous__20703) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__21345,Vvar__1___24Anonymous__21346] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21345,Vvar__1___24Anonymous__21346) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__29844,Vvar__1__req__29845,Vvar__2__reqb__29846,Vvar__3___24Anonymous__29847] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__29844,Vvar__1__req__29845,Vvar__2__reqb__29846) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_fix_19691_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__19691__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__19695] :
( t(Vvar__1___24Anonymous__19695,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__19696] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__19696)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19695,Vvar__2___24Anonymous__19696)
& c_24__fix__19691__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__19695,c_24__fix__19691__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__19696,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_32330_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__32331] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32331)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32331)
& c_24__fix__32330__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__32330__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__32331)) )
| ? [Vvar__0___24Anonymous__32332] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32332)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32332)
& c_24__fix__32330__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32332) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__32330__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__13917,Vvar__0__P__13918,Vvar__1___24Anonymous__13919,Vvar__1___24Anonymous__13920] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__13917) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__13918)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__13917 = Vvar__0__P__13918 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__13913,Vvar__0__P__13914,Vvar__1___24Anonymous__13915,Vvar__1___24Anonymous__13916] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__13913) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__13914)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__13913 = Vvar__0__P__13914 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__27488,Vvar__0___24Anonymous__27489,Vvar__1___24Anonymous__27490,Vvar__1___24Anonymous__27491,Vvar__2___24Anonymous__27492,Vvar__2___24Anonymous__27493] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__27488,Vvar__1___24Anonymous__27490,Vvar__2___24Anonymous__27492) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__27489,Vvar__1___24Anonymous__27491,Vvar__2___24Anonymous__27493)
=> ( Vvar__2___24Anonymous__27492 = Vvar__2___24Anonymous__27493
& Vvar__1___24Anonymous__27490 = Vvar__1___24Anonymous__27491
& Vvar__0___24Anonymous__27488 = Vvar__0___24Anonymous__27489 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__30835,Vvar__0__Peq__30836,Vvar__1__Plt__30837,Vvar__1__Plt__30838,Vvar__2__Pgt__30839,Vvar__2__Pgt__30840,Vvar__3___24Anonymous__30841,Vvar__3___24Anonymous__30842] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__30835,Vvar__1__Plt__30837,Vvar__2__Pgt__30839) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__30836,Vvar__1__Plt__30838,Vvar__2__Pgt__30840)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__30839 = Vvar__2__Pgt__30840
& Vvar__1__Plt__30837 = Vvar__1__Plt__30838
& Vvar__0__Peq__30835 = Vvar__0__Peq__30836 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__30851,Vvar__0__Peq__30852,Vvar__1__Plt__30853,Vvar__1__Plt__30854,Vvar__2__Pgt__30855,Vvar__2__Pgt__30856,Vvar__3___24Anonymous__30857,Vvar__3___24Anonymous__30858] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__30851,Vvar__1__Plt__30853,Vvar__2__Pgt__30855) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__30852,Vvar__1__Plt__30854,Vvar__2__Pgt__30856)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__30855 = Vvar__2__Pgt__30856
& Vvar__1__Plt__30853 = Vvar__1__Plt__30854
& Vvar__0__Peq__30851 = Vvar__0__Peq__30852 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__30843,Vvar__0__Peq__30844,Vvar__1__Plt__30845,Vvar__1__Plt__30846,Vvar__2__Pgt__30847,Vvar__2__Pgt__30848,Vvar__3___24Anonymous__30849,Vvar__3___24Anonymous__30850] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__30843,Vvar__1__Plt__30845,Vvar__2__Pgt__30847) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__30844,Vvar__1__Plt__30846,Vvar__2__Pgt__30848)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__30847 = Vvar__2__Pgt__30848
& Vvar__1__Plt__30845 = Vvar__1__Plt__30846
& Vvar__0__Peq__30843 = Vvar__0__Peq__30844 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__10485,Vvar__0__A__10486] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__10485) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__10486)
=> Vvar__0__A__10485 = Vvar__0__A__10486 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__1780,Vvar__0___24Anonymous__1781] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1780) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1781)
=> Vvar__0___24Anonymous__1780 = Vvar__0___24Anonymous__1781 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__10481,Vvar__0__A__10482,Vvar__1___24Anonymous__10483,Vvar__1___24Anonymous__10484] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__10481,Vvar__1___24Anonymous__10483) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__10482,Vvar__1___24Anonymous__10484)
=> ( Vvar__1___24Anonymous__10483 = Vvar__1___24Anonymous__10484
& Vvar__0__A__10481 = Vvar__0__A__10482 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__1798,Vvar__0__A__1799,Vvar__1___24Anonymous__1800,Vvar__1___24Anonymous__1801,Vvar__2___24Anonymous__1802,Vvar__2___24Anonymous__1803] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1798,Vvar__1___24Anonymous__1800,Vvar__2___24Anonymous__1802) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1799,Vvar__1___24Anonymous__1801,Vvar__2___24Anonymous__1803)
=> ( Vvar__2___24Anonymous__1802 = Vvar__2___24Anonymous__1803
& Vvar__1___24Anonymous__1800 = Vvar__1___24Anonymous__1801
& Vvar__0__A__1798 = Vvar__0__A__1799 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__27574,Vvar__0__A__27575,Vvar__1__B__27576,Vvar__1__B__27577,Vvar__2___24Anonymous__27578,Vvar__2___24Anonymous__27579] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__27574,Vvar__1__B__27576,Vvar__2___24Anonymous__27578) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__27575,Vvar__1__B__27577,Vvar__2___24Anonymous__27579)
=> ( Vvar__2___24Anonymous__27578 = Vvar__2___24Anonymous__27579
& Vvar__1__B__27576 = Vvar__1__B__27577
& Vvar__0__A__27574 = Vvar__0__A__27575 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__27580,Vvar__0__A__27581,Vvar__1__B__27582,Vvar__1__B__27583,Vvar__2___24Anonymous__27584,Vvar__2___24Anonymous__27585] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__27580,Vvar__1__B__27582,Vvar__2___24Anonymous__27584) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__27581,Vvar__1__B__27583,Vvar__2___24Anonymous__27585)
=> ( Vvar__2___24Anonymous__27584 = Vvar__2___24Anonymous__27585
& Vvar__1__B__27582 = Vvar__1__B__27583
& Vvar__0__A__27580 = Vvar__0__A__27581 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__1796,Vvar__0__A__1797] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1796) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1797)
=> Vvar__0__A__1796 = Vvar__0__A__1797 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__10497,Vvar__0__A__10498,Vvar__1__B__10499,Vvar__1__B__10500,Vvar__2___24Anonymous__10501,Vvar__2___24Anonymous__10502,Vvar__3___24Anonymous__10503,Vvar__3___24Anonymous__10504] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__10497,Vvar__1__B__10499,Vvar__2___24Anonymous__10501,Vvar__3___24Anonymous__10503) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__10498,Vvar__1__B__10500,Vvar__2___24Anonymous__10502,Vvar__3___24Anonymous__10504)
=> ( Vvar__3___24Anonymous__10503 = Vvar__3___24Anonymous__10504
& Vvar__2___24Anonymous__10501 = Vvar__2___24Anonymous__10502
& Vvar__1__B__10499 = Vvar__1__B__10500
& Vvar__0__A__10497 = Vvar__0__A__10498 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__26913,Vvar__0___24Anonymous__26914] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__26913) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__26914)
=> Vvar__0___24Anonymous__26913 = Vvar__0___24Anonymous__26914 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__26915,Vvar__0___24Anonymous__26916] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__26915) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__26916)
=> Vvar__0___24Anonymous__26915 = Vvar__0___24Anonymous__26916 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__26917,Vvar__0___24Anonymous__26918] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__26917) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__26918)
=> Vvar__0___24Anonymous__26917 = Vvar__0___24Anonymous__26918 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__26919,Vvar__0___24Anonymous__26920] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__26919) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__26920)
=> Vvar__0___24Anonymous__26919 = Vvar__0___24Anonymous__26920 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__26921,Vvar__0___24Anonymous__26922] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__26921) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__26922)
=> Vvar__0___24Anonymous__26921 = Vvar__0___24Anonymous__26922 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__26923,Vvar__0___24Anonymous__26924] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__26923) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__26924)
=> Vvar__0___24Anonymous__26923 = Vvar__0___24Anonymous__26924 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__26925,Vvar__0___24Anonymous__26926] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__26925) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__26926)
=> Vvar__0___24Anonymous__26925 = Vvar__0___24Anonymous__26926 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__26927,Vvar__0___24Anonymous__26928] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__26927) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__26928)
=> Vvar__0___24Anonymous__26927 = Vvar__0___24Anonymous__26928 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__26929,Vvar__0___24Anonymous__26930] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__26929) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__26930)
=> Vvar__0___24Anonymous__26929 = Vvar__0___24Anonymous__26930 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__26931,Vvar__0___24Anonymous__26932] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__26931) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__26932)
=> Vvar__0___24Anonymous__26931 = Vvar__0___24Anonymous__26932 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__30871,Vvar__0__i__30872,Vvar__1__f__30873,Vvar__1__f__30874] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30871,Vvar__1__f__30873) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30872,Vvar__1__f__30874)
=> ( Vvar__1__f__30873 = Vvar__1__f__30874
& Vvar__0__i__30871 = Vvar__0__i__30872 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__30875,Vvar__0__i__30876,Vvar__1__f__30877,Vvar__1__f__30878,Vvar__2__e__30879,Vvar__2__e__30880] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30875,Vvar__1__f__30877,Vvar__2__e__30879) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30876,Vvar__1__f__30878,Vvar__2__e__30880)
=> ( Vvar__2__e__30879 = Vvar__2__e__30880
& Vvar__1__f__30877 = Vvar__1__f__30878
& Vvar__0__i__30875 = Vvar__0__i__30876 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__27599,Vvar__0__d__27600] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__27599) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__27600)
=> Vvar__0__d__27599 = Vvar__0__d__27600 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__27597,Vvar__0__d__27598] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__27597) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__27598)
=> Vvar__0__d__27597 = Vvar__0__d__27598 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__10126,Vvar__0__A__10127,Vvar__1__P__10128,Vvar__1__P__10129,Vvar__2__x__10130,Vvar__2__x__10131,Vvar__3___24Anonymous__10132,Vvar__3___24Anonymous__10133] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__10126,Vvar__1__P__10128,Vvar__2__x__10130) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__10127,Vvar__1__P__10129,Vvar__2__x__10131)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__10130 = Vvar__2__x__10131
& Vvar__1__P__10128 = Vvar__1__P__10129
& Vvar__0__A__10126 = Vvar__0__A__10127 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__29966,Vvar__0__A__29967,Vvar__1__P__29968,Vvar__1__P__29969,Vvar__2__Q__29970,Vvar__2__Q__29971,Vvar__3__x__29972,Vvar__3__x__29973,Vvar__4___24Anonymous__29974,Vvar__4___24Anonymous__29975,Vvar__5___24Anonymous__29976,Vvar__5___24Anonymous__29977] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__29966,Vvar__1__P__29968,Vvar__2__Q__29970,Vvar__3__x__29972) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__29967,Vvar__1__P__29969,Vvar__2__Q__29971,Vvar__3__x__29973)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__29972 = Vvar__3__x__29973
& Vvar__2__Q__29970 = Vvar__2__Q__29971
& Vvar__1__P__29968 = Vvar__1__P__29969
& Vvar__0__A__29966 = Vvar__0__A__29967 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__24915,Vvar__0__A__24916,Vvar__1__P__24917,Vvar__1__P__24918,Vvar__2__x__24919,Vvar__2__x__24920,Vvar__3___24Anonymous__24921,Vvar__3___24Anonymous__24922] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__24915,Vvar__1__P__24917,Vvar__2__x__24919,Vvar__3___24Anonymous__24921) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__24916,Vvar__1__P__24918,Vvar__2__x__24920,Vvar__3___24Anonymous__24922)
=> ( Vvar__3___24Anonymous__24921 = Vvar__3___24Anonymous__24922
& Vvar__2__x__24919 = Vvar__2__x__24920
& Vvar__1__P__24917 = Vvar__1__P__24918
& Vvar__0__A__24915 = Vvar__0__A__24916 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__30022,Vvar__0__A__30023,Vvar__1__P__30024,Vvar__1__P__30025,Vvar__2__Q__30026,Vvar__2__Q__30027,Vvar__3__x__30028,Vvar__3__x__30029,Vvar__4___24Anonymous__30030,Vvar__4___24Anonymous__30031,Vvar__5___24Anonymous__30032,Vvar__5___24Anonymous__30033] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__30022,Vvar__1__P__30024,Vvar__2__Q__30026,Vvar__3__x__30028,Vvar__4___24Anonymous__30030,Vvar__5___24Anonymous__30032) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__30023,Vvar__1__P__30025,Vvar__2__Q__30027,Vvar__3__x__30029,Vvar__4___24Anonymous__30031,Vvar__5___24Anonymous__30033)
=> ( Vvar__5___24Anonymous__30032 = Vvar__5___24Anonymous__30033
& Vvar__4___24Anonymous__30030 = Vvar__4___24Anonymous__30031
& Vvar__3__x__30028 = Vvar__3__x__30029
& Vvar__2__Q__30026 = Vvar__2__Q__30027
& Vvar__1__P__30024 = Vvar__1__P__30025
& Vvar__0__A__30022 = Vvar__0__A__30023 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__27463,Vvar__0__A__27464,Vvar__1__B__27465,Vvar__1__B__27466,Vvar__2___24Anonymous__27467,Vvar__2___24Anonymous__27468] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__27463,Vvar__1__B__27465,Vvar__2___24Anonymous__27467) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__27464,Vvar__1__B__27466,Vvar__2___24Anonymous__27468)
=> ( Vvar__2___24Anonymous__27467 = Vvar__2___24Anonymous__27468
& Vvar__1__B__27465 = Vvar__1__B__27466
& Vvar__0__A__27463 = Vvar__0__A__27464 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__27469,Vvar__0__A__27470,Vvar__1__B__27471,Vvar__1__B__27472,Vvar__2___24Anonymous__27473,Vvar__2___24Anonymous__27474] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__27469,Vvar__1__B__27471) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__27470,Vvar__1__B__27472)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__27471 = Vvar__1__B__27472
& Vvar__0__A__27469 = Vvar__0__A__27470 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__74,Vvar__0__A__75,Vvar__1__B__76,Vvar__1__B__77,Vvar__2___24Anonymous__78,Vvar__2___24Anonymous__79] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__74,Vvar__1__B__76) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__75,Vvar__1__B__77)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__76 = Vvar__1__B__77
& Vvar__0__A__74 = Vvar__0__A__75 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__80,Vvar__0__A__81,Vvar__1__B__82,Vvar__1__B__83,Vvar__2___24Anonymous__84,Vvar__2___24Anonymous__85] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__80,Vvar__1__B__82) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__81,Vvar__1__B__83)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__82 = Vvar__1__B__83
& Vvar__0__A__80 = Vvar__0__A__81 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__50,Vvar__0___24Anonymous__51] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__50) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__51)
=> Vvar__0___24Anonymous__50 = Vvar__0___24Anonymous__51 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__10,Vvar__0___24Anonymous__11] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__10) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__11)
=> Vvar__0___24Anonymous__10 = Vvar__0___24Anonymous__11 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__8,Vvar__0___24Anonymous__9] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__8) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9)
=> Vvar__0___24Anonymous__8 = Vvar__0___24Anonymous__9 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__1767,Vvar__0___24Anonymous__1768] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1767) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1768)
=> Vvar__0___24Anonymous__1767 = Vvar__0___24Anonymous__1768 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__1769,Vvar__0___24Anonymous__1770] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1769) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1770)
=> Vvar__0___24Anonymous__1769 = Vvar__0___24Anonymous__1770 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__32335,Vvar__0__p__32336,Vvar__1___24Anonymous__32337,Vvar__1___24Anonymous__32338] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__32335,Vvar__1___24Anonymous__32337) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__32336,Vvar__1___24Anonymous__32338)
=> ( Vvar__1___24Anonymous__32337 = Vvar__1___24Anonymous__32338
& Vvar__0__p__32335 = Vvar__0__p__32336 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__27479,Vvar__0___24Anonymous__27480] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__27479) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__27480)
=> Vvar__0___24Anonymous__27479 = Vvar__0___24Anonymous__27480 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__19151,Vvar__0__Qnum__19152,Vvar__1__Qden__19153,Vvar__1__Qden__19154] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19151,Vvar__1__Qden__19153) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19152,Vvar__1__Qden__19154)
=> ( Vvar__1__Qden__19153 = Vvar__1__Qden__19154
& Vvar__0__Qnum__19151 = Vvar__0__Qnum__19152 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__30982,Vvar__0__neg__30983,Vvar__1__cond__neg__30984,Vvar__1__cond__neg__30985] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__30982) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__30983)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__30982 = Vvar__0__neg__30983 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__30961,Vvar__0__nonneg__30962,Vvar__1__cond__nonneg__30963,Vvar__1__cond__nonneg__30964] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__30961) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__30962)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__30961 = Vvar__0__nonneg__30962 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__30975,Vvar__0__nonpos__30976,Vvar__1__cond__nonpos__30977,Vvar__1__cond__nonpos__30978] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__30975) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__30976)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__30975 = Vvar__0__nonpos__30976 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__30989,Vvar__0__nonzero__30990,Vvar__1__cond__nonzero__30991,Vvar__1__cond__nonzero__30992] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__30989) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__30990)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__30989 = Vvar__0__nonzero__30990 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__30968,Vvar__0__pos__30969,Vvar__1__cond__pos__30970,Vvar__1__cond__pos__30971] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__30968) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__30969)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__30968 = Vvar__0__pos__30969 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__29253,Vvar__0__x__29254,Vvar__1__n__29255,Vvar__1__n__29256,Vvar__2___24Anonymous__29257,Vvar__2___24Anonymous__29258] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__29253,Vvar__1__n__29255) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__29254,Vvar__1__n__29256)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__29255 = Vvar__1__n__29256
& Vvar__0__x__29253 = Vvar__0__x__29254 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__29243,Vvar__0__x__29244,Vvar__1___24Anonymous__29245,Vvar__1___24Anonymous__29246] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__29243) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__29244)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__29243 = Vvar__0__x__29244 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__29247,Vvar__0__x__29248,Vvar__1__n__29249,Vvar__1__n__29250,Vvar__2___24Anonymous__29251,Vvar__2___24Anonymous__29252] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__29247,Vvar__1__n__29249) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__29248,Vvar__1__n__29250)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__29249 = Vvar__1__n__29250
& Vvar__0__x__29247 = Vvar__0__x__29248 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__26769,Vvar__0___24Anonymous__26770,Vvar__1___24Anonymous__26771,Vvar__1___24Anonymous__26772,Vvar__2___24Anonymous__26773,Vvar__2___24Anonymous__26774,Vvar__3___24Anonymous__26775,Vvar__3___24Anonymous__26776,Vvar__4___24Anonymous__26777,Vvar__4___24Anonymous__26778,Vvar__5___24Anonymous__26779,Vvar__5___24Anonymous__26780,Vvar__6___24Anonymous__26781,Vvar__6___24Anonymous__26782,Vvar__7___24Anonymous__26783,Vvar__7___24Anonymous__26784] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__26769,Vvar__1___24Anonymous__26771,Vvar__2___24Anonymous__26773,Vvar__3___24Anonymous__26775,Vvar__4___24Anonymous__26777,Vvar__5___24Anonymous__26779,Vvar__6___24Anonymous__26781,Vvar__7___24Anonymous__26783) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__26770,Vvar__1___24Anonymous__26772,Vvar__2___24Anonymous__26774,Vvar__3___24Anonymous__26776,Vvar__4___24Anonymous__26778,Vvar__5___24Anonymous__26780,Vvar__6___24Anonymous__26782,Vvar__7___24Anonymous__26784)
=> ( Vvar__7___24Anonymous__26783 = Vvar__7___24Anonymous__26784
& Vvar__6___24Anonymous__26781 = Vvar__6___24Anonymous__26782
& Vvar__5___24Anonymous__26779 = Vvar__5___24Anonymous__26780
& Vvar__4___24Anonymous__26777 = Vvar__4___24Anonymous__26778
& Vvar__3___24Anonymous__26775 = Vvar__3___24Anonymous__26776
& Vvar__2___24Anonymous__26773 = Vvar__2___24Anonymous__26774
& Vvar__1___24Anonymous__26771 = Vvar__1___24Anonymous__26772
& Vvar__0___24Anonymous__26769 = Vvar__0___24Anonymous__26770 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__25496,Vvar__0___24Anonymous__25497,Vvar__1___24Anonymous__25498,Vvar__1___24Anonymous__25499] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25496,Vvar__1___24Anonymous__25498) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25497,Vvar__1___24Anonymous__25499)
=> ( Vvar__1___24Anonymous__25498 = Vvar__1___24Anonymous__25499
& Vvar__0___24Anonymous__25496 = Vvar__0___24Anonymous__25497 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__28997,Vvar__0__X__28998,Vvar__1__lt__28999,Vvar__1__lt__29000,Vvar__2__eq__29001,Vvar__2__eq__29002,Vvar__3__x__29003,Vvar__3__x__29004,Vvar__4__y__29005,Vvar__4__y__29006,Vvar__5___24Anonymous__29007,Vvar__5___24Anonymous__29008] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__28997,Vvar__1__lt__28999,Vvar__2__eq__29001,Vvar__3__x__29003,Vvar__4__y__29005) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__28998,Vvar__1__lt__29000,Vvar__2__eq__29002,Vvar__3__x__29004,Vvar__4__y__29006)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__29005 = Vvar__4__y__29006
& Vvar__3__x__29003 = Vvar__3__x__29004
& Vvar__2__eq__29001 = Vvar__2__eq__29002
& Vvar__1__lt__28999 = Vvar__1__lt__29000
& Vvar__0__X__28997 = Vvar__0__X__28998 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__29009,Vvar__0__X__29010,Vvar__1__lt__29011,Vvar__1__lt__29012,Vvar__2__eq__29013,Vvar__2__eq__29014,Vvar__3__x__29015,Vvar__3__x__29016,Vvar__4__y__29017,Vvar__4__y__29018,Vvar__5___24Anonymous__29019,Vvar__5___24Anonymous__29020] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__29009,Vvar__1__lt__29011,Vvar__2__eq__29013,Vvar__3__x__29015,Vvar__4__y__29017) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__29010,Vvar__1__lt__29012,Vvar__2__eq__29014,Vvar__3__x__29016,Vvar__4__y__29018)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__29017 = Vvar__4__y__29018
& Vvar__3__x__29015 = Vvar__3__x__29016
& Vvar__2__eq__29013 = Vvar__2__eq__29014
& Vvar__1__lt__29011 = Vvar__1__lt__29012
& Vvar__0__X__29009 = Vvar__0__X__29010 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__28985,Vvar__0__X__28986,Vvar__1__lt__28987,Vvar__1__lt__28988,Vvar__2__eq__28989,Vvar__2__eq__28990,Vvar__3__x__28991,Vvar__3__x__28992,Vvar__4__y__28993,Vvar__4__y__28994,Vvar__5___24Anonymous__28995,Vvar__5___24Anonymous__28996] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__28985,Vvar__1__lt__28987,Vvar__2__eq__28989,Vvar__3__x__28991,Vvar__4__y__28993) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__28986,Vvar__1__lt__28988,Vvar__2__eq__28990,Vvar__3__x__28992,Vvar__4__y__28994)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__28993 = Vvar__4__y__28994
& Vvar__3__x__28991 = Vvar__3__x__28992
& Vvar__2__eq__28989 = Vvar__2__eq__28990
& Vvar__1__lt__28987 = Vvar__1__lt__28988
& Vvar__0__X__28985 = Vvar__0__X__28986 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__1874,Vvar__0__n__1875] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1874) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1875)
=> Vvar__0__n__1874 = Vvar__0__n__1875 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__1876,Vvar__0__n__1877,Vvar__1___24Anonymous__1878,Vvar__1___24Anonymous__1879] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1876,Vvar__1___24Anonymous__1878) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1877,Vvar__1___24Anonymous__1879)
=> ( Vvar__1___24Anonymous__1878 = Vvar__1___24Anonymous__1879
& Vvar__0__n__1876 = Vvar__0__n__1877 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__25716,Vvar__0__A__25717,Vvar__1__h__25718,Vvar__1__h__25719,Vvar__2__n__25720,Vvar__2__n__25721,Vvar__3___24Anonymous__25722,Vvar__3___24Anonymous__25723] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25716,Vvar__1__h__25718,Vvar__2__n__25720,Vvar__3___24Anonymous__25722) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25717,Vvar__1__h__25719,Vvar__2__n__25721,Vvar__3___24Anonymous__25723)
=> ( Vvar__3___24Anonymous__25722 = Vvar__3___24Anonymous__25723
& Vvar__2__n__25720 = Vvar__2__n__25721
& Vvar__1__h__25718 = Vvar__1__h__25719
& Vvar__0__A__25716 = Vvar__0__A__25717 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__25714,Vvar__0__A__25715] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25714) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25715)
=> Vvar__0__A__25714 = Vvar__0__A__25715 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__30527,Vvar__0__a__30528,Vvar__1__b__30529,Vvar__1__b__30530,Vvar__2__u__30531,Vvar__2__u__30532,Vvar__3__v__30533,Vvar__3__v__30534,Vvar__4__d__30535,Vvar__4__d__30536,Vvar__5___24Anonymous__30537,Vvar__5___24Anonymous__30538,Vvar__6___24Anonymous__30539,Vvar__6___24Anonymous__30540] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__30527,Vvar__1__b__30529,Vvar__2__u__30531,Vvar__3__v__30533,Vvar__4__d__30535) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__30528,Vvar__1__b__30530,Vvar__2__u__30532,Vvar__3__v__30534,Vvar__4__d__30536)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__30535 = Vvar__4__d__30536
& Vvar__3__v__30533 = Vvar__3__v__30534
& Vvar__2__u__30531 = Vvar__2__u__30532
& Vvar__1__b__30529 = Vvar__1__b__30530
& Vvar__0__a__30527 = Vvar__0__a__30528 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__32243,Vvar__0__x__32244,Vvar__1__p__32245,Vvar__1__p__32246,Vvar__2__q__32247,Vvar__2__q__32248,Vvar__3__r__32249,Vvar__3__r__32250,Vvar__4___24Anonymous__32251,Vvar__4___24Anonymous__32252,Vvar__5___24Anonymous__32253,Vvar__5___24Anonymous__32254,Vvar__6___24Anonymous__32255,Vvar__6___24Anonymous__32256] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__32243,Vvar__1__p__32245,Vvar__2__q__32247,Vvar__3__r__32249) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__32244,Vvar__1__p__32246,Vvar__2__q__32248,Vvar__3__r__32250)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__32249 = Vvar__3__r__32250
& Vvar__2__q__32247 = Vvar__2__q__32248
& Vvar__1__p__32245 = Vvar__1__p__32246
& Vvar__0__x__32243 = Vvar__0__x__32244 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__14882,Vvar__0__C__14883,Vvar__1___24Anonymous__14884,Vvar__1___24Anonymous__14885] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14882,Vvar__1___24Anonymous__14884) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14883,Vvar__1___24Anonymous__14885)
=> ( Vvar__1___24Anonymous__14884 = Vvar__1___24Anonymous__14885
& Vvar__0__C__14882 = Vvar__0__C__14883 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__14886,Vvar__0__C__14887,Vvar__1___24Anonymous__14888,Vvar__1___24Anonymous__14889,Vvar__2___24Anonymous__14890,Vvar__2___24Anonymous__14891] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__14886,Vvar__1___24Anonymous__14888,Vvar__2___24Anonymous__14890) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__14887,Vvar__1___24Anonymous__14889,Vvar__2___24Anonymous__14891)
=> ( Vvar__2___24Anonymous__14890 = Vvar__2___24Anonymous__14891
& Vvar__1___24Anonymous__14888 = Vvar__1___24Anonymous__14889
& Vvar__0__C__14886 = Vvar__0__C__14887 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__14878,Vvar__0__C__14879,Vvar__1___24Anonymous__14880,Vvar__1___24Anonymous__14881] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14878,Vvar__1___24Anonymous__14880) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14879,Vvar__1___24Anonymous__14881)
=> ( Vvar__1___24Anonymous__14880 = Vvar__1___24Anonymous__14881
& Vvar__0__C__14878 = Vvar__0__C__14879 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__14898,Vvar__0__C__14899,Vvar__1___24Anonymous__14900,Vvar__1___24Anonymous__14901,Vvar__2___24Anonymous__14902,Vvar__2___24Anonymous__14903] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__14898,Vvar__1___24Anonymous__14900,Vvar__2___24Anonymous__14902) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__14899,Vvar__1___24Anonymous__14901,Vvar__2___24Anonymous__14903)
=> ( Vvar__2___24Anonymous__14902 = Vvar__2___24Anonymous__14903
& Vvar__1___24Anonymous__14900 = Vvar__1___24Anonymous__14901
& Vvar__0__C__14898 = Vvar__0__C__14899 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__14904,Vvar__0__C__14905,Vvar__1___24Anonymous__14906,Vvar__1___24Anonymous__14907] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__14904,Vvar__1___24Anonymous__14906) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__14905,Vvar__1___24Anonymous__14907)
=> ( Vvar__1___24Anonymous__14906 = Vvar__1___24Anonymous__14907
& Vvar__0__C__14904 = Vvar__0__C__14905 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__14908,Vvar__0__C__14909,Vvar__1___24Anonymous__14910,Vvar__1___24Anonymous__14911,Vvar__2___24Anonymous__14912,Vvar__2___24Anonymous__14913] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__14908,Vvar__1___24Anonymous__14910,Vvar__2___24Anonymous__14912) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__14909,Vvar__1___24Anonymous__14911,Vvar__2___24Anonymous__14913)
=> ( Vvar__2___24Anonymous__14912 = Vvar__2___24Anonymous__14913
& Vvar__1___24Anonymous__14910 = Vvar__1___24Anonymous__14911
& Vvar__0__C__14908 = Vvar__0__C__14909 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__14892,Vvar__0__C__14893,Vvar__1___24Anonymous__14894,Vvar__1___24Anonymous__14895,Vvar__2___24Anonymous__14896,Vvar__2___24Anonymous__14897] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__14892,Vvar__1___24Anonymous__14894,Vvar__2___24Anonymous__14896) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__14893,Vvar__1___24Anonymous__14895,Vvar__2___24Anonymous__14897)
=> ( Vvar__2___24Anonymous__14896 = Vvar__2___24Anonymous__14897
& Vvar__1___24Anonymous__14894 = Vvar__1___24Anonymous__14895
& Vvar__0__C__14892 = Vvar__0__C__14893 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__14953,Vvar__0__C__14954,Vvar__1___24Anonymous__14955,Vvar__1___24Anonymous__14956,Vvar__2___24Anonymous__14957,Vvar__2___24Anonymous__14958,Vvar__3___24Anonymous__14959,Vvar__3___24Anonymous__14960] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__14953,Vvar__1___24Anonymous__14955,Vvar__2___24Anonymous__14957,Vvar__3___24Anonymous__14959) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__14954,Vvar__1___24Anonymous__14956,Vvar__2___24Anonymous__14958,Vvar__3___24Anonymous__14960)
=> ( Vvar__3___24Anonymous__14959 = Vvar__3___24Anonymous__14960
& Vvar__2___24Anonymous__14957 = Vvar__2___24Anonymous__14958
& Vvar__1___24Anonymous__14955 = Vvar__1___24Anonymous__14956
& Vvar__0__C__14953 = Vvar__0__C__14954 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__14943,Vvar__0__C__14944,Vvar__1___24Anonymous__14945,Vvar__1___24Anonymous__14946] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14943,Vvar__1___24Anonymous__14945) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14944,Vvar__1___24Anonymous__14946)
=> ( Vvar__1___24Anonymous__14945 = Vvar__1___24Anonymous__14946
& Vvar__0__C__14943 = Vvar__0__C__14944 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__14947,Vvar__0__C__14948,Vvar__1___24Anonymous__14949,Vvar__1___24Anonymous__14950,Vvar__2___24Anonymous__14951,Vvar__2___24Anonymous__14952] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14947,Vvar__1___24Anonymous__14949,Vvar__2___24Anonymous__14951) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14948,Vvar__1___24Anonymous__14950,Vvar__2___24Anonymous__14952)
=> ( Vvar__2___24Anonymous__14951 = Vvar__2___24Anonymous__14952
& Vvar__1___24Anonymous__14949 = Vvar__1___24Anonymous__14950
& Vvar__0__C__14947 = Vvar__0__C__14948 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__27623,Vvar__0___24Anonymous__27624,Vvar__1___24Anonymous__27625,Vvar__1___24Anonymous__27626] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__27623,Vvar__1___24Anonymous__27625) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__27624,Vvar__1___24Anonymous__27626)
=> ( Vvar__1___24Anonymous__27625 = Vvar__1___24Anonymous__27626
& Vvar__0___24Anonymous__27623 = Vvar__0___24Anonymous__27624 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__27619,Vvar__0___24Anonymous__27620,Vvar__1___24Anonymous__27621,Vvar__1___24Anonymous__27622] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27619,Vvar__1___24Anonymous__27621) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27620,Vvar__1___24Anonymous__27622)
=> ( Vvar__1___24Anonymous__27621 = Vvar__1___24Anonymous__27622
& Vvar__0___24Anonymous__27619 = Vvar__0___24Anonymous__27620 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__29162,Vvar__0__r__29163] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__29162) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__29163)
=> Vvar__0__r__29162 = Vvar__0__r__29163 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__29150,Vvar__0__r1__29151,Vvar__1__r2__29152,Vvar__1__r2__29153] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__29150,Vvar__1__r2__29152) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__29151,Vvar__1__r2__29153)
=> ( Vvar__1__r2__29152 = Vvar__1__r2__29153
& Vvar__0__r1__29150 = Vvar__0__r1__29151 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__29154,Vvar__0__r1__29155,Vvar__1__r2__29156,Vvar__1__r2__29157] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__29154,Vvar__1__r2__29156) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__29155,Vvar__1__r2__29157)
=> ( Vvar__1__r2__29156 = Vvar__1__r2__29157
& Vvar__0__r1__29154 = Vvar__0__r1__29155 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__29164,Vvar__0__r__29165] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__29164) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__29165)
=> Vvar__0__r__29164 = Vvar__0__r__29165 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__29146,Vvar__0__r1__29147,Vvar__1__r2__29148,Vvar__1__r2__29149] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__29146,Vvar__1__r2__29148) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__29147,Vvar__1__r2__29149)
=> ( Vvar__1__r2__29148 = Vvar__1__r2__29149
& Vvar__0__r1__29146 = Vvar__0__r1__29147 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__29158,Vvar__0__r1__29159,Vvar__1__z__29160,Vvar__1__z__29161] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__29158,Vvar__1__z__29160) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__29159,Vvar__1__z__29161)
=> ( Vvar__1__z__29160 = Vvar__1__z__29161
& Vvar__0__r1__29158 = Vvar__0__r1__29159 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__29142,Vvar__0__r__29143] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__29142) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__29143)
=> Vvar__0__r__29142 = Vvar__0__r__29143 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__29144,Vvar__0__r__29145] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__29144) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__29145)
=> Vvar__0__r__29144 = Vvar__0__r__29145 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__29411,Vvar__0__T__29412,Vvar__1__Flhs__29413,Vvar__1__Flhs__29414,Vvar__2__Fop__29415,Vvar__2__Fop__29416,Vvar__3__Frhs__29417,Vvar__3__Frhs__29418] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__29411,Vvar__1__Flhs__29413,Vvar__2__Fop__29415,Vvar__3__Frhs__29417) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__29412,Vvar__1__Flhs__29414,Vvar__2__Fop__29416,Vvar__3__Frhs__29418)
=> ( Vvar__3__Frhs__29417 = Vvar__3__Frhs__29418
& Vvar__2__Fop__29415 = Vvar__2__Fop__29416
& Vvar__1__Flhs__29413 = Vvar__1__Flhs__29414
& Vvar__0__T__29411 = Vvar__0__T__29412 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__29393,Vvar__0__C__29394,Vvar__1___24Anonymous__29395,Vvar__1___24Anonymous__29396,Vvar__2___24Anonymous__29397,Vvar__2___24Anonymous__29398] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__29393,Vvar__1___24Anonymous__29395,Vvar__2___24Anonymous__29397) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__29394,Vvar__1___24Anonymous__29396,Vvar__2___24Anonymous__29398)
=> ( Vvar__2___24Anonymous__29397 = Vvar__2___24Anonymous__29398
& Vvar__1___24Anonymous__29395 = Vvar__1___24Anonymous__29396
& Vvar__0__C__29393 = Vvar__0__C__29394 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__29399,Vvar__0__C__29400,Vvar__1___24Anonymous__29401,Vvar__1___24Anonymous__29402] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__29399,Vvar__1___24Anonymous__29401) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__29400,Vvar__1___24Anonymous__29402)
=> ( Vvar__1___24Anonymous__29401 = Vvar__1___24Anonymous__29402
& Vvar__0__C__29399 = Vvar__0__C__29400 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__29373,Vvar__0__C__29374,Vvar__1___24Anonymous__29375,Vvar__1___24Anonymous__29376] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__29373,Vvar__1___24Anonymous__29375) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__29374,Vvar__1___24Anonymous__29376)
=> ( Vvar__1___24Anonymous__29375 = Vvar__1___24Anonymous__29376
& Vvar__0__C__29373 = Vvar__0__C__29374 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__29381,Vvar__0__C__29382,Vvar__1___24Anonymous__29383,Vvar__1___24Anonymous__29384,Vvar__2___24Anonymous__29385,Vvar__2___24Anonymous__29386] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__29381,Vvar__1___24Anonymous__29383,Vvar__2___24Anonymous__29385) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__29382,Vvar__1___24Anonymous__29384,Vvar__2___24Anonymous__29386)
=> ( Vvar__2___24Anonymous__29385 = Vvar__2___24Anonymous__29386
& Vvar__1___24Anonymous__29383 = Vvar__1___24Anonymous__29384
& Vvar__0__C__29381 = Vvar__0__C__29382 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__29387,Vvar__0__C__29388,Vvar__1___24Anonymous__29389,Vvar__1___24Anonymous__29390,Vvar__2___24Anonymous__29391,Vvar__2___24Anonymous__29392] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__29387,Vvar__1___24Anonymous__29389,Vvar__2___24Anonymous__29391) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__29388,Vvar__1___24Anonymous__29390,Vvar__2___24Anonymous__29392)
=> ( Vvar__2___24Anonymous__29391 = Vvar__2___24Anonymous__29392
& Vvar__1___24Anonymous__29389 = Vvar__1___24Anonymous__29390
& Vvar__0__C__29387 = Vvar__0__C__29388 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__29377,Vvar__0__C__29378,Vvar__1___24Anonymous__29379,Vvar__1___24Anonymous__29380] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__29377,Vvar__1___24Anonymous__29379) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__29378,Vvar__1___24Anonymous__29380)
=> ( Vvar__1___24Anonymous__29379 = Vvar__1___24Anonymous__29380
& Vvar__0__C__29377 = Vvar__0__C__29378 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__29403,Vvar__0__C__29404] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__29403) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__29404)
=> Vvar__0__C__29403 = Vvar__0__C__29404 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__30417,Vvar__0__TA__30418,Vvar__1__TX__30419,Vvar__1__TX__30420,Vvar__2__AA__30421,Vvar__2__AA__30422,Vvar__3__AF__30423,Vvar__3__AF__30424,Vvar__4___24Anonymous__30425,Vvar__4___24Anonymous__30426,Vvar__5___24Anonymous__30427,Vvar__5___24Anonymous__30428] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__30417,Vvar__1__TX__30419,Vvar__2__AA__30421,Vvar__3__AF__30423,Vvar__4___24Anonymous__30425,Vvar__5___24Anonymous__30427) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__30418,Vvar__1__TX__30420,Vvar__2__AA__30422,Vvar__3__AF__30424,Vvar__4___24Anonymous__30426,Vvar__5___24Anonymous__30428)
=> ( Vvar__5___24Anonymous__30427 = Vvar__5___24Anonymous__30428
& Vvar__4___24Anonymous__30425 = Vvar__4___24Anonymous__30426
& Vvar__3__AF__30423 = Vvar__3__AF__30424
& Vvar__2__AA__30421 = Vvar__2__AA__30422
& Vvar__1__TX__30419 = Vvar__1__TX__30420
& Vvar__0__TA__30417 = Vvar__0__TA__30418 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__30429,Vvar__0__TA__30430,Vvar__1__TX__30431,Vvar__1__TX__30432,Vvar__2__AA__30433,Vvar__2__AA__30434,Vvar__3__AF__30435,Vvar__3__AF__30436,Vvar__4___24Anonymous__30437,Vvar__4___24Anonymous__30438,Vvar__5___24Anonymous__30439,Vvar__5___24Anonymous__30440] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__30429,Vvar__1__TX__30431,Vvar__2__AA__30433,Vvar__3__AF__30435,Vvar__4___24Anonymous__30437,Vvar__5___24Anonymous__30439) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__30430,Vvar__1__TX__30432,Vvar__2__AA__30434,Vvar__3__AF__30436,Vvar__4___24Anonymous__30438,Vvar__5___24Anonymous__30440)
=> ( Vvar__5___24Anonymous__30439 = Vvar__5___24Anonymous__30440
& Vvar__4___24Anonymous__30437 = Vvar__4___24Anonymous__30438
& Vvar__3__AF__30435 = Vvar__3__AF__30436
& Vvar__2__AA__30433 = Vvar__2__AA__30434
& Vvar__1__TX__30431 = Vvar__1__TX__30432
& Vvar__0__TA__30429 = Vvar__0__TA__30430 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__30441,Vvar__0__TA__30442,Vvar__1__TX__30443,Vvar__1__TX__30444,Vvar__2__AA__30445,Vvar__2__AA__30446,Vvar__3__AF__30447,Vvar__3__AF__30448,Vvar__4___24Anonymous__30449,Vvar__4___24Anonymous__30450,Vvar__5___24Anonymous__30451,Vvar__5___24Anonymous__30452] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__30441,Vvar__1__TX__30443,Vvar__2__AA__30445,Vvar__3__AF__30447,Vvar__4___24Anonymous__30449,Vvar__5___24Anonymous__30451) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__30442,Vvar__1__TX__30444,Vvar__2__AA__30446,Vvar__3__AF__30448,Vvar__4___24Anonymous__30450,Vvar__5___24Anonymous__30452)
=> ( Vvar__5___24Anonymous__30451 = Vvar__5___24Anonymous__30452
& Vvar__4___24Anonymous__30449 = Vvar__4___24Anonymous__30450
& Vvar__3__AF__30447 = Vvar__3__AF__30448
& Vvar__2__AA__30445 = Vvar__2__AA__30446
& Vvar__1__TX__30443 = Vvar__1__TX__30444
& Vvar__0__TA__30441 = Vvar__0__TA__30442 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__30399,Vvar__0__TA__30400,Vvar__1__TX__30401,Vvar__1__TX__30402,Vvar__2__AA__30403,Vvar__2__AA__30404,Vvar__3__AF__30405,Vvar__3__AF__30406] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30399,Vvar__1__TX__30401,Vvar__2__AA__30403,Vvar__3__AF__30405) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30400,Vvar__1__TX__30402,Vvar__2__AA__30404,Vvar__3__AF__30406)
=> ( Vvar__3__AF__30405 = Vvar__3__AF__30406
& Vvar__2__AA__30403 = Vvar__2__AA__30404
& Vvar__1__TX__30401 = Vvar__1__TX__30402
& Vvar__0__TA__30399 = Vvar__0__TA__30400 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__30463,Vvar__0__TA__30464,Vvar__1__TX__30465,Vvar__1__TX__30466,Vvar__2__AA__30467,Vvar__2__AA__30468,Vvar__3__AF__30469,Vvar__3__AF__30470,Vvar__4___24Anonymous__30471,Vvar__4___24Anonymous__30472,Vvar__5___24Anonymous__30473,Vvar__5___24Anonymous__30474,Vvar__6___24Anonymous__30475,Vvar__6___24Anonymous__30476] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__30463,Vvar__1__TX__30465,Vvar__2__AA__30467,Vvar__3__AF__30469,Vvar__4___24Anonymous__30471,Vvar__5___24Anonymous__30473,Vvar__6___24Anonymous__30475) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__30464,Vvar__1__TX__30466,Vvar__2__AA__30468,Vvar__3__AF__30470,Vvar__4___24Anonymous__30472,Vvar__5___24Anonymous__30474,Vvar__6___24Anonymous__30476)
=> ( Vvar__6___24Anonymous__30475 = Vvar__6___24Anonymous__30476
& Vvar__5___24Anonymous__30473 = Vvar__5___24Anonymous__30474
& Vvar__4___24Anonymous__30471 = Vvar__4___24Anonymous__30472
& Vvar__3__AF__30469 = Vvar__3__AF__30470
& Vvar__2__AA__30467 = Vvar__2__AA__30468
& Vvar__1__TX__30465 = Vvar__1__TX__30466
& Vvar__0__TA__30463 = Vvar__0__TA__30464 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__30453,Vvar__0__TA__30454,Vvar__1__TX__30455,Vvar__1__TX__30456,Vvar__2__AA__30457,Vvar__2__AA__30458,Vvar__3__AF__30459,Vvar__3__AF__30460,Vvar__4___24Anonymous__30461,Vvar__4___24Anonymous__30462] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__30453,Vvar__1__TX__30455,Vvar__2__AA__30457,Vvar__3__AF__30459,Vvar__4___24Anonymous__30461) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__30454,Vvar__1__TX__30456,Vvar__2__AA__30458,Vvar__3__AF__30460,Vvar__4___24Anonymous__30462)
=> ( Vvar__4___24Anonymous__30461 = Vvar__4___24Anonymous__30462
& Vvar__3__AF__30459 = Vvar__3__AF__30460
& Vvar__2__AA__30457 = Vvar__2__AA__30458
& Vvar__1__TX__30455 = Vvar__1__TX__30456
& Vvar__0__TA__30453 = Vvar__0__TA__30454 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__30391,Vvar__0__TA__30392,Vvar__1__TX__30393,Vvar__1__TX__30394,Vvar__2__AA__30395,Vvar__2__AA__30396,Vvar__3__AF__30397,Vvar__3__AF__30398] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30391,Vvar__1__TX__30393,Vvar__2__AA__30395,Vvar__3__AF__30397) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30392,Vvar__1__TX__30394,Vvar__2__AA__30396,Vvar__3__AF__30398)
=> ( Vvar__3__AF__30397 = Vvar__3__AF__30398
& Vvar__2__AA__30395 = Vvar__2__AA__30396
& Vvar__1__TX__30393 = Vvar__1__TX__30394
& Vvar__0__TA__30391 = Vvar__0__TA__30392 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__30407,Vvar__0__TA__30408,Vvar__1__TX__30409,Vvar__1__TX__30410,Vvar__2__AA__30411,Vvar__2__AA__30412,Vvar__3__AF__30413,Vvar__3__AF__30414,Vvar__4___24Anonymous__30415,Vvar__4___24Anonymous__30416] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__30407,Vvar__1__TX__30409,Vvar__2__AA__30411,Vvar__3__AF__30413,Vvar__4___24Anonymous__30415) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__30408,Vvar__1__TX__30410,Vvar__2__AA__30412,Vvar__3__AF__30414,Vvar__4___24Anonymous__30416)
=> ( Vvar__4___24Anonymous__30415 = Vvar__4___24Anonymous__30416
& Vvar__3__AF__30413 = Vvar__3__AF__30414
& Vvar__2__AA__30411 = Vvar__2__AA__30412
& Vvar__1__TX__30409 = Vvar__1__TX__30410
& Vvar__0__TA__30407 = Vvar__0__TA__30408 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__25529,Vvar__0__A__25530,Vvar__1___24Anonymous__25531,Vvar__1___24Anonymous__25532,Vvar__2___24Anonymous__25533,Vvar__2___24Anonymous__25534,Vvar__3___24Anonymous__25535,Vvar__3___24Anonymous__25536] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__25529,Vvar__1___24Anonymous__25531,Vvar__2___24Anonymous__25533,Vvar__3___24Anonymous__25535) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__25530,Vvar__1___24Anonymous__25532,Vvar__2___24Anonymous__25534,Vvar__3___24Anonymous__25536)
=> ( Vvar__3___24Anonymous__25535 = Vvar__3___24Anonymous__25536
& Vvar__2___24Anonymous__25533 = Vvar__2___24Anonymous__25534
& Vvar__1___24Anonymous__25531 = Vvar__1___24Anonymous__25532
& Vvar__0__A__25529 = Vvar__0__A__25530 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__25525,Vvar__0__A__25526,Vvar__1___24Anonymous__25527,Vvar__1___24Anonymous__25528] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25525,Vvar__1___24Anonymous__25527) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25526,Vvar__1___24Anonymous__25528)
=> ( Vvar__1___24Anonymous__25527 = Vvar__1___24Anonymous__25528
& Vvar__0__A__25525 = Vvar__0__A__25526 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__25523,Vvar__0__A__25524] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25523) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25524)
=> Vvar__0__A__25523 = Vvar__0__A__25524 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__25907,Vvar__0___24Anonymous__25908,Vvar__1___24Anonymous__25909,Vvar__1___24Anonymous__25910] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__25907,Vvar__1___24Anonymous__25909) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__25908,Vvar__1___24Anonymous__25910)
=> ( Vvar__1___24Anonymous__25909 = Vvar__1___24Anonymous__25910
& Vvar__0___24Anonymous__25907 = Vvar__0___24Anonymous__25908 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__25911,Vvar__0___24Anonymous__25912,Vvar__1___24Anonymous__25913,Vvar__1___24Anonymous__25914,Vvar__2___24Anonymous__25915,Vvar__2___24Anonymous__25916] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__25911,Vvar__1___24Anonymous__25913,Vvar__2___24Anonymous__25915) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__25912,Vvar__1___24Anonymous__25914,Vvar__2___24Anonymous__25916)
=> ( Vvar__2___24Anonymous__25915 = Vvar__2___24Anonymous__25916
& Vvar__1___24Anonymous__25913 = Vvar__1___24Anonymous__25914
& Vvar__0___24Anonymous__25911 = Vvar__0___24Anonymous__25912 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__25903,Vvar__0___24Anonymous__25904,Vvar__1___24Anonymous__25905,Vvar__1___24Anonymous__25906] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25903,Vvar__1___24Anonymous__25905) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25904,Vvar__1___24Anonymous__25906)
=> ( Vvar__1___24Anonymous__25905 = Vvar__1___24Anonymous__25906
& Vvar__0___24Anonymous__25903 = Vvar__0___24Anonymous__25904 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__17801,Vvar__0__C__17802] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17801) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17802)
=> Vvar__0__C__17801 = Vvar__0__C__17802 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__17799,Vvar__0__C__17800] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17799) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17800)
=> Vvar__0__C__17799 = Vvar__0__C__17800 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__17807,Vvar__0__C__17808,Vvar__1___24Anonymous__17809,Vvar__1___24Anonymous__17810] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__17807,Vvar__1___24Anonymous__17809) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__17808,Vvar__1___24Anonymous__17810)
=> ( Vvar__1___24Anonymous__17809 = Vvar__1___24Anonymous__17810
& Vvar__0__C__17807 = Vvar__0__C__17808 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__17811,Vvar__0__C__17812,Vvar__1___24Anonymous__17813,Vvar__1___24Anonymous__17814,Vvar__2___24Anonymous__17815,Vvar__2___24Anonymous__17816] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__17811,Vvar__1___24Anonymous__17813,Vvar__2___24Anonymous__17815) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__17812,Vvar__1___24Anonymous__17814,Vvar__2___24Anonymous__17816)
=> ( Vvar__2___24Anonymous__17815 = Vvar__2___24Anonymous__17816
& Vvar__1___24Anonymous__17813 = Vvar__1___24Anonymous__17814
& Vvar__0__C__17811 = Vvar__0__C__17812 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__17803,Vvar__0__C__17804,Vvar__1___24Anonymous__17805,Vvar__1___24Anonymous__17806] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__17803,Vvar__1___24Anonymous__17805) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__17804,Vvar__1___24Anonymous__17806)
=> ( Vvar__1___24Anonymous__17805 = Vvar__1___24Anonymous__17806
& Vvar__0__C__17803 = Vvar__0__C__17804 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__17837,Vvar__0__C__17838,Vvar__1___24Anonymous__17839,Vvar__1___24Anonymous__17840,Vvar__2___24Anonymous__17841,Vvar__2___24Anonymous__17842] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__17837,Vvar__1___24Anonymous__17839,Vvar__2___24Anonymous__17841) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__17838,Vvar__1___24Anonymous__17840,Vvar__2___24Anonymous__17842)
=> ( Vvar__2___24Anonymous__17841 = Vvar__2___24Anonymous__17842
& Vvar__1___24Anonymous__17839 = Vvar__1___24Anonymous__17840
& Vvar__0__C__17837 = Vvar__0__C__17838 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__17833,Vvar__0__C__17834,Vvar__1___24Anonymous__17835,Vvar__1___24Anonymous__17836] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__17833,Vvar__1___24Anonymous__17835) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__17834,Vvar__1___24Anonymous__17836)
=> ( Vvar__1___24Anonymous__17835 = Vvar__1___24Anonymous__17836
& Vvar__0__C__17833 = Vvar__0__C__17834 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__17823,Vvar__0__C__17824,Vvar__1___24Anonymous__17825,Vvar__1___24Anonymous__17826,Vvar__2___24Anonymous__17827,Vvar__2___24Anonymous__17828] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__17823,Vvar__1___24Anonymous__17825,Vvar__2___24Anonymous__17827) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__17824,Vvar__1___24Anonymous__17826,Vvar__2___24Anonymous__17828)
=> ( Vvar__2___24Anonymous__17827 = Vvar__2___24Anonymous__17828
& Vvar__1___24Anonymous__17825 = Vvar__1___24Anonymous__17826
& Vvar__0__C__17823 = Vvar__0__C__17824 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__17829,Vvar__0__C__17830,Vvar__1___24Anonymous__17831,Vvar__1___24Anonymous__17832] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__17829,Vvar__1___24Anonymous__17831) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__17830,Vvar__1___24Anonymous__17832)
=> ( Vvar__1___24Anonymous__17831 = Vvar__1___24Anonymous__17832
& Vvar__0__C__17829 = Vvar__0__C__17830 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__17843,Vvar__0__C__17844,Vvar__1___24Anonymous__17845,Vvar__1___24Anonymous__17846,Vvar__2___24Anonymous__17847,Vvar__2___24Anonymous__17848] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__17843,Vvar__1___24Anonymous__17845,Vvar__2___24Anonymous__17847) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__17844,Vvar__1___24Anonymous__17846,Vvar__2___24Anonymous__17848)
=> ( Vvar__2___24Anonymous__17847 = Vvar__2___24Anonymous__17848
& Vvar__1___24Anonymous__17845 = Vvar__1___24Anonymous__17846
& Vvar__0__C__17843 = Vvar__0__C__17844 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__17817,Vvar__0__C__17818,Vvar__1___24Anonymous__17819,Vvar__1___24Anonymous__17820,Vvar__2___24Anonymous__17821,Vvar__2___24Anonymous__17822] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__17817,Vvar__1___24Anonymous__17819,Vvar__2___24Anonymous__17821) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__17818,Vvar__1___24Anonymous__17820,Vvar__2___24Anonymous__17822)
=> ( Vvar__2___24Anonymous__17821 = Vvar__2___24Anonymous__17822
& Vvar__1___24Anonymous__17819 = Vvar__1___24Anonymous__17820
& Vvar__0__C__17817 = Vvar__0__C__17818 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__18151,Vvar__0__C__18152,Vvar__1__num__18153,Vvar__1__num__18154,Vvar__2__denum__18155,Vvar__2__denum__18156,Vvar__3__condition__18157,Vvar__3__condition__18158] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__18151,Vvar__1__num__18153,Vvar__2__denum__18155,Vvar__3__condition__18157) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__18152,Vvar__1__num__18154,Vvar__2__denum__18156,Vvar__3__condition__18158)
=> ( Vvar__3__condition__18157 = Vvar__3__condition__18158
& Vvar__2__denum__18155 = Vvar__2__denum__18156
& Vvar__1__num__18153 = Vvar__1__num__18154
& Vvar__0__C__18151 = Vvar__0__C__18152 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__18229,Vvar__0__C__18230,Vvar__1__rsplit__left__18231,Vvar__1__rsplit__left__18232,Vvar__2__rsplit__common__18233,Vvar__2__rsplit__common__18234,Vvar__3__rsplit__right__18235,Vvar__3__rsplit__right__18236] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__18229,Vvar__1__rsplit__left__18231,Vvar__2__rsplit__common__18233,Vvar__3__rsplit__right__18235) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__18230,Vvar__1__rsplit__left__18232,Vvar__2__rsplit__common__18234,Vvar__3__rsplit__right__18236)
=> ( Vvar__3__rsplit__right__18235 = Vvar__3__rsplit__right__18236
& Vvar__2__rsplit__common__18233 = Vvar__2__rsplit__common__18234
& Vvar__1__rsplit__left__18231 = Vvar__1__rsplit__left__18232
& Vvar__0__C__18229 = Vvar__0__C__18230 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__30952,Vvar__0__hypo__type__30953,Vvar__1__hypo__proof__30954,Vvar__1__hypo__proof__30955] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__30952,Vvar__1__hypo__proof__30954) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__30953,Vvar__1__hypo__proof__30955)
=> ( Vvar__1__hypo__proof__30954 = Vvar__1__hypo__proof__30955
& Vvar__0__hypo__type__30952 = Vvar__0__hypo__type__30953 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__12455,Vvar__0__C__12456] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12455) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12456)
=> Vvar__0__C__12455 = Vvar__0__C__12456 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__12453,Vvar__0__C__12454] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12453) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12454)
=> Vvar__0__C__12453 = Vvar__0__C__12454 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__12461,Vvar__0__C__12462,Vvar__1___24Anonymous__12463,Vvar__1___24Anonymous__12464] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__12461,Vvar__1___24Anonymous__12463) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__12462,Vvar__1___24Anonymous__12464)
=> ( Vvar__1___24Anonymous__12463 = Vvar__1___24Anonymous__12464
& Vvar__0__C__12461 = Vvar__0__C__12462 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__12465,Vvar__0__C__12466,Vvar__1___24Anonymous__12467,Vvar__1___24Anonymous__12468,Vvar__2___24Anonymous__12469,Vvar__2___24Anonymous__12470] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__12465,Vvar__1___24Anonymous__12467,Vvar__2___24Anonymous__12469) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__12466,Vvar__1___24Anonymous__12468,Vvar__2___24Anonymous__12470)
=> ( Vvar__2___24Anonymous__12469 = Vvar__2___24Anonymous__12470
& Vvar__1___24Anonymous__12467 = Vvar__1___24Anonymous__12468
& Vvar__0__C__12465 = Vvar__0__C__12466 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__12457,Vvar__0__C__12458,Vvar__1___24Anonymous__12459,Vvar__1___24Anonymous__12460] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__12457,Vvar__1___24Anonymous__12459) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__12458,Vvar__1___24Anonymous__12460)
=> ( Vvar__1___24Anonymous__12459 = Vvar__1___24Anonymous__12460
& Vvar__0__C__12457 = Vvar__0__C__12458 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__12477,Vvar__0__C__12478,Vvar__1___24Anonymous__12479,Vvar__1___24Anonymous__12480,Vvar__2___24Anonymous__12481,Vvar__2___24Anonymous__12482] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__12477,Vvar__1___24Anonymous__12479,Vvar__2___24Anonymous__12481) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__12478,Vvar__1___24Anonymous__12480,Vvar__2___24Anonymous__12482)
=> ( Vvar__2___24Anonymous__12481 = Vvar__2___24Anonymous__12482
& Vvar__1___24Anonymous__12479 = Vvar__1___24Anonymous__12480
& Vvar__0__C__12477 = Vvar__0__C__12478 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__12483,Vvar__0__C__12484,Vvar__1___24Anonymous__12485,Vvar__1___24Anonymous__12486] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__12483,Vvar__1___24Anonymous__12485) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__12484,Vvar__1___24Anonymous__12486)
=> ( Vvar__1___24Anonymous__12485 = Vvar__1___24Anonymous__12486
& Vvar__0__C__12483 = Vvar__0__C__12484 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__12487,Vvar__0__C__12488,Vvar__1___24Anonymous__12489,Vvar__1___24Anonymous__12490,Vvar__2___24Anonymous__12491,Vvar__2___24Anonymous__12492] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__12487,Vvar__1___24Anonymous__12489,Vvar__2___24Anonymous__12491) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__12488,Vvar__1___24Anonymous__12490,Vvar__2___24Anonymous__12492)
=> ( Vvar__2___24Anonymous__12491 = Vvar__2___24Anonymous__12492
& Vvar__1___24Anonymous__12489 = Vvar__1___24Anonymous__12490
& Vvar__0__C__12487 = Vvar__0__C__12488 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__12471,Vvar__0__C__12472,Vvar__1___24Anonymous__12473,Vvar__1___24Anonymous__12474,Vvar__2___24Anonymous__12475,Vvar__2___24Anonymous__12476] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__12471,Vvar__1___24Anonymous__12473,Vvar__2___24Anonymous__12475) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__12472,Vvar__1___24Anonymous__12474,Vvar__2___24Anonymous__12476)
=> ( Vvar__2___24Anonymous__12475 = Vvar__2___24Anonymous__12476
& Vvar__1___24Anonymous__12473 = Vvar__1___24Anonymous__12474
& Vvar__0__C__12471 = Vvar__0__C__12472 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__20714,Vvar__0__C__20715,Vvar__1___24Anonymous__20716,Vvar__1___24Anonymous__20717,Vvar__2___24Anonymous__20718,Vvar__2___24Anonymous__20719,Vvar__3___24Anonymous__20720,Vvar__3___24Anonymous__20721] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__20714,Vvar__1___24Anonymous__20716,Vvar__2___24Anonymous__20718,Vvar__3___24Anonymous__20720) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__20715,Vvar__1___24Anonymous__20717,Vvar__2___24Anonymous__20719,Vvar__3___24Anonymous__20721)
=> ( Vvar__3___24Anonymous__20720 = Vvar__3___24Anonymous__20721
& Vvar__2___24Anonymous__20718 = Vvar__2___24Anonymous__20719
& Vvar__1___24Anonymous__20716 = Vvar__1___24Anonymous__20717
& Vvar__0__C__20714 = Vvar__0__C__20715 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__20704,Vvar__0__C__20705,Vvar__1___24Anonymous__20706,Vvar__1___24Anonymous__20707] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20704,Vvar__1___24Anonymous__20706) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20705,Vvar__1___24Anonymous__20707)
=> ( Vvar__1___24Anonymous__20706 = Vvar__1___24Anonymous__20707
& Vvar__0__C__20704 = Vvar__0__C__20705 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__20708,Vvar__0__C__20709,Vvar__1___24Anonymous__20710,Vvar__1___24Anonymous__20711,Vvar__2___24Anonymous__20712,Vvar__2___24Anonymous__20713] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20708,Vvar__1___24Anonymous__20710,Vvar__2___24Anonymous__20712) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20709,Vvar__1___24Anonymous__20711,Vvar__2___24Anonymous__20713)
=> ( Vvar__2___24Anonymous__20712 = Vvar__2___24Anonymous__20713
& Vvar__1___24Anonymous__20710 = Vvar__1___24Anonymous__20711
& Vvar__0__C__20708 = Vvar__0__C__20709 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__21351,Vvar__0___24Anonymous__21352,Vvar__1___24Anonymous__21353,Vvar__1___24Anonymous__21354] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21351,Vvar__1___24Anonymous__21353) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21352,Vvar__1___24Anonymous__21354)
=> ( Vvar__1___24Anonymous__21353 = Vvar__1___24Anonymous__21354
& Vvar__0___24Anonymous__21351 = Vvar__0___24Anonymous__21352 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__21347,Vvar__0___24Anonymous__21348,Vvar__1___24Anonymous__21349,Vvar__1___24Anonymous__21350] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21347,Vvar__1___24Anonymous__21349) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21348,Vvar__1___24Anonymous__21350)
=> ( Vvar__1___24Anonymous__21349 = Vvar__1___24Anonymous__21350
& Vvar__0___24Anonymous__21347 = Vvar__0___24Anonymous__21348 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__29848,Vvar__0__R__29849,Vvar__1__req__29850,Vvar__1__req__29851,Vvar__2__reqb__29852,Vvar__2__reqb__29853,Vvar__3___24Anonymous__29854,Vvar__3___24Anonymous__29855] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__29848,Vvar__1__req__29850,Vvar__2__reqb__29852) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__29849,Vvar__1__req__29851,Vvar__2__reqb__29853)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__29852 = Vvar__2__reqb__29853
& Vvar__1__req__29850 = Vvar__1__req__29851
& Vvar__0__R__29848 = Vvar__0__R__29849 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__29856,Vvar__0__R__29857,Vvar__1__rO__29858,Vvar__1__rO__29859,Vvar__2__rI__29860,Vvar__2__rI__29861,Vvar__3__radd__29862,Vvar__3__radd__29863,Vvar__4__rmul__29864,Vvar__4__rmul__29865,Vvar__5__rsub__29866,Vvar__5__rsub__29867,Vvar__6__ropp__29868,Vvar__6__ropp__29869,Vvar__7__req__29870,Vvar__7__req__29871,Vvar__8__C__29872,Vvar__8__C__29873,Vvar__9__cO__29874,Vvar__9__cO__29875,Vvar__10__cI__29876,Vvar__10__cI__29877,Vvar__11__cadd__29878,Vvar__11__cadd__29879,Vvar__12__cmul__29880,Vvar__12__cmul__29881,Vvar__13__csub__29882,Vvar__13__csub__29883,Vvar__14__copp__29884,Vvar__14__copp__29885,Vvar__15__ceqb__29886,Vvar__15__ceqb__29887,Vvar__16__phi__29888,Vvar__16__phi__29889,Vvar__17___24Anonymous__29890,Vvar__17___24Anonymous__29891] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__29856,Vvar__1__rO__29858,Vvar__2__rI__29860,Vvar__3__radd__29862,Vvar__4__rmul__29864,Vvar__5__rsub__29866,Vvar__6__ropp__29868,Vvar__7__req__29870,Vvar__8__C__29872,Vvar__9__cO__29874,Vvar__10__cI__29876,Vvar__11__cadd__29878,Vvar__12__cmul__29880,Vvar__13__csub__29882,Vvar__14__copp__29884,Vvar__15__ceqb__29886,Vvar__16__phi__29888) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__29857,Vvar__1__rO__29859,Vvar__2__rI__29861,Vvar__3__radd__29863,Vvar__4__rmul__29865,Vvar__5__rsub__29867,Vvar__6__ropp__29869,Vvar__7__req__29871,Vvar__8__C__29873,Vvar__9__cO__29875,Vvar__10__cI__29877,Vvar__11__cadd__29879,Vvar__12__cmul__29881,Vvar__13__csub__29883,Vvar__14__copp__29885,Vvar__15__ceqb__29887,Vvar__16__phi__29889)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__29888 = Vvar__16__phi__29889
& Vvar__15__ceqb__29886 = Vvar__15__ceqb__29887
& Vvar__14__copp__29884 = Vvar__14__copp__29885
& Vvar__13__csub__29882 = Vvar__13__csub__29883
& Vvar__12__cmul__29880 = Vvar__12__cmul__29881
& Vvar__11__cadd__29878 = Vvar__11__cadd__29879
& Vvar__10__cI__29876 = Vvar__10__cI__29877
& Vvar__9__cO__29874 = Vvar__9__cO__29875
& Vvar__8__C__29872 = Vvar__8__C__29873
& Vvar__7__req__29870 = Vvar__7__req__29871
& Vvar__6__ropp__29868 = Vvar__6__ropp__29869
& Vvar__5__rsub__29866 = Vvar__5__rsub__29867
& Vvar__4__rmul__29864 = Vvar__4__rmul__29865
& Vvar__3__radd__29862 = Vvar__3__radd__29863
& Vvar__2__rI__29860 = Vvar__2__rI__29861
& Vvar__1__rO__29858 = Vvar__1__rO__29859
& Vvar__0__R__29856 = Vvar__0__R__29857 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Mixin',axiom,
! [Vvar__0__T__26016,Vvar__0__T__26017,Vvar__1__op__26018,Vvar__1__op__26019,Vvar__2___24Anonymous__26020,Vvar__2___24Anonymous__26021] :
( chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__26016,Vvar__1__op__26018,Vvar__2___24Anonymous__26020) = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__26017,Vvar__1__op__26019,Vvar__2___24Anonymous__26021)
=> ( Vvar__2___24Anonymous__26020 = Vvar__2___24Anonymous__26021
& Vvar__1__op__26018 = Vvar__1__op__26019
& Vvar__0__T__26016 = Vvar__0__T__26017 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Pack',axiom,
! [Vvar__0__sort__26048,Vvar__0__sort__26049,Vvar__1___24Anonymous__26050,Vvar__1___24Anonymous__26051,Vvar__2___24Anonymous__26052,Vvar__2___24Anonymous__26053] :
( chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__26048,Vvar__1___24Anonymous__26050,Vvar__2___24Anonymous__26052) = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__26049,Vvar__1___24Anonymous__26051,Vvar__2___24Anonymous__26053)
=> ( Vvar__2___24Anonymous__26052 = Vvar__2___24Anonymous__26053
& Vvar__1___24Anonymous__26050 = Vvar__1___24Anonymous__26051
& Vvar__0__sort__26048 = Vvar__0__sort__26049 ) ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__30670,Vvar__1__Q__30672,Vvar__2__init__30675,Vvar__3___24Anonymous__30676,Vvar__4___24Anonymous__30677] :
( c_24__type__30703___24t(Vvar__0__P__30670,Vvar__1__Q__30672,Vvar__2__init__30675,Vvar__3___24Anonymous__30676,Vvar__4___24Anonymous__30677,Vvar__0__P__30670)
=> ( c_24__type__30711___24t(Vvar__0__P__30670,Vvar__1__Q__30672,Vvar__2__init__30675,Vvar__3___24Anonymous__30676,Vvar__4___24Anonymous__30677,Vvar__1__Q__30672)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__30675)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__30676)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__30677)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__30670,Vvar__1__Q__30672,Vvar__2__init__30675,Vvar__3___24Anonymous__30676,Vvar__4___24Anonymous__30677)
=> ( ( Vvar__4___24Anonymous__30677 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__30676 = Vvar__2__init__30675 )
| ? [Vvar__3__k__30691] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__30691)
& ? [Vvar__4__l__30692] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__30692)
& ? [Vvar__5__n__30693] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__30693)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__30670,Vvar__1__Q__30672,Vvar__2__init__30675,Vvar__3__k__30691,Vvar__5__n__30693)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30670,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__30691),Vvar__4__l__30692)
& p(happ(Vvar__1__Q__30672,Vvar__4__l__30692))
& Vvar__4___24Anonymous__30677 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__30693)
& Vvar__3___24Anonymous__30676 = Vvar__4__l__30692 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__30630,Vvar__1__k__30632,Vvar__2___24Anonymous__30633] :
( c_24__type__30647___24t(Vvar__0__P__30630,Vvar__1__k__30632,Vvar__2___24Anonymous__30633,Vvar__0__P__30630)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__30632)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__30633)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30630,Vvar__1__k__30632,Vvar__2___24Anonymous__30633)
=> ( Vvar__2___24Anonymous__30633 = Vvar__1__k__30632
| ? [Vvar__2__l__30641] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30641)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30630,Vvar__1__k__30632,Vvar__2__l__30641)
& p(happ(Vvar__0__P__30630,Vvar__2__l__30641))
& Vvar__2___24Anonymous__30633 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30641) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__30649,Vvar__1__k__30651,Vvar__2___24Anonymous__30652] :
( c_24__type__30668___24t(Vvar__0__Q__30649,Vvar__1__k__30651,Vvar__2___24Anonymous__30652,Vvar__0__Q__30649)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__30651)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__30652)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__30649,Vvar__1__k__30651,Vvar__2___24Anonymous__30652)
=> ( ? [Vvar__2__l__30657] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30657)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__30649,Vvar__1__k__30651,Vvar__2__l__30657)
& Vvar__2___24Anonymous__30652 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30657) )
| ? [Vvar__2__l__30662] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30662)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__30651,Vvar__2__l__30662)
& p(happ(Vvar__0__Q__30649,Vvar__2__l__30662))
& Vvar__2___24Anonymous__30652 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30662) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__27655] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27655)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__27655)
=> ( Vvar__0___24Anonymous__27655 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__27657] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__27657)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__27657)
& Vvar__0___24Anonymous__27655 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__27657) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__27659] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27659)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__27659)
=> ? [Vvar__0__n__27661] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__27661)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__27661)
& Vvar__0___24Anonymous__27659 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__27661) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__13899,Vvar__1___24Anonymous__13900,VX13901] :
( cProp___24t(Vvar__0__P__13899)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__13900)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__13899,Vvar__1___24Anonymous__13900,VX13901)
=> ( ( p(Vvar__0__P__13899)
& Vvar__1___24Anonymous__13900 = cCoq_2eInit_2eDatatypes_2etrue
& VX13901 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__13899) )
| ( ~ p(Vvar__0__P__13899)
& Vvar__1___24Anonymous__13900 = cCoq_2eInit_2eDatatypes_2efalse
& VX13901 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__13899) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__32339,Vvar__1___24Anonymous__32340,Vvar__2___24Anonymous__32341] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__32339)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__32340)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__32341)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__32339,Vvar__1___24Anonymous__32340,Vvar__2___24Anonymous__32341)
=> ( ? [Vvar__0__x__32343] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__32343)
& Vvar__2___24Anonymous__32341 = Vvar__0__x__32343
& Vvar__1___24Anonymous__32340 = Vvar__0__x__32343
& Vvar__0___24Anonymous__32339 = Vvar__0__x__32343 )
| ? [Vvar__0__x__32344] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__32344)
& Vvar__2___24Anonymous__32341 = Vvar__0__x__32344
& Vvar__1___24Anonymous__32340 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__32339 = Vvar__0__x__32344 )
| ? [Vvar__0__x__32345] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__32345)
& Vvar__2___24Anonymous__32341 = Vvar__0__x__32345
& Vvar__1___24Anonymous__32340 = Vvar__0__x__32345
& Vvar__0___24Anonymous__32339 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__32346] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__32346)
& Vvar__2___24Anonymous__32341 = Vvar__0__x__32346
& Vvar__1___24Anonymous__32340 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__32339 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__32347] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__32347)
& Vvar__2___24Anonymous__32341 = Vvar__0__x__32347
& Vvar__1___24Anonymous__32340 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__32339 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX27481] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX27481)
=> ( VX27481 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__27482] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__27482)
& ? [Vvar__1___24Anonymous__27483] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__27483)
& ? [Vvar__2___24Anonymous__27484] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__27484)
& VX27481 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__27482,Vvar__1___24Anonymous__27483,Vvar__2___24Anonymous__27484) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX13921] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX13921)
=> ( VX13921 = cCoq_2eInit_2eByte_2ex00
| VX13921 = cCoq_2eInit_2eByte_2ex01
| VX13921 = cCoq_2eInit_2eByte_2ex02
| VX13921 = cCoq_2eInit_2eByte_2ex03
| VX13921 = cCoq_2eInit_2eByte_2ex04
| VX13921 = cCoq_2eInit_2eByte_2ex05
| VX13921 = cCoq_2eInit_2eByte_2ex06
| VX13921 = cCoq_2eInit_2eByte_2ex07
| VX13921 = cCoq_2eInit_2eByte_2ex08
| VX13921 = cCoq_2eInit_2eByte_2ex09
| VX13921 = cCoq_2eInit_2eByte_2ex0a
| VX13921 = cCoq_2eInit_2eByte_2ex0b
| VX13921 = cCoq_2eInit_2eByte_2ex0c
| VX13921 = cCoq_2eInit_2eByte_2ex0d
| VX13921 = cCoq_2eInit_2eByte_2ex0e
| VX13921 = cCoq_2eInit_2eByte_2ex0f
| VX13921 = cCoq_2eInit_2eByte_2ex10
| VX13921 = cCoq_2eInit_2eByte_2ex11
| VX13921 = cCoq_2eInit_2eByte_2ex12
| VX13921 = cCoq_2eInit_2eByte_2ex13
| VX13921 = cCoq_2eInit_2eByte_2ex14
| VX13921 = cCoq_2eInit_2eByte_2ex15
| VX13921 = cCoq_2eInit_2eByte_2ex16
| VX13921 = cCoq_2eInit_2eByte_2ex17
| VX13921 = cCoq_2eInit_2eByte_2ex18
| VX13921 = cCoq_2eInit_2eByte_2ex19
| VX13921 = cCoq_2eInit_2eByte_2ex1a
| VX13921 = cCoq_2eInit_2eByte_2ex1b
| VX13921 = cCoq_2eInit_2eByte_2ex1c
| VX13921 = cCoq_2eInit_2eByte_2ex1d
| VX13921 = cCoq_2eInit_2eByte_2ex1e
| VX13921 = cCoq_2eInit_2eByte_2ex1f
| VX13921 = cCoq_2eInit_2eByte_2ex20
| VX13921 = cCoq_2eInit_2eByte_2ex21
| VX13921 = cCoq_2eInit_2eByte_2ex22
| VX13921 = cCoq_2eInit_2eByte_2ex23
| VX13921 = cCoq_2eInit_2eByte_2ex24
| VX13921 = cCoq_2eInit_2eByte_2ex25
| VX13921 = cCoq_2eInit_2eByte_2ex26
| VX13921 = cCoq_2eInit_2eByte_2ex27
| VX13921 = cCoq_2eInit_2eByte_2ex28
| VX13921 = cCoq_2eInit_2eByte_2ex29
| VX13921 = cCoq_2eInit_2eByte_2ex2a
| VX13921 = cCoq_2eInit_2eByte_2ex2b
| VX13921 = cCoq_2eInit_2eByte_2ex2c
| VX13921 = cCoq_2eInit_2eByte_2ex2d
| VX13921 = cCoq_2eInit_2eByte_2ex2e
| VX13921 = cCoq_2eInit_2eByte_2ex2f
| VX13921 = cCoq_2eInit_2eByte_2ex30
| VX13921 = cCoq_2eInit_2eByte_2ex31
| VX13921 = cCoq_2eInit_2eByte_2ex32
| VX13921 = cCoq_2eInit_2eByte_2ex33
| VX13921 = cCoq_2eInit_2eByte_2ex34
| VX13921 = cCoq_2eInit_2eByte_2ex35
| VX13921 = cCoq_2eInit_2eByte_2ex36
| VX13921 = cCoq_2eInit_2eByte_2ex37
| VX13921 = cCoq_2eInit_2eByte_2ex38
| VX13921 = cCoq_2eInit_2eByte_2ex39
| VX13921 = cCoq_2eInit_2eByte_2ex3a
| VX13921 = cCoq_2eInit_2eByte_2ex3b
| VX13921 = cCoq_2eInit_2eByte_2ex3c
| VX13921 = cCoq_2eInit_2eByte_2ex3d
| VX13921 = cCoq_2eInit_2eByte_2ex3e
| VX13921 = cCoq_2eInit_2eByte_2ex3f
| VX13921 = cCoq_2eInit_2eByte_2ex40
| VX13921 = cCoq_2eInit_2eByte_2ex41
| VX13921 = cCoq_2eInit_2eByte_2ex42
| VX13921 = cCoq_2eInit_2eByte_2ex43
| VX13921 = cCoq_2eInit_2eByte_2ex44
| VX13921 = cCoq_2eInit_2eByte_2ex45
| VX13921 = cCoq_2eInit_2eByte_2ex46
| VX13921 = cCoq_2eInit_2eByte_2ex47
| VX13921 = cCoq_2eInit_2eByte_2ex48
| VX13921 = cCoq_2eInit_2eByte_2ex49
| VX13921 = cCoq_2eInit_2eByte_2ex4a
| VX13921 = cCoq_2eInit_2eByte_2ex4b
| VX13921 = cCoq_2eInit_2eByte_2ex4c
| VX13921 = cCoq_2eInit_2eByte_2ex4d
| VX13921 = cCoq_2eInit_2eByte_2ex4e
| VX13921 = cCoq_2eInit_2eByte_2ex4f
| VX13921 = cCoq_2eInit_2eByte_2ex50
| VX13921 = cCoq_2eInit_2eByte_2ex51
| VX13921 = cCoq_2eInit_2eByte_2ex52
| VX13921 = cCoq_2eInit_2eByte_2ex53
| VX13921 = cCoq_2eInit_2eByte_2ex54
| VX13921 = cCoq_2eInit_2eByte_2ex55
| VX13921 = cCoq_2eInit_2eByte_2ex56
| VX13921 = cCoq_2eInit_2eByte_2ex57
| VX13921 = cCoq_2eInit_2eByte_2ex58
| VX13921 = cCoq_2eInit_2eByte_2ex59
| VX13921 = cCoq_2eInit_2eByte_2ex5a
| VX13921 = cCoq_2eInit_2eByte_2ex5b
| VX13921 = cCoq_2eInit_2eByte_2ex5c
| VX13921 = cCoq_2eInit_2eByte_2ex5d
| VX13921 = cCoq_2eInit_2eByte_2ex5e
| VX13921 = cCoq_2eInit_2eByte_2ex5f
| VX13921 = cCoq_2eInit_2eByte_2ex60
| VX13921 = cCoq_2eInit_2eByte_2ex61
| VX13921 = cCoq_2eInit_2eByte_2ex62
| VX13921 = cCoq_2eInit_2eByte_2ex63
| VX13921 = cCoq_2eInit_2eByte_2ex64
| VX13921 = cCoq_2eInit_2eByte_2ex65
| VX13921 = cCoq_2eInit_2eByte_2ex66
| VX13921 = cCoq_2eInit_2eByte_2ex67
| VX13921 = cCoq_2eInit_2eByte_2ex68
| VX13921 = cCoq_2eInit_2eByte_2ex69
| VX13921 = cCoq_2eInit_2eByte_2ex6a
| VX13921 = cCoq_2eInit_2eByte_2ex6b
| VX13921 = cCoq_2eInit_2eByte_2ex6c
| VX13921 = cCoq_2eInit_2eByte_2ex6d
| VX13921 = cCoq_2eInit_2eByte_2ex6e
| VX13921 = cCoq_2eInit_2eByte_2ex6f
| VX13921 = cCoq_2eInit_2eByte_2ex70
| VX13921 = cCoq_2eInit_2eByte_2ex71
| VX13921 = cCoq_2eInit_2eByte_2ex72
| VX13921 = cCoq_2eInit_2eByte_2ex73
| VX13921 = cCoq_2eInit_2eByte_2ex74
| VX13921 = cCoq_2eInit_2eByte_2ex75
| VX13921 = cCoq_2eInit_2eByte_2ex76
| VX13921 = cCoq_2eInit_2eByte_2ex77
| VX13921 = cCoq_2eInit_2eByte_2ex78
| VX13921 = cCoq_2eInit_2eByte_2ex79
| VX13921 = cCoq_2eInit_2eByte_2ex7a
| VX13921 = cCoq_2eInit_2eByte_2ex7b
| VX13921 = cCoq_2eInit_2eByte_2ex7c
| VX13921 = cCoq_2eInit_2eByte_2ex7d
| VX13921 = cCoq_2eInit_2eByte_2ex7e
| VX13921 = cCoq_2eInit_2eByte_2ex7f
| VX13921 = cCoq_2eInit_2eByte_2ex80
| VX13921 = cCoq_2eInit_2eByte_2ex81
| VX13921 = cCoq_2eInit_2eByte_2ex82
| VX13921 = cCoq_2eInit_2eByte_2ex83
| VX13921 = cCoq_2eInit_2eByte_2ex84
| VX13921 = cCoq_2eInit_2eByte_2ex85
| VX13921 = cCoq_2eInit_2eByte_2ex86
| VX13921 = cCoq_2eInit_2eByte_2ex87
| VX13921 = cCoq_2eInit_2eByte_2ex88
| VX13921 = cCoq_2eInit_2eByte_2ex89
| VX13921 = cCoq_2eInit_2eByte_2ex8a
| VX13921 = cCoq_2eInit_2eByte_2ex8b
| VX13921 = cCoq_2eInit_2eByte_2ex8c
| VX13921 = cCoq_2eInit_2eByte_2ex8d
| VX13921 = cCoq_2eInit_2eByte_2ex8e
| VX13921 = cCoq_2eInit_2eByte_2ex8f
| VX13921 = cCoq_2eInit_2eByte_2ex90
| VX13921 = cCoq_2eInit_2eByte_2ex91
| VX13921 = cCoq_2eInit_2eByte_2ex92
| VX13921 = cCoq_2eInit_2eByte_2ex93
| VX13921 = cCoq_2eInit_2eByte_2ex94
| VX13921 = cCoq_2eInit_2eByte_2ex95
| VX13921 = cCoq_2eInit_2eByte_2ex96
| VX13921 = cCoq_2eInit_2eByte_2ex97
| VX13921 = cCoq_2eInit_2eByte_2ex98
| VX13921 = cCoq_2eInit_2eByte_2ex99
| VX13921 = cCoq_2eInit_2eByte_2ex9a
| VX13921 = cCoq_2eInit_2eByte_2ex9b
| VX13921 = cCoq_2eInit_2eByte_2ex9c
| VX13921 = cCoq_2eInit_2eByte_2ex9d
| VX13921 = cCoq_2eInit_2eByte_2ex9e
| VX13921 = cCoq_2eInit_2eByte_2ex9f
| VX13921 = cCoq_2eInit_2eByte_2exa0
| VX13921 = cCoq_2eInit_2eByte_2exa1
| VX13921 = cCoq_2eInit_2eByte_2exa2
| VX13921 = cCoq_2eInit_2eByte_2exa3
| VX13921 = cCoq_2eInit_2eByte_2exa4
| VX13921 = cCoq_2eInit_2eByte_2exa5
| VX13921 = cCoq_2eInit_2eByte_2exa6
| VX13921 = cCoq_2eInit_2eByte_2exa7
| VX13921 = cCoq_2eInit_2eByte_2exa8
| VX13921 = cCoq_2eInit_2eByte_2exa9
| VX13921 = cCoq_2eInit_2eByte_2exaa
| VX13921 = cCoq_2eInit_2eByte_2exab
| VX13921 = cCoq_2eInit_2eByte_2exac
| VX13921 = cCoq_2eInit_2eByte_2exad
| VX13921 = cCoq_2eInit_2eByte_2exae
| VX13921 = cCoq_2eInit_2eByte_2exaf
| VX13921 = cCoq_2eInit_2eByte_2exb0
| VX13921 = cCoq_2eInit_2eByte_2exb1
| VX13921 = cCoq_2eInit_2eByte_2exb2
| VX13921 = cCoq_2eInit_2eByte_2exb3
| VX13921 = cCoq_2eInit_2eByte_2exb4
| VX13921 = cCoq_2eInit_2eByte_2exb5
| VX13921 = cCoq_2eInit_2eByte_2exb6
| VX13921 = cCoq_2eInit_2eByte_2exb7
| VX13921 = cCoq_2eInit_2eByte_2exb8
| VX13921 = cCoq_2eInit_2eByte_2exb9
| VX13921 = cCoq_2eInit_2eByte_2exba
| VX13921 = cCoq_2eInit_2eByte_2exbb
| VX13921 = cCoq_2eInit_2eByte_2exbc
| VX13921 = cCoq_2eInit_2eByte_2exbd
| VX13921 = cCoq_2eInit_2eByte_2exbe
| VX13921 = cCoq_2eInit_2eByte_2exbf
| VX13921 = cCoq_2eInit_2eByte_2exc0
| VX13921 = cCoq_2eInit_2eByte_2exc1
| VX13921 = cCoq_2eInit_2eByte_2exc2
| VX13921 = cCoq_2eInit_2eByte_2exc3
| VX13921 = cCoq_2eInit_2eByte_2exc4
| VX13921 = cCoq_2eInit_2eByte_2exc5
| VX13921 = cCoq_2eInit_2eByte_2exc6
| VX13921 = cCoq_2eInit_2eByte_2exc7
| VX13921 = cCoq_2eInit_2eByte_2exc8
| VX13921 = cCoq_2eInit_2eByte_2exc9
| VX13921 = cCoq_2eInit_2eByte_2exca
| VX13921 = cCoq_2eInit_2eByte_2excb
| VX13921 = cCoq_2eInit_2eByte_2excc
| VX13921 = cCoq_2eInit_2eByte_2excd
| VX13921 = cCoq_2eInit_2eByte_2exce
| VX13921 = cCoq_2eInit_2eByte_2excf
| VX13921 = cCoq_2eInit_2eByte_2exd0
| VX13921 = cCoq_2eInit_2eByte_2exd1
| VX13921 = cCoq_2eInit_2eByte_2exd2
| VX13921 = cCoq_2eInit_2eByte_2exd3
| VX13921 = cCoq_2eInit_2eByte_2exd4
| VX13921 = cCoq_2eInit_2eByte_2exd5
| VX13921 = cCoq_2eInit_2eByte_2exd6
| VX13921 = cCoq_2eInit_2eByte_2exd7
| VX13921 = cCoq_2eInit_2eByte_2exd8
| VX13921 = cCoq_2eInit_2eByte_2exd9
| VX13921 = cCoq_2eInit_2eByte_2exda
| VX13921 = cCoq_2eInit_2eByte_2exdb
| VX13921 = cCoq_2eInit_2eByte_2exdc
| VX13921 = cCoq_2eInit_2eByte_2exdd
| VX13921 = cCoq_2eInit_2eByte_2exde
| VX13921 = cCoq_2eInit_2eByte_2exdf
| VX13921 = cCoq_2eInit_2eByte_2exe0
| VX13921 = cCoq_2eInit_2eByte_2exe1
| VX13921 = cCoq_2eInit_2eByte_2exe2
| VX13921 = cCoq_2eInit_2eByte_2exe3
| VX13921 = cCoq_2eInit_2eByte_2exe4
| VX13921 = cCoq_2eInit_2eByte_2exe5
| VX13921 = cCoq_2eInit_2eByte_2exe6
| VX13921 = cCoq_2eInit_2eByte_2exe7
| VX13921 = cCoq_2eInit_2eByte_2exe8
| VX13921 = cCoq_2eInit_2eByte_2exe9
| VX13921 = cCoq_2eInit_2eByte_2exea
| VX13921 = cCoq_2eInit_2eByte_2exeb
| VX13921 = cCoq_2eInit_2eByte_2exec
| VX13921 = cCoq_2eInit_2eByte_2exed
| VX13921 = cCoq_2eInit_2eByte_2exee
| VX13921 = cCoq_2eInit_2eByte_2exef
| VX13921 = cCoq_2eInit_2eByte_2exf0
| VX13921 = cCoq_2eInit_2eByte_2exf1
| VX13921 = cCoq_2eInit_2eByte_2exf2
| VX13921 = cCoq_2eInit_2eByte_2exf3
| VX13921 = cCoq_2eInit_2eByte_2exf4
| VX13921 = cCoq_2eInit_2eByte_2exf5
| VX13921 = cCoq_2eInit_2eByte_2exf6
| VX13921 = cCoq_2eInit_2eByte_2exf7
| VX13921 = cCoq_2eInit_2eByte_2exf8
| VX13921 = cCoq_2eInit_2eByte_2exf9
| VX13921 = cCoq_2eInit_2eByte_2exfa
| VX13921 = cCoq_2eInit_2eByte_2exfb
| VX13921 = cCoq_2eInit_2eByte_2exfc
| VX13921 = cCoq_2eInit_2eByte_2exfd
| VX13921 = cCoq_2eInit_2eByte_2exfe
| VX13921 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__14623,Vvar__1__Q__14624,Vvar__2___24Anonymous__14625] :
( cProp___24t(Vvar__0__P__14623)
=> ( cProp___24t(Vvar__1__Q__14624)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__14625)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__14623,Vvar__1__Q__14624,Vvar__2___24Anonymous__14625)
=> ( ( p(Vvar__0__P__14623)
& Vvar__2___24Anonymous__14625 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__14624)
& Vvar__2___24Anonymous__14625 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__26785,Vvar__1__Plt__26786,Vvar__2__Pgt__26787,Vvar__3___24Anonymous__26788] :
( cProp___24t(Vvar__0__Peq__26785)
=> ( cProp___24t(Vvar__1__Plt__26786)
=> ( cProp___24t(Vvar__2__Pgt__26787)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__26788)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__26785,Vvar__1__Plt__26786,Vvar__2__Pgt__26787,Vvar__3___24Anonymous__26788)
=> ( ( p(Vvar__0__Peq__26785)
& Vvar__3___24Anonymous__26788 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__26786)
& Vvar__3___24Anonymous__26788 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__26787)
& Vvar__3___24Anonymous__26788 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__30786,Vvar__1__Plt__30787,Vvar__2__Pgt__30788,Vvar__3___24Anonymous__30789,VX30790] :
( cProp___24t(Vvar__0__Peq__30786)
=> ( cProp___24t(Vvar__1__Plt__30787)
=> ( cProp___24t(Vvar__2__Pgt__30788)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__30789)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__30786,Vvar__1__Plt__30787,Vvar__2__Pgt__30788,Vvar__3___24Anonymous__30789,VX30790)
=> ( ( p(Vvar__0__Peq__30786)
& Vvar__3___24Anonymous__30789 = cCoq_2eInit_2eDatatypes_2eEq
& VX30790 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__30786,Vvar__1__Plt__30787,Vvar__2__Pgt__30788) )
| ( p(Vvar__1__Plt__30787)
& Vvar__3___24Anonymous__30789 = cCoq_2eInit_2eDatatypes_2eLt
& VX30790 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__30786,Vvar__1__Plt__30787,Vvar__2__Pgt__30788) )
| ( p(Vvar__2__Pgt__30788)
& Vvar__3___24Anonymous__30789 = cCoq_2eInit_2eDatatypes_2eGt
& VX30790 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__30786,Vvar__1__Plt__30787,Vvar__2__Pgt__30788) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1773] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1773)
=> ( VX1773 = cCoq_2eInit_2eDatatypes_2etrue
| VX1773 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX1863] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX1863)
=> ( VX1863 = cCoq_2eInit_2eDatatypes_2eEq
| VX1863 = cCoq_2eInit_2eDatatypes_2eLt
| VX1863 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__30784] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__30784)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__30784)
=> Vvar__0___24Anonymous__30784 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__27586,Vvar__1__a__27587,Vvar__2___24Anonymous__27588] :
( cType___24t(Vvar__0__A__27586)
=> ( t(Vvar__1__a__27587,Vvar__0__A__27586)
=> ( t(Vvar__2___24Anonymous__27588,Vvar__0__A__27586)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__27586,Vvar__1__a__27587,Vvar__2___24Anonymous__27588)
=> Vvar__2___24Anonymous__27588 = Vvar__1__a__27587 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__1784,VX1785] :
( cType___24t(Vvar__0__A__1784)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1784,VX1785)
=> ( VX1785 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1784)
| ? [Vvar__1___24Anonymous__1788] :
( t(Vvar__1___24Anonymous__1788,Vvar__0__A__1784)
& ? [Vvar__2___24Anonymous__1789] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1784,Vvar__2___24Anonymous__1789)
& VX1785 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1784,Vvar__1___24Anonymous__1788,Vvar__2___24Anonymous__1789) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1777] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1777)
=> ( VX1777 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__1778] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1778)
& VX1777 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1778) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__10473,VX10474] :
( cType___24t(Vvar__0__A__10473)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__10473,VX10474)
=> ( ? [Vvar__1___24Anonymous__10476] :
( t(Vvar__1___24Anonymous__10476,Vvar__0__A__10473)
& VX10474 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__10473,Vvar__1___24Anonymous__10476) )
| VX10474 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__10473) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__10487,Vvar__1__B__10488,VX10489] :
( cType___24t(Vvar__0__A__10487)
=> ( cType___24t(Vvar__1__B__10488)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__10487,Vvar__1__B__10488,VX10489)
=> ? [Vvar__2___24Anonymous__10492] :
( t(Vvar__2___24Anonymous__10492,Vvar__0__A__10487)
& ? [Vvar__3___24Anonymous__10493] :
( t(Vvar__3___24Anonymous__10493,Vvar__1__B__10488)
& VX10489 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__10487,Vvar__1__B__10488,Vvar__2___24Anonymous__10492,Vvar__3___24Anonymous__10493) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__27558,Vvar__1__B__27559,VX27560] :
( cType___24t(Vvar__0__A__27558)
=> ( cType___24t(Vvar__1__B__27559)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__27558,Vvar__1__B__27559,VX27560)
=> ( ? [Vvar__2___24Anonymous__27563] :
( t(Vvar__2___24Anonymous__27563,Vvar__0__A__27558)
& VX27560 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__27558,Vvar__1__B__27559,Vvar__2___24Anonymous__27563) )
| ? [Vvar__2___24Anonymous__27566] :
( t(Vvar__2___24Anonymous__27566,Vvar__1__B__27559)
& VX27560 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__27558,Vvar__1__B__27559,Vvar__2___24Anonymous__27566) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX10470] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX10470)
=> VX10470 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX30860] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX30860)
=> ( ? [Vvar__0__i__30861] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__30861)
& ? [Vvar__1__f__30862] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__30862)
& VX30860 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__30861,Vvar__1__f__30862) ) )
| ? [Vvar__0__i__30863] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__30863)
& ? [Vvar__1__f__30864] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__30864)
& ? [Vvar__2__e__30865] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__30865)
& VX30860 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__30863,Vvar__1__f__30864,Vvar__2__e__30865) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX27592] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX27592)
=> ( ? [Vvar__0__d__27593] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__27593)
& VX27592 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__27593) )
| ? [Vvar__0__d__27594] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__27594)
& VX27592 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__27594) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX26802] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX26802)
=> ( VX26802 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__26803] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26803)
& VX26802 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__26803) )
| ? [Vvar__0___24Anonymous__26804] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26804)
& VX26802 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__26804) )
| ? [Vvar__0___24Anonymous__26805] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26805)
& VX26802 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__26805) )
| ? [Vvar__0___24Anonymous__26806] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26806)
& VX26802 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__26806) )
| ? [Vvar__0___24Anonymous__26807] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26807)
& VX26802 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__26807) )
| ? [Vvar__0___24Anonymous__26808] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26808)
& VX26802 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__26808) )
| ? [Vvar__0___24Anonymous__26809] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26809)
& VX26802 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__26809) )
| ? [Vvar__0___24Anonymous__26810] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26810)
& VX26802 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__26810) )
| ? [Vvar__0___24Anonymous__26811] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26811)
& VX26802 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__26811) )
| ? [Vvar__0___24Anonymous__26812] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__26812)
& VX26802 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__26812) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__12248,Vvar__1___24Anonymous__12249] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__12248)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__12249)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__12248,Vvar__1___24Anonymous__12249)
=> ( Vvar__1___24Anonymous__12249 = Vvar__0__n__12248
| ? [Vvar__1__m__12253] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__12253)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__12248,Vvar__1__m__12253)
& Vvar__1___24Anonymous__12249 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__12253) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__10105,Vvar__1__P__10106,VX10109] :
( cType___24t(Vvar__0__A__10105)
=> ( c_24__type__10119___24t(Vvar__0__A__10105,Vvar__1__P__10106,Vvar__1__P__10106)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__10105,Vvar__1__P__10106,VX10109)
=> ? [Vvar__2__x__10114] :
( t(Vvar__2__x__10114,Vvar__0__A__10105)
& p(happ(Vvar__1__P__10106,Vvar__2__x__10114))
& VX10109 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__10105,Vvar__1__P__10106,Vvar__2__x__10114) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__29922,Vvar__1__P__29923,Vvar__2__Q__29926,VX29929] :
( cType___24t(Vvar__0__A__29922)
=> ( c_24__type__29946___24t(Vvar__0__A__29922,Vvar__1__P__29923,Vvar__2__Q__29926,Vvar__1__P__29923)
=> ( c_24__type__29954___24t(Vvar__0__A__29922,Vvar__1__P__29923,Vvar__2__Q__29926,Vvar__2__Q__29926)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__29922,Vvar__1__P__29923,Vvar__2__Q__29926,VX29929)
=> ? [Vvar__3__x__29937] :
( t(Vvar__3__x__29937,Vvar__0__A__29922)
& p(happ(Vvar__1__P__29923,Vvar__3__x__29937))
& p(happ(Vvar__2__Q__29926,Vvar__3__x__29937))
& VX29929 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__29922,Vvar__1__P__29923,Vvar__2__Q__29926,Vvar__3__x__29937) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__24894,Vvar__1__P__24895,VX24898] :
( cType___24t(Vvar__0__A__24894)
=> ( c_24__type__24908___24t(Vvar__0__A__24894,Vvar__1__P__24895,Vvar__1__P__24895)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__24894,Vvar__1__P__24895,VX24898)
=> ? [Vvar__2__x__24903] :
( t(Vvar__2__x__24903,Vvar__0__A__24894)
& ? [Vvar__3___24Anonymous__24904] :
( t(Vvar__3___24Anonymous__24904,happ(Vvar__1__P__24895,Vvar__2__x__24903))
& VX24898 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__24894,Vvar__1__P__24895,Vvar__2__x__24903,Vvar__3___24Anonymous__24904) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__29978,Vvar__1__P__29979,Vvar__2__Q__29982,VX29985] :
( cType___24t(Vvar__0__A__29978)
=> ( c_24__type__30002___24t(Vvar__0__A__29978,Vvar__1__P__29979,Vvar__2__Q__29982,Vvar__1__P__29979)
=> ( c_24__type__30010___24t(Vvar__0__A__29978,Vvar__1__P__29979,Vvar__2__Q__29982,Vvar__2__Q__29982)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__29978,Vvar__1__P__29979,Vvar__2__Q__29982,VX29985)
=> ? [Vvar__3__x__29993] :
( t(Vvar__3__x__29993,Vvar__0__A__29978)
& ? [Vvar__4___24Anonymous__29994] :
( t(Vvar__4___24Anonymous__29994,happ(Vvar__1__P__29979,Vvar__3__x__29993))
& ? [Vvar__5___24Anonymous__29995] :
( t(Vvar__5___24Anonymous__29995,happ(Vvar__2__Q__29982,Vvar__3__x__29993))
& VX29985 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__29978,Vvar__1__P__29979,Vvar__2__Q__29982,Vvar__3__x__29993,Vvar__4___24Anonymous__29994,Vvar__5___24Anonymous__29995) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__56,Vvar__1__B__57,VX58] :
( cProp___24t(Vvar__0__A__56)
=> ( cProp___24t(Vvar__1__B__57)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__56,Vvar__1__B__57,VX58)
=> ( ( p(Vvar__0__A__56)
& VX58 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__56,Vvar__1__B__57) )
| ( p(Vvar__1__B__57)
& VX58 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__56,Vvar__1__B__57) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__27445,Vvar__1__B__27446,VX27447] :
( cType___24t(Vvar__0__A__27445)
=> ( cProp___24t(Vvar__1__B__27446)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__27445,Vvar__1__B__27446,VX27447)
=> ( ? [Vvar__2___24Anonymous__27450] :
( t(Vvar__2___24Anonymous__27450,Vvar__0__A__27445)
& VX27447 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__27445,Vvar__1__B__27446,Vvar__2___24Anonymous__27450) )
| ( p(Vvar__1__B__27446)
& VX27447 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__27445,Vvar__1__B__27446) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__30477,Vvar__1__R__30478,Vvar__2__x__30483] :
( cType___24t(Vvar__0__A__30477)
=> ( c_24__type__30512___24t(Vvar__0__A__30477,Vvar__1__R__30478,Vvar__2__x__30483,Vvar__1__R__30478)
=> ( t(Vvar__2__x__30483,Vvar__0__A__30477)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__30477,Vvar__1__R__30478,Vvar__2__x__30483)
=> ( ! [Vvar__var__var__var__var__3__y__30493__30495__30497__30499__30501] :
( t(Vvar__var__var__var__var__3__y__30493__30495__30497__30499__30501,Vvar__0__A__30477)
=> ( p(happ(happ(Vvar__1__R__30478,Vvar__var__var__var__var__3__y__30493__30495__30497__30499__30501),Vvar__2__x__30483))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__30477,Vvar__1__R__30478,Vvar__var__var__var__var__3__y__30493__30495__30497__30499__30501) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__32968,Vvar__1__a__32969,Vvar__2___24Anonymous__32970,Vvar__3___24Anonymous__32971] :
( cType___24t(Vvar__0__A__32968)
=> ( t(Vvar__1__a__32969,Vvar__0__A__32968)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32968,Vvar__2___24Anonymous__32970)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32968,Vvar__3___24Anonymous__32971)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__32968,Vvar__1__a__32969,Vvar__2___24Anonymous__32970,Vvar__3___24Anonymous__32971)
=> ( ? [Vvar__2__l__32975] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32968,Vvar__2__l__32975)
& Vvar__3___24Anonymous__32971 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32968,Vvar__1__a__32969,Vvar__2__l__32975)
& Vvar__2___24Anonymous__32970 = Vvar__2__l__32975 )
| ? [Vvar__2__x__32978] :
( t(Vvar__2__x__32978,Vvar__0__A__32968)
& ? [Vvar__3__l__32979] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32968,Vvar__3__l__32979)
& ? [Vvar__4__l_27__32980] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32968,Vvar__4__l_27__32980)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__32968,Vvar__1__a__32969,Vvar__3__l__32979,Vvar__4__l_27__32980)
& Vvar__3___24Anonymous__32971 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32968,Vvar__2__x__32978,Vvar__4__l_27__32980)
& Vvar__2___24Anonymous__32970 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32968,Vvar__2__x__32978,Vvar__3__l__32979) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__18879,Vvar__1__P__18880,Vvar__2___24Anonymous__18883] :
( cType___24t(Vvar__0__A__18879)
=> ( c_24__type__18903___24t(Vvar__0__A__18879,Vvar__1__P__18880,Vvar__2___24Anonymous__18883,Vvar__1__P__18880)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18879,Vvar__2___24Anonymous__18883)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__18879,Vvar__1__P__18880,Vvar__2___24Anonymous__18883)
=> ( ? [Vvar__2__x__18889] :
( t(Vvar__2__x__18889,Vvar__0__A__18879)
& ? [Vvar__3__l__18890] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18879,Vvar__3__l__18890)
& p(happ(Vvar__1__P__18880,Vvar__2__x__18889))
& Vvar__2___24Anonymous__18883 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18879,Vvar__2__x__18889,Vvar__3__l__18890) ) )
| ? [Vvar__2__x__18896] :
( t(Vvar__2__x__18896,Vvar__0__A__18879)
& ? [Vvar__3__l__18897] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__18879,Vvar__3__l__18897)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__18879,Vvar__1__P__18880,Vvar__3__l__18897)
& Vvar__2___24Anonymous__18883 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__18879,Vvar__2__x__18896,Vvar__3__l__18897) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__32991,Vvar__1__P__32992,Vvar__2___24Anonymous__32995] :
( cType___24t(Vvar__0__A__32991)
=> ( c_24__type__33013___24t(Vvar__0__A__32991,Vvar__1__P__32992,Vvar__2___24Anonymous__32995,Vvar__1__P__32992)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32991,Vvar__2___24Anonymous__32995)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__32991,Vvar__1__P__32992,Vvar__2___24Anonymous__32995)
=> ( Vvar__2___24Anonymous__32995 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32991)
| ? [Vvar__2__x__33005] :
( t(Vvar__2__x__33005,Vvar__0__A__32991)
& ? [Vvar__3__l__33006] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32991,Vvar__3__l__33006)
& p(happ(Vvar__1__P__32992,Vvar__2__x__33005))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__32991,Vvar__1__P__32992,Vvar__3__l__33006)
& Vvar__2___24Anonymous__32995 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32991,Vvar__2__x__33005,Vvar__3__l__33006) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__33015,Vvar__1__B__33016,Vvar__2__R__33017,Vvar__3___24Anonymous__33022,Vvar__4___24Anonymous__33023] :
( cType___24t(Vvar__0__A__33015)
=> ( cType___24t(Vvar__1__B__33016)
=> ( c_24__type__33060___24t(Vvar__0__A__33015,Vvar__1__B__33016,Vvar__2__R__33017,Vvar__3___24Anonymous__33022,Vvar__4___24Anonymous__33023,Vvar__2__R__33017)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33015,Vvar__3___24Anonymous__33022)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__33016,Vvar__4___24Anonymous__33023)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__33015,Vvar__1__B__33016,Vvar__2__R__33017,Vvar__3___24Anonymous__33022,Vvar__4___24Anonymous__33023)
=> ( ( Vvar__4___24Anonymous__33023 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__33016)
& Vvar__3___24Anonymous__33022 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__33015) )
| ? [Vvar__3__x__33039] :
( t(Vvar__3__x__33039,Vvar__0__A__33015)
& ? [Vvar__4__y__33040] :
( t(Vvar__4__y__33040,Vvar__1__B__33016)
& ? [Vvar__5__l__33041] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33015,Vvar__5__l__33041)
& ? [Vvar__6__l_27__33042] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__33016,Vvar__6__l_27__33042)
& p(happ(happ(Vvar__2__R__33017,Vvar__3__x__33039),Vvar__4__y__33040))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__33015,Vvar__1__B__33016,Vvar__2__R__33017,Vvar__5__l__33041,Vvar__6__l_27__33042)
& Vvar__4___24Anonymous__33023 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__33016,Vvar__4__y__33040,Vvar__6__l_27__33042)
& Vvar__3___24Anonymous__33022 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33015,Vvar__3__x__33039,Vvar__5__l__33041) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__33062,Vvar__1__R__33063,Vvar__2___24Anonymous__33068] :
( cType___24t(Vvar__0__A__33062)
=> ( c_24__type__33095___24t(Vvar__0__A__33062,Vvar__1__R__33063,Vvar__2___24Anonymous__33068,Vvar__1__R__33063)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33062,Vvar__2___24Anonymous__33068)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__33062,Vvar__1__R__33063,Vvar__2___24Anonymous__33068)
=> ( Vvar__2___24Anonymous__33068 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__33062)
| ? [Vvar__2__a__33082] :
( t(Vvar__2__a__33082,Vvar__0__A__33062)
& ? [Vvar__3__l__33083] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__33062,Vvar__3__l__33083)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__33062,happ(Vvar__1__R__33063,Vvar__2__a__33082),Vvar__3__l__33083)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__33062,Vvar__1__R__33063,Vvar__3__l__33083)
& Vvar__2___24Anonymous__33068 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__33062,Vvar__2__a__33082,Vvar__3__l__33083) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__32982,Vvar__1___24Anonymous__32983] :
( cType___24t(Vvar__0__A__32982)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32982,Vvar__1___24Anonymous__32983)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__32982,Vvar__1___24Anonymous__32983)
=> ( Vvar__1___24Anonymous__32983 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32982)
| ? [Vvar__1__x__32987] :
( t(Vvar__1__x__32987,Vvar__0__A__32982)
& ? [Vvar__2__l__32988] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32982,Vvar__2__l__32988)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__32982,Vvar__1__x__32987,Vvar__2__l__32988)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__32982,Vvar__2__l__32988)
& Vvar__1___24Anonymous__32983 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32982,Vvar__1__x__32987,Vvar__2__l__32988) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__10054,Vvar__1__eqA__10055,Vvar__2__x__10060,Vvar__3___24Anonymous__10061] :
( cType___24t(Vvar__0__A__10054)
=> ( c_24__type__10094___24t(Vvar__0__A__10054,Vvar__1__eqA__10055,Vvar__2__x__10060,Vvar__3___24Anonymous__10061,Vvar__1__eqA__10055)
=> ( t(Vvar__2__x__10060,Vvar__0__A__10054)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10054,Vvar__3___24Anonymous__10061)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__10054,Vvar__1__eqA__10055,Vvar__2__x__10060,Vvar__3___24Anonymous__10061)
=> ( ? [Vvar__3__y__10070] :
( t(Vvar__3__y__10070,Vvar__0__A__10054)
& ? [Vvar__4__l__10071] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10054,Vvar__4__l__10071)
& p(happ(happ(Vvar__1__eqA__10055,Vvar__2__x__10060),Vvar__3__y__10070))
& Vvar__3___24Anonymous__10061 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10054,Vvar__3__y__10070,Vvar__4__l__10071) ) )
| ? [Vvar__3__y__10080] :
( t(Vvar__3__y__10080,Vvar__0__A__10054)
& ? [Vvar__4__l__10081] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__10054,Vvar__4__l__10081)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__10054,Vvar__1__eqA__10055,Vvar__2__x__10060,Vvar__4__l__10081)
& Vvar__3___24Anonymous__10061 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__10054,Vvar__3__y__10080,Vvar__4__l__10081) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__32017,Vvar__1__eqA__32018,Vvar__2___24Anonymous__32023] :
( cType___24t(Vvar__0__A__32017)
=> ( c_24__type__32050___24t(Vvar__0__A__32017,Vvar__1__eqA__32018,Vvar__2___24Anonymous__32023,Vvar__1__eqA__32018)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32017,Vvar__2___24Anonymous__32023)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__32017,Vvar__1__eqA__32018,Vvar__2___24Anonymous__32023)
=> ( Vvar__2___24Anonymous__32023 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__32017)
| ? [Vvar__2__x__32037] :
( t(Vvar__2__x__32037,Vvar__0__A__32017)
& ? [Vvar__3__l__32038] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__32017,Vvar__3__l__32038)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__32017,Vvar__1__eqA__32018,Vvar__2__x__32037,Vvar__3__l__32038)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__32017,Vvar__1__eqA__32018,Vvar__3__l__32038)
& Vvar__2___24Anonymous__32023 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__32017,Vvar__2__x__32037,Vvar__3__l__32038) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__34668,Vvar__1__eqA__34669,Vvar__2___24Anonymous__34674,Vvar__3___24Anonymous__34675] :
( cType___24t(Vvar__0__A__34668)
=> ( c_24__type__34706___24t(Vvar__0__A__34668,Vvar__1__eqA__34669,Vvar__2___24Anonymous__34674,Vvar__3___24Anonymous__34675,Vvar__1__eqA__34669)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34668,Vvar__2___24Anonymous__34674)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34668,Vvar__3___24Anonymous__34675)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__34668,Vvar__1__eqA__34669,Vvar__2___24Anonymous__34674,Vvar__3___24Anonymous__34675)
=> ( ( Vvar__3___24Anonymous__34675 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34668)
& Vvar__2___24Anonymous__34674 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34668) )
| ? [Vvar__2__x__34689] :
( t(Vvar__2__x__34689,Vvar__0__A__34668)
& ? [Vvar__3__x_27__34690] :
( t(Vvar__3__x_27__34690,Vvar__0__A__34668)
& ? [Vvar__4__l__34691] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34668,Vvar__4__l__34691)
& ? [Vvar__5__l_27__34692] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34668,Vvar__5__l_27__34692)
& p(happ(happ(Vvar__1__eqA__34669,Vvar__2__x__34689),Vvar__3__x_27__34690))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__34668,Vvar__1__eqA__34669,Vvar__4__l__34691,Vvar__5__l_27__34692)
& Vvar__3___24Anonymous__34675 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34668,Vvar__3__x_27__34690,Vvar__5__l_27__34692)
& Vvar__2___24Anonymous__34674 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34668,Vvar__2__x__34689,Vvar__4__l__34691) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.boolP',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(c_24True) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.has_fixpoint',axiom,
! [Vvar__0__A__27530] :
( cProp___24t(Vvar__0__A__27530)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__27530)
=> ( ( ( p(Vvar__0__A__27530)
=> p(Vvar__0__A__27530) )
=> p(Vvar__0__A__27530) )
& ( ( p(Vvar__0__A__27530)
=> p(Vvar__0__A__27530) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__27506,Vvar__1__B__27507] :
( cProp___24t(Vvar__0__A__27506)
=> ( cProp___24t(Vvar__1__B__27507)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__27506,Vvar__1__B__27507)
=> ( ( p(Vvar__0__A__27506)
=> p(Vvar__1__B__27507) )
& ( p(Vvar__1__B__27507)
=> p(Vvar__0__A__27506) )
& ( p(Vvar__1__B__27507)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__26933,Vvar__1__P__26934,Vvar__2__p__26937,Vvar__3__x__26938,Vvar__4__q__26939,Vvar__5___24Anonymous__26940] :
( cType___24t(Vvar__0__U__26933)
=> ( c_24__type__26955___24t(Vvar__0__U__26933,Vvar__1__P__26934,Vvar__2__p__26937,Vvar__3__x__26938,Vvar__4__q__26939,Vvar__5___24Anonymous__26940,Vvar__1__P__26934)
=> ( t(Vvar__2__p__26937,Vvar__0__U__26933)
=> ( t(Vvar__3__x__26938,happ(Vvar__1__P__26934,Vvar__2__p__26937))
=> ( t(Vvar__4__q__26939,Vvar__0__U__26933)
=> ( t(Vvar__5___24Anonymous__26940,happ(Vvar__1__P__26934,Vvar__4__q__26939))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__26933,Vvar__1__P__26934,Vvar__2__p__26937,Vvar__3__x__26938,Vvar__4__q__26939,Vvar__5___24Anonymous__26940)
=> ( Vvar__5___24Anonymous__26940 = Vvar__3__x__26938
& Vvar__4__q__26939 = Vvar__2__p__26937 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__27627,Vvar__1__P__27628,Vvar__2__p__27631,Vvar__3__x__27632,Vvar__4__q__27633,Vvar__5__y__27634] :
( cType___24t(Vvar__0__U__27627)
=> ( c_24__type__27653___24t(Vvar__0__U__27627,Vvar__1__P__27628,Vvar__2__p__27631,Vvar__3__x__27632,Vvar__4__q__27633,Vvar__5__y__27634,Vvar__1__P__27628)
=> ( t(Vvar__2__p__27631,Vvar__0__U__27627)
=> ( t(Vvar__3__x__27632,happ(Vvar__1__P__27628,Vvar__2__p__27631))
=> ( t(Vvar__4__q__27633,Vvar__0__U__27627)
=> ( t(Vvar__5__y__27634,happ(Vvar__1__P__27628,Vvar__4__q__27633))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__27627,Vvar__1__P__27628,Vvar__2__p__27631,Vvar__3__x__27632,Vvar__4__q__27633,Vvar__5__y__27634)
=> ( Vvar__4__q__27633 = Vvar__2__p__27631
& Vvar__3__x__27632 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__27627,Vvar__4__q__27633,Vvar__1__P__27628,Vvar__5__y__27634,Vvar__2__p__27631)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX47] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX47)
=> ( VX47 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__48] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__48)
& VX47 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__48) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1)
=> ( VX1 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2) )
| ? [Vvar__0___24Anonymous__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3)
& VX1 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX1760] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1760)
=> ( ? [Vvar__0___24Anonymous__1761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1761)
& VX1760 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1761) )
| ? [Vvar__0___24Anonymous__1762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1762)
& VX1760 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1762) )
| VX1760 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__32276,VX32277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32276)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__32276,VX32277)
=> ( ( Vvar__0___24Anonymous__32276 = cCoq_2eNumbers_2eBinNums_2exH
& VX32277 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__32278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__32278)
& ? [Vvar__1___24Anonymous__32279] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__32278,Vvar__1___24Anonymous__32279)
& Vvar__0___24Anonymous__32276 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2432314___24a2(Vvar__0___24Anonymous__32276,Vvar__0__p__32278)
& VX32277 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__32278,Vvar__1___24Anonymous__32279) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__35285,Vvar__1__q__35286,Vvar__2___24Anonymous__35287] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__35285)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__35286)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__35287)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__35285,Vvar__1__q__35286,Vvar__2___24Anonymous__35287)
=> ( ( Vvar__0__p__35285 = Vvar__1__q__35286
& Vvar__2___24Anonymous__35287 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__35294] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__35294)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__35286,Vvar__2__r__35294) = Vvar__0__p__35285
& Vvar__2___24Anonymous__35287 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__35294) )
| ? [Vvar__2__r__35298] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__35298)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__35285,Vvar__2__r__35298) = Vvar__1__q__35286
& Vvar__2___24Anonymous__35287 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX27475] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX27475)
=> ( VX27475 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__27476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27476)
& VX27475 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__27476) )
| VX27475 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX19148] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX19148)
=> ? [Vvar__0__Qnum__19149] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__19149)
& ? [Vvar__1__Qden__19150] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__19150)
& VX19148 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__19149,Vvar__1__Qden__19150) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX30979] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX30979)
=> ? [Vvar__0__neg__30980] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__30980)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__30980,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX30979 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__30980) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX30958] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX30958)
=> ? [Vvar__0__nonneg__30959] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__30959)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__30959)
& VX30958 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__30959) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX30972] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX30972)
=> ? [Vvar__0__nonpos__30973] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__30973)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__30973,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX30972 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__30973) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX30986] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX30986)
=> ? [Vvar__0__nonzero__30987] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__30987)
& Vvar__0__nonzero__30987 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX30986 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__30987) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX30965] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX30965)
=> ? [Vvar__0__pos__30966] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__30966)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__30966)
& VX30965 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__30966) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__29170,Vvar__1___24Anonymous__29171,VX29172] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__29170)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__29171)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__29170,Vvar__1___24Anonymous__29171,VX29172)
=> ( ( Vvar__0__x__29170 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__29171 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX29172 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__29170) )
| ? [Vvar__1__n__29176] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__29176)
& Vvar__0__x__29170 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__29176)
& Vvar__1___24Anonymous__29171 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2429196___24a3(Vvar__0__x__29170,Vvar__1___24Anonymous__29171,Vvar__1__n__29176)
& VX29172 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__29170,Vvar__1__n__29176) )
| ? [Vvar__1__n__29181] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__29181)
& Vvar__0__x__29170 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__29181))
& Vvar__1___24Anonymous__29171 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2429213___24a3(Vvar__0__x__29170,Vvar__1___24Anonymous__29171,Vvar__1__n__29181)
& VX29172 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__29170,Vvar__1__n__29181) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__33832,Vvar__1__R__33833] :
( cType___24t(Vvar__0__A__33832)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33832,Vvar__1__R__33833)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__33832,Vvar__1__R__33833)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__33832,Vvar__1__R__33833)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__33832,Vvar__1__R__33833)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__33824,Vvar__1__R__33825] :
( cType___24t(Vvar__0__A__33824)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33824,Vvar__1__R__33825)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__33824,Vvar__1__R__33825)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__33824,Vvar__1__R__33825)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__33824,Vvar__1__R__33825)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__33824,Vvar__1__R__33825)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__33816,Vvar__1__R__33817] :
( cType___24t(Vvar__0__A__33816)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33816,Vvar__1__R__33817)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__33816,Vvar__1__R__33817)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__33816,Vvar__1__R__33817)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__33816,Vvar__1__R__33817)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__33816,Vvar__1__R__33817)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__33809,Vvar__1__R__33810] :
( cType___24t(Vvar__0__A__33809)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33809,Vvar__1__R__33810)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__33809,Vvar__1__R__33810)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__33809,Vvar__1__R__33810)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__33809,Vvar__1__R__33810)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__19265,Vvar__1__leA__19266,Vvar__2___24Anonymous__19271] :
( cType___24t(Vvar__0__A__19265)
=> ( c_24__type__19361___24t(Vvar__0__A__19265,Vvar__1__leA__19266,Vvar__2___24Anonymous__19271,Vvar__1__leA__19266)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19265,Vvar__2___24Anonymous__19271)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__19265,Vvar__1__leA__19266,Vvar__2___24Anonymous__19271)
=> ( Vvar__2___24Anonymous__19271 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__19265)
| ? [Vvar__2__x__19285] :
( t(Vvar__2__x__19285,Vvar__0__A__19265)
& Vvar__2___24Anonymous__19271 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19265,Vvar__2__x__19285,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__19265)) )
| ? [Vvar__2__x__19292] :
( t(Vvar__2__x__19292,Vvar__0__A__19265)
& ? [Vvar__3__y__19293] :
( t(Vvar__3__y__19293,Vvar__0__A__19265)
& ? [Vvar__4__l__19294] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__19265,Vvar__4__l__19294)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__19265,Vvar__1__leA__19266,Vvar__2__x__19292,Vvar__3__y__19293)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__19265,Vvar__1__leA__19266,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__19265,Vvar__4__l__19294,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__19265,Vvar__3__y__19293,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__19265))))
& Vvar__2___24Anonymous__19271 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419559___24a6(Vvar__0__A__19265,Vvar__1__leA__19266,Vvar__2___24Anonymous__19271,Vvar__2__x__19292,Vvar__3__y__19293,Vvar__4__l__19294) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__34331,Vvar__1__leA__34332,Vvar__2___24Anonymous__34337,Vvar__3___24Anonymous__34338] :
( cType___24t(Vvar__0__A__34331)
=> ( c_24__type__34380___24t(Vvar__0__A__34331,Vvar__1__leA__34332,Vvar__2___24Anonymous__34337,Vvar__3___24Anonymous__34338,Vvar__1__leA__34332)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__2___24Anonymous__34337)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__3___24Anonymous__34338)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__34331,Vvar__1__leA__34332,Vvar__2___24Anonymous__34337,Vvar__3___24Anonymous__34338)
=> ( ? [Vvar__2__a__34346] :
( t(Vvar__2__a__34346,Vvar__0__A__34331)
& ? [Vvar__3__x__34347] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__3__x__34347)
& Vvar__3___24Anonymous__34338 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34331,Vvar__2__a__34346,Vvar__3__x__34347)
& Vvar__2___24Anonymous__34337 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34331) ) )
| ? [Vvar__2__a__34354] :
( t(Vvar__2__a__34354,Vvar__0__A__34331)
& ? [Vvar__3__b__34355] :
( t(Vvar__3__b__34355,Vvar__0__A__34331)
& p(happ(happ(Vvar__1__leA__34332,Vvar__2__a__34354),Vvar__3__b__34355))
& ? [Vvar__5__x__34357] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__5__x__34357)
& ? [Vvar__6__y__34358] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__6__y__34358)
& Vvar__3___24Anonymous__34338 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34331,Vvar__3__b__34355,Vvar__6__y__34358)
& Vvar__2___24Anonymous__34337 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34331,Vvar__2__a__34354,Vvar__5__x__34357) ) ) ) )
| ? [Vvar__2__a__34365] :
( t(Vvar__2__a__34365,Vvar__0__A__34331)
& ? [Vvar__3__x__34366] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__3__x__34366)
& ? [Vvar__4__y__34367] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34331,Vvar__4__y__34367)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__34331,Vvar__1__leA__34332,Vvar__3__x__34366,Vvar__4__y__34367)
& Vvar__3___24Anonymous__34338 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34331,Vvar__2__a__34365,Vvar__4__y__34367)
& Vvar__2___24Anonymous__34337 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34331,Vvar__2__a__34365,Vvar__3__x__34366) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__19214,Vvar__1__R__19215,Vvar__2__x__19216,Vvar__3___24Anonymous__19217] :
( cType___24t(Vvar__0__A__19214)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__19214,Vvar__1__R__19215)
=> ( t(Vvar__2__x__19216,Vvar__0__A__19214)
=> ( t(Vvar__3___24Anonymous__19217,Vvar__0__A__19214)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__19214,Vvar__1__R__19215,Vvar__2__x__19216,Vvar__3___24Anonymous__19217)
=> ( ? [Vvar__3__y__19222] :
( t(Vvar__3__y__19222,Vvar__0__A__19214)
& p(happ(happ(Vvar__1__R__19215,Vvar__2__x__19216),Vvar__3__y__19222))
& Vvar__3___24Anonymous__19217 = Vvar__3__y__19222 )
| Vvar__3___24Anonymous__19217 = Vvar__2__x__19216 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__33905,Vvar__1__R__33906,Vvar__2__x__33907,Vvar__3___24Anonymous__33908] :
( cType___24t(Vvar__0__A__33905)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33905,Vvar__1__R__33906)
=> ( t(Vvar__2__x__33907,Vvar__0__A__33905)
=> ( t(Vvar__3___24Anonymous__33908,Vvar__0__A__33905)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__33905,Vvar__1__R__33906,Vvar__2__x__33907,Vvar__3___24Anonymous__33908)
=> ( Vvar__3___24Anonymous__33908 = Vvar__2__x__33907
| ? [Vvar__3__y__33916] :
( t(Vvar__3__y__33916,Vvar__0__A__33905)
& ? [Vvar__4__z__33917] :
( t(Vvar__4__z__33917,Vvar__0__A__33905)
& ( p(happ(happ(Vvar__1__R__33906,Vvar__2__x__33907),Vvar__3__y__33916))
| p(happ(happ(Vvar__1__R__33906,Vvar__3__y__33916),Vvar__2__x__33907)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__33905,Vvar__1__R__33906,Vvar__3__y__33916,Vvar__4__z__33917)
& Vvar__3___24Anonymous__33908 = Vvar__4__z__33917 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__33920,Vvar__1__R__33921,Vvar__2__x__33922,Vvar__3___24Anonymous__33923] :
( cType___24t(Vvar__0__A__33920)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33920,Vvar__1__R__33921)
=> ( t(Vvar__2__x__33922,Vvar__0__A__33920)
=> ( t(Vvar__3___24Anonymous__33923,Vvar__0__A__33920)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__33920,Vvar__1__R__33921,Vvar__2__x__33922,Vvar__3___24Anonymous__33923)
=> ( Vvar__3___24Anonymous__33923 = Vvar__2__x__33922
| ? [Vvar__3__y__33931] :
( t(Vvar__3__y__33931,Vvar__0__A__33920)
& ? [Vvar__4__z__33932] :
( t(Vvar__4__z__33932,Vvar__0__A__33920)
& ( p(happ(happ(Vvar__1__R__33921,Vvar__3__y__33931),Vvar__4__z__33932))
| p(happ(happ(Vvar__1__R__33921,Vvar__4__z__33932),Vvar__3__y__33931)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__33920,Vvar__1__R__33921,Vvar__2__x__33922,Vvar__3__y__33931)
& Vvar__3___24Anonymous__33923 = Vvar__4__z__33932 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__19230,Vvar__1__R__19231,Vvar__2__x__19232,Vvar__3___24Anonymous__19233] :
( cType___24t(Vvar__0__A__19230)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__19230,Vvar__1__R__19231)
=> ( t(Vvar__2__x__19232,Vvar__0__A__19230)
=> ( t(Vvar__3___24Anonymous__19233,Vvar__0__A__19230)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__19230,Vvar__1__R__19231,Vvar__2__x__19232,Vvar__3___24Anonymous__19233)
=> ( ? [Vvar__3__y__19238] :
( t(Vvar__3__y__19238,Vvar__0__A__19230)
& p(happ(happ(Vvar__1__R__19231,Vvar__2__x__19232),Vvar__3__y__19238))
& Vvar__3___24Anonymous__19233 = Vvar__3__y__19238 )
| Vvar__3___24Anonymous__19233 = Vvar__2__x__19232
| ? [Vvar__3__y__19246] :
( t(Vvar__3__y__19246,Vvar__0__A__19230)
& ? [Vvar__4__z__19247] :
( t(Vvar__4__z__19247,Vvar__0__A__19230)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__19230,Vvar__1__R__19231,Vvar__2__x__19232,Vvar__3__y__19246)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__19230,Vvar__1__R__19231,Vvar__3__y__19246,Vvar__4__z__19247)
& Vvar__3___24Anonymous__19233 = Vvar__4__z__19247 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__33890,Vvar__1__R__33891,Vvar__2__x__33892,Vvar__3___24Anonymous__33893] :
( cType___24t(Vvar__0__A__33890)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33890,Vvar__1__R__33891)
=> ( t(Vvar__2__x__33892,Vvar__0__A__33890)
=> ( t(Vvar__3___24Anonymous__33893,Vvar__0__A__33890)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__33890,Vvar__1__R__33891,Vvar__2__x__33892,Vvar__3___24Anonymous__33893)
=> ( Vvar__3___24Anonymous__33893 = Vvar__2__x__33892
| ? [Vvar__3__y__33901] :
( t(Vvar__3__y__33901,Vvar__0__A__33890)
& ? [Vvar__4__z__33902] :
( t(Vvar__4__z__33902,Vvar__0__A__33890)
& p(happ(happ(Vvar__1__R__33891,Vvar__2__x__33892),Vvar__3__y__33901))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__33890,Vvar__1__R__33891,Vvar__3__y__33901,Vvar__4__z__33902)
& Vvar__3___24Anonymous__33893 = Vvar__4__z__33902 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__19250,Vvar__1__R__19251,Vvar__2__x__19252,Vvar__3___24Anonymous__19253] :
( cType___24t(Vvar__0__A__19250)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__19250,Vvar__1__R__19251)
=> ( t(Vvar__2__x__19252,Vvar__0__A__19250)
=> ( t(Vvar__3___24Anonymous__19253,Vvar__0__A__19250)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__19250,Vvar__1__R__19251,Vvar__2__x__19252,Vvar__3___24Anonymous__19253)
=> ( Vvar__3___24Anonymous__19253 = Vvar__2__x__19252
| ? [Vvar__3__y__19261] :
( t(Vvar__3__y__19261,Vvar__0__A__19250)
& ? [Vvar__4__z__19262] :
( t(Vvar__4__z__19262,Vvar__0__A__19250)
& p(happ(happ(Vvar__1__R__19251,Vvar__3__y__19261),Vvar__4__z__19262))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__19250,Vvar__1__R__19251,Vvar__2__x__19252,Vvar__3__y__19261)
& Vvar__3___24Anonymous__19253 = Vvar__4__z__19262 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__33839,Vvar__1__R__33840,Vvar__2__x__33841,Vvar__3___24Anonymous__33842] :
( cType___24t(Vvar__0__A__33839)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33839,Vvar__1__R__33840)
=> ( t(Vvar__2__x__33841,Vvar__0__A__33839)
=> ( t(Vvar__3___24Anonymous__33842,Vvar__0__A__33839)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__33839,Vvar__1__R__33840,Vvar__2__x__33841,Vvar__3___24Anonymous__33842)
=> ( ? [Vvar__3__y__33847] :
( t(Vvar__3__y__33847,Vvar__0__A__33839)
& p(happ(happ(Vvar__1__R__33840,Vvar__2__x__33841),Vvar__3__y__33847))
& Vvar__3___24Anonymous__33842 = Vvar__3__y__33847 )
| ? [Vvar__3__y__33852] :
( t(Vvar__3__y__33852,Vvar__0__A__33839)
& ? [Vvar__4__z__33853] :
( t(Vvar__4__z__33853,Vvar__0__A__33839)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__33839,Vvar__1__R__33840,Vvar__2__x__33841,Vvar__3__y__33852)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__33839,Vvar__1__R__33840,Vvar__3__y__33852,Vvar__4__z__33853)
& Vvar__3___24Anonymous__33842 = Vvar__4__z__33853 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__33856,Vvar__1__R__33857,Vvar__2__x__33858,Vvar__3___24Anonymous__33859] :
( cType___24t(Vvar__0__A__33856)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33856,Vvar__1__R__33857)
=> ( t(Vvar__2__x__33858,Vvar__0__A__33856)
=> ( t(Vvar__3___24Anonymous__33859,Vvar__0__A__33856)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__33856,Vvar__1__R__33857,Vvar__2__x__33858,Vvar__3___24Anonymous__33859)
=> ( ? [Vvar__3__y__33864] :
( t(Vvar__3__y__33864,Vvar__0__A__33856)
& p(happ(happ(Vvar__1__R__33857,Vvar__2__x__33858),Vvar__3__y__33864))
& Vvar__3___24Anonymous__33859 = Vvar__3__y__33864 )
| ? [Vvar__3__y__33869] :
( t(Vvar__3__y__33869,Vvar__0__A__33856)
& ? [Vvar__4__z__33870] :
( t(Vvar__4__z__33870,Vvar__0__A__33856)
& p(happ(happ(Vvar__1__R__33857,Vvar__2__x__33858),Vvar__3__y__33869))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__33856,Vvar__1__R__33857,Vvar__3__y__33869,Vvar__4__z__33870)
& Vvar__3___24Anonymous__33859 = Vvar__4__z__33870 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__33873,Vvar__1__R__33874,Vvar__2__x__33875,Vvar__3___24Anonymous__33876] :
( cType___24t(Vvar__0__A__33873)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__33873,Vvar__1__R__33874)
=> ( t(Vvar__2__x__33875,Vvar__0__A__33873)
=> ( t(Vvar__3___24Anonymous__33876,Vvar__0__A__33873)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__33873,Vvar__1__R__33874,Vvar__2__x__33875,Vvar__3___24Anonymous__33876)
=> ( ? [Vvar__3__y__33881] :
( t(Vvar__3__y__33881,Vvar__0__A__33873)
& p(happ(happ(Vvar__1__R__33874,Vvar__2__x__33875),Vvar__3__y__33881))
& Vvar__3___24Anonymous__33876 = Vvar__3__y__33881 )
| ? [Vvar__3__y__33886] :
( t(Vvar__3__y__33886,Vvar__0__A__33873)
& ? [Vvar__4__z__33887] :
( t(Vvar__4__z__33887,Vvar__0__A__33873)
& p(happ(happ(Vvar__1__R__33874,Vvar__3__y__33886),Vvar__4__z__33887))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__33873,Vvar__1__R__33874,Vvar__2__x__33875,Vvar__3__y__33886)
& Vvar__3___24Anonymous__33876 = Vvar__4__z__33887 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.le_AsB',axiom,
! [Vvar__0__A__33935,Vvar__1__B__33936,Vvar__2__leA__33937,Vvar__3__leB__33942,Vvar__4___24Anonymous__33947,Vvar__5___24Anonymous__33948] :
( cType___24t(Vvar__0__A__33935)
=> ( cType___24t(Vvar__1__B__33936)
=> ( c_24__type__34017___24t(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__2__leA__33937,Vvar__3__leB__33942,Vvar__4___24Anonymous__33947,Vvar__5___24Anonymous__33948,Vvar__2__leA__33937)
=> ( c_24__type__34042___24t(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__2__leA__33937,Vvar__3__leB__33942,Vvar__4___24Anonymous__33947,Vvar__5___24Anonymous__33948,Vvar__3__leB__33942)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__4___24Anonymous__33947)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__5___24Anonymous__33948)
=> ( cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__2__leA__33937,Vvar__3__leB__33942,Vvar__4___24Anonymous__33947,Vvar__5___24Anonymous__33948)
=> ( ? [Vvar__4__x__33962] :
( t(Vvar__4__x__33962,Vvar__0__A__33935)
& ? [Vvar__5__y__33963] :
( t(Vvar__5__y__33963,Vvar__0__A__33935)
& p(happ(happ(Vvar__2__leA__33937,Vvar__4__x__33962),Vvar__5__y__33963))
& Vvar__5___24Anonymous__33948 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__5__y__33963)
& Vvar__4___24Anonymous__33947 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__4__x__33962) ) )
| ? [Vvar__4__x__33977] :
( t(Vvar__4__x__33977,Vvar__0__A__33935)
& ? [Vvar__5__y__33978] :
( t(Vvar__5__y__33978,Vvar__1__B__33936)
& Vvar__5___24Anonymous__33948 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__5__y__33978)
& Vvar__4___24Anonymous__33947 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__4__x__33977) ) )
| ? [Vvar__4__x__33991] :
( t(Vvar__4__x__33991,Vvar__1__B__33936)
& ? [Vvar__5__y__33992] :
( t(Vvar__5__y__33992,Vvar__1__B__33936)
& p(happ(happ(Vvar__3__leB__33942,Vvar__4__x__33991),Vvar__5__y__33992))
& Vvar__5___24Anonymous__33948 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__5__y__33992)
& Vvar__4___24Anonymous__33947 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__33935,Vvar__1__B__33936,Vvar__4__x__33991) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
! [Vvar__0__A__34044,Vvar__1__B__34045,Vvar__2__leA__34048,Vvar__3__leB__34053,Vvar__4___24Anonymous__34060,Vvar__5___24Anonymous__34061] :
( cType___24t(Vvar__0__A__34044)
=> ( c_24__type__34124___24t(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__2__leA__34048,Vvar__3__leB__34053,Vvar__4___24Anonymous__34060,Vvar__5___24Anonymous__34061,Vvar__1__B__34045)
=> ( c_24__type__34153___24t(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__2__leA__34048,Vvar__3__leB__34053,Vvar__4___24Anonymous__34060,Vvar__5___24Anonymous__34061,Vvar__2__leA__34048)
=> ( c_24__type__34190___24t(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__2__leA__34048,Vvar__3__leB__34053,Vvar__4___24Anonymous__34060,Vvar__5___24Anonymous__34061,Vvar__3__leB__34053)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__4___24Anonymous__34060)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__5___24Anonymous__34061)
=> ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__2__leA__34048,Vvar__3__leB__34053,Vvar__4___24Anonymous__34060,Vvar__5___24Anonymous__34061)
=> ( ? [Vvar__4__x__34079] :
( t(Vvar__4__x__34079,Vvar__0__A__34044)
& ? [Vvar__5__x_27__34080] :
( t(Vvar__5__x_27__34080,Vvar__0__A__34044)
& ? [Vvar__6__y__34081] :
( t(Vvar__6__y__34081,happ(Vvar__1__B__34045,Vvar__4__x__34079))
& ? [Vvar__7__y_27__34082] :
( t(Vvar__7__y_27__34082,happ(Vvar__1__B__34045,Vvar__5__x_27__34080))
& p(happ(happ(Vvar__2__leA__34048,Vvar__4__x__34079),Vvar__5__x_27__34080))
& Vvar__5___24Anonymous__34061 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__5__x_27__34080,Vvar__7__y_27__34082)
& Vvar__4___24Anonymous__34060 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__4__x__34079,Vvar__6__y__34081) ) ) ) )
| ? [Vvar__4__x__34100] :
( t(Vvar__4__x__34100,Vvar__0__A__34044)
& ? [Vvar__5__y__34101] :
( t(Vvar__5__y__34101,happ(Vvar__1__B__34045,Vvar__4__x__34100))
& ? [Vvar__6__y_27__34102] :
( t(Vvar__6__y_27__34102,happ(Vvar__1__B__34045,Vvar__4__x__34100))
& p(happ(happ(happ(Vvar__3__leB__34053,Vvar__4__x__34100),Vvar__5__y__34101),Vvar__6__y_27__34102))
& Vvar__5___24Anonymous__34061 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__4__x__34100,Vvar__6__y_27__34102)
& Vvar__4___24Anonymous__34060 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__34044,Vvar__1__B__34045,Vvar__4__x__34100,Vvar__5__y__34101) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
! [Vvar__0__A__34289,Vvar__1__R__34290,Vvar__2___24Anonymous__34295,Vvar__3___24Anonymous__34296] :
( cType___24t(Vvar__0__A__34289)
=> ( c_24__type__34329___24t(Vvar__0__A__34289,Vvar__1__R__34290,Vvar__2___24Anonymous__34295,Vvar__3___24Anonymous__34296,Vvar__1__R__34290)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__2___24Anonymous__34295)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__3___24Anonymous__34296)
=> ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__34289,Vvar__1__R__34290,Vvar__2___24Anonymous__34295,Vvar__3___24Anonymous__34296)
=> ( ? [Vvar__2__x__34304] :
( t(Vvar__2__x__34304,Vvar__0__A__34289)
& ? [Vvar__3__y__34305] :
( t(Vvar__3__y__34305,Vvar__0__A__34289)
& ? [Vvar__4__p__34306] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__4__p__34306)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__1__R__34290,Vvar__1__R__34290,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__2__x__34304,Vvar__3__y__34305),Vvar__4__p__34306)
& Vvar__3___24Anonymous__34296 = Vvar__4__p__34306
& Vvar__2___24Anonymous__34295 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__2__x__34304,Vvar__3__y__34305) ) ) )
| ? [Vvar__2__x__34314] :
( t(Vvar__2__x__34314,Vvar__0__A__34289)
& ? [Vvar__3__y__34315] :
( t(Vvar__3__y__34315,Vvar__0__A__34289)
& ? [Vvar__4__p__34316] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__4__p__34316)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__1__R__34290,Vvar__1__R__34290,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__2__x__34314,Vvar__3__y__34315),Vvar__4__p__34316)
& Vvar__3___24Anonymous__34296 = Vvar__4__p__34316
& Vvar__2___24Anonymous__34295 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34289,Vvar__0__A__34289,Vvar__3__y__34315,Vvar__2__x__34314) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
! [Vvar__0__A__34192,Vvar__1__B__34193,Vvar__2__leA__34194,Vvar__3__leB__34199,Vvar__4___24Anonymous__34204,Vvar__5___24Anonymous__34205] :
( cType___24t(Vvar__0__A__34192)
=> ( cType___24t(Vvar__1__B__34193)
=> ( c_24__type__34262___24t(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__2__leA__34194,Vvar__3__leB__34199,Vvar__4___24Anonymous__34204,Vvar__5___24Anonymous__34205,Vvar__2__leA__34194)
=> ( c_24__type__34287___24t(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__2__leA__34194,Vvar__3__leB__34199,Vvar__4___24Anonymous__34204,Vvar__5___24Anonymous__34205,Vvar__3__leB__34199)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__4___24Anonymous__34204)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__5___24Anonymous__34205)
=> ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__2__leA__34194,Vvar__3__leB__34199,Vvar__4___24Anonymous__34204,Vvar__5___24Anonymous__34205)
=> ( ? [Vvar__4__x__34219] :
( t(Vvar__4__x__34219,Vvar__0__A__34192)
& ? [Vvar__5__x_27__34220] :
( t(Vvar__5__x_27__34220,Vvar__0__A__34192)
& p(happ(happ(Vvar__2__leA__34194,Vvar__4__x__34219),Vvar__5__x_27__34220))
& ? [Vvar__7__y__34222] :
( t(Vvar__7__y__34222,Vvar__1__B__34193)
& Vvar__5___24Anonymous__34205 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__5__x_27__34220,Vvar__7__y__34222)
& Vvar__4___24Anonymous__34204 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__4__x__34219,Vvar__7__y__34222) ) ) )
| ? [Vvar__4__y__34235] :
( t(Vvar__4__y__34235,Vvar__1__B__34193)
& ? [Vvar__5__y_27__34236] :
( t(Vvar__5__y_27__34236,Vvar__1__B__34193)
& p(happ(happ(Vvar__3__leB__34199,Vvar__4__y__34235),Vvar__5__y_27__34236))
& ? [Vvar__7__x__34238] :
( t(Vvar__7__x__34238,Vvar__0__A__34192)
& Vvar__5___24Anonymous__34205 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__7__x__34238,Vvar__5__y_27__34236)
& Vvar__4___24Anonymous__34204 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__34192,Vvar__1__B__34193,Vvar__7__x__34238,Vvar__4__y__34235) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Equivalence',axiom,
! [Vvar__0__U__34397,Vvar__1__R__34398] :
( cType___24t(Vvar__0__U__34397)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__34397,Vvar__1__R__34398)
=> ( cCoq_2eSets_2eRelations__1_2eEquivalence___24a2(Vvar__0__U__34397,Vvar__1__R__34398)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__34397,Vvar__1__R__34398)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__34397,Vvar__1__R__34398)
& cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(Vvar__0__U__34397,Vvar__1__R__34398)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.PER',axiom,
! [Vvar__0__U__34405,Vvar__1__R__34406] :
( cType___24t(Vvar__0__U__34405)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__34405,Vvar__1__R__34406)
=> ( cCoq_2eSets_2eRelations__1_2ePER___24a2(Vvar__0__U__34405,Vvar__1__R__34406)
=> ( cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(Vvar__0__U__34405,Vvar__1__R__34406)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__34405,Vvar__1__R__34406)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Preorder',axiom,
! [Vvar__0__U__34382,Vvar__1__R__34383] :
( cType___24t(Vvar__0__U__34382)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__34382,Vvar__1__R__34383)
=> ( cCoq_2eSets_2eRelations__1_2ePreorder___24a2(Vvar__0__U__34382,Vvar__1__R__34383)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__34382,Vvar__1__R__34383)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__34382,Vvar__1__R__34383)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__24796,Vvar__1__R__24797,Vvar__2__a__24802,Vvar__3___24Anonymous__24803] :
( cType___24t(Vvar__0__A__24796)
=> ( c_24__type__24833___24t(Vvar__0__A__24796,Vvar__1__R__24797,Vvar__2__a__24802,Vvar__3___24Anonymous__24803,Vvar__1__R__24797)
=> ( t(Vvar__2__a__24802,Vvar__0__A__24796)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24796,Vvar__3___24Anonymous__24803)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__24796,Vvar__1__R__24797,Vvar__2__a__24802,Vvar__3___24Anonymous__24803)
=> ( Vvar__3___24Anonymous__24803 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24796)
| ? [Vvar__3__b__24819] :
( t(Vvar__3__b__24819,Vvar__0__A__24796)
& ? [Vvar__4__l__24820] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24796,Vvar__4__l__24820)
& p(happ(happ(Vvar__1__R__24797,Vvar__2__a__24802),Vvar__3__b__24819))
& Vvar__3___24Anonymous__24803 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24796,Vvar__3__b__24819,Vvar__4__l__24820) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__24733,Vvar__1__R__24734,Vvar__2___24Anonymous__24739] :
( cType___24t(Vvar__0__A__24733)
=> ( c_24__type__24774___24t(Vvar__0__A__24733,Vvar__1__R__24734,Vvar__2___24Anonymous__24739,Vvar__1__R__24734)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24733,Vvar__2___24Anonymous__24739)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__24733,Vvar__1__R__24734,Vvar__2___24Anonymous__24739)
=> ( Vvar__2___24Anonymous__24739 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24733)
| ? [Vvar__2__a__24753] :
( t(Vvar__2__a__24753,Vvar__0__A__24733)
& Vvar__2___24Anonymous__24739 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24733,Vvar__2__a__24753,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24733)) )
| ? [Vvar__2__a__24760] :
( t(Vvar__2__a__24760,Vvar__0__A__24733)
& ? [Vvar__3__b__24761] :
( t(Vvar__3__b__24761,Vvar__0__A__24733)
& ? [Vvar__4__l__24762] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24733,Vvar__4__l__24762)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__24733,Vvar__1__R__24734,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24733,Vvar__3__b__24761,Vvar__4__l__24762))
& p(happ(happ(Vvar__1__R__24734,Vvar__2__a__24760),Vvar__3__b__24761))
& Vvar__2___24Anonymous__24739 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24733,Vvar__2__a__24760,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24733,Vvar__3__b__24761,Vvar__4__l__24762)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__24841,Vvar__1__R__24842,Vvar__2___24Anonymous__24847] :
( cType___24t(Vvar__0__A__24841)
=> ( c_24__type__24874___24t(Vvar__0__A__24841,Vvar__1__R__24842,Vvar__2___24Anonymous__24847,Vvar__1__R__24842)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24841,Vvar__2___24Anonymous__24847)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__24841,Vvar__1__R__24842,Vvar__2___24Anonymous__24847)
=> ( Vvar__2___24Anonymous__24847 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__24841)
| ? [Vvar__2__a__24861] :
( t(Vvar__2__a__24861,Vvar__0__A__24841)
& ? [Vvar__3__l__24862] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__24841,Vvar__3__l__24862)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__24841,Vvar__1__R__24842,Vvar__3__l__24862)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__24841,Vvar__1__R__24842,Vvar__2__a__24861,Vvar__3__l__24862)
& Vvar__2___24Anonymous__24847 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__24841,Vvar__2__a__24861,Vvar__3__l__24862) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__34761,Vvar__1__R__34762,Vvar__2___24Anonymous__34767] :
( cType___24t(Vvar__0__A__34761)
=> ( c_24__type__34794___24t(Vvar__0__A__34761,Vvar__1__R__34762,Vvar__2___24Anonymous__34767,Vvar__1__R__34762)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34761,Vvar__2___24Anonymous__34767)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__34761,Vvar__1__R__34762,Vvar__2___24Anonymous__34767)
=> ( Vvar__2___24Anonymous__34767 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__34761)
| ? [Vvar__2__a__34781] :
( t(Vvar__2__a__34781,Vvar__0__A__34761)
& ? [Vvar__3__l__34782] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34761,Vvar__3__l__34782)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__34761,Vvar__1__R__34762,Vvar__3__l__34782)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__34761,happ(Vvar__1__R__34762,Vvar__2__a__34781),Vvar__3__l__34782)
& Vvar__2___24Anonymous__34767 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34761,Vvar__2__a__34781,Vvar__3__l__34782) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX26760] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX26760)
=> ? [Vvar__0___24Anonymous__26761] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__26761)
& ? [Vvar__1___24Anonymous__26762] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__26762)
& ? [Vvar__2___24Anonymous__26763] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__26763)
& ? [Vvar__3___24Anonymous__26764] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__26764)
& ? [Vvar__4___24Anonymous__26765] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__26765)
& ? [Vvar__5___24Anonymous__26766] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__26766)
& ? [Vvar__6___24Anonymous__26767] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__26767)
& ? [Vvar__7___24Anonymous__26768] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__26768)
& VX26760 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__26761,Vvar__1___24Anonymous__26762,Vvar__2___24Anonymous__26763,Vvar__3___24Anonymous__26764,Vvar__4___24Anonymous__26765,Vvar__5___24Anonymous__26766,Vvar__6___24Anonymous__26767,Vvar__7___24Anonymous__26768) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX25491] :
( cCoq_2eStrings_2eString_2estring___24t(VX25491)
=> ( VX25491 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__25492] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__25492)
& ? [Vvar__1___24Anonymous__25493] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__25493)
& VX25491 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__25492,Vvar__1___24Anonymous__25493) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841,VX28842] :
( cType___24t(Vvar__0__X__28829)
=> ( c_24__type__28902___24t(Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841,Vvar__1__lt__28830)
=> ( c_24__type__28921___24t(Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841,Vvar__2__eq__28835)
=> ( t(Vvar__3__x__28840,Vvar__0__X__28829)
=> ( t(Vvar__4__y__28841,Vvar__0__X__28829)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841,VX28842)
=> ( ( p(happ(happ(Vvar__1__lt__28830,Vvar__3__x__28840),Vvar__4__y__28841))
& VX28842 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841) )
| ( p(happ(happ(Vvar__2__eq__28835,Vvar__3__x__28840),Vvar__4__y__28841))
& VX28842 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841) )
| ( p(happ(happ(Vvar__1__lt__28830,Vvar__4__y__28841),Vvar__3__x__28840))
& VX28842 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__28829,Vvar__1__lt__28830,Vvar__2__eq__28835,Vvar__3__x__28840,Vvar__4__y__28841) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__26648,Vvar__1___24Anonymous__26649] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__26648)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__26649)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__26648,Vvar__1___24Anonymous__26649)
=> ( ? [Vvar__0__a__26651] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__26651)
& ? [Vvar__1__s__26652] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__26652)
& Vvar__1___24Anonymous__26649 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__26651,Vvar__1__s__26652)
& Vvar__0___24Anonymous__26648 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__26653] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__26653)
& ? [Vvar__1__s1__26654] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__26654)
& ? [Vvar__2__s2__26655] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__26655)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__26654,Vvar__2__s2__26655)
& Vvar__1___24Anonymous__26649 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__26653,Vvar__2__s2__26655)
& Vvar__0___24Anonymous__26648 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__26653,Vvar__1__s1__26654) ) ) )
| ? [Vvar__0__a__26657] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__26657)
& ? [Vvar__1__b__26658] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__26658)
& ? [Vvar__2__s1__26659] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__26659)
& ? [Vvar__3__s2__26660] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__26660)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__26657),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__26658))
& Vvar__1___24Anonymous__26649 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__26658,Vvar__3__s2__26660)
& Vvar__0___24Anonymous__26648 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__26657,Vvar__2__s1__26659) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX19147] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX19147)
=> ( VX19147 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX19147 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX19147 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__1864,VX1865] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1864)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__1864,VX1865)
=> ( ? [Vvar__0__n__1866] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1866)
& Vvar__0___24Anonymous__1864 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1866)
& VX1865 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__1866) )
| ? [Vvar__0__n__1867] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1867)
& ? [Vvar__1___24Anonymous__1868] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__1867,Vvar__1___24Anonymous__1868)
& Vvar__0___24Anonymous__1864 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__1867)
& VX1865 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__1867,Vvar__1___24Anonymous__1868) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists',axiom,
! [Vvar__0__A__34911,Vvar__1__P__34912,Vvar__2__n__34915,Vvar__3___24Anonymous__34916] :
( cType___24t(Vvar__0__A__34911)
=> ( c_24__type__34939___24t(Vvar__0__A__34911,Vvar__1__P__34912,Vvar__2__n__34915,Vvar__3___24Anonymous__34916,Vvar__1__P__34912)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__34915)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34911,Vvar__2__n__34915,Vvar__3___24Anonymous__34916)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__34911,Vvar__1__P__34912,Vvar__2__n__34915,Vvar__3___24Anonymous__34916)
=> ( ? [Vvar__2__m__34922] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__34922)
& ? [Vvar__3__x__34923] :
( t(Vvar__3__x__34923,Vvar__0__A__34911)
& ? [Vvar__4__v__34924] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34911,Vvar__2__m__34922,Vvar__4__v__34924)
& p(happ(Vvar__1__P__34912,Vvar__3__x__34923))
& Vvar__3___24Anonymous__34916 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__34911,Vvar__3__x__34923,Vvar__2__m__34922,Vvar__4__v__34924)
& Vvar__2__n__34915 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__34922) ) ) )
| ? [Vvar__2__m__34930] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__34930)
& ? [Vvar__3__x__34931] :
( t(Vvar__3__x__34931,Vvar__0__A__34911)
& ? [Vvar__4__v__34932] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34911,Vvar__2__m__34930,Vvar__4__v__34932)
& cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__34911,Vvar__1__P__34912,Vvar__2__m__34930,Vvar__4__v__34932)
& Vvar__3___24Anonymous__34916 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__34911,Vvar__3__x__34931,Vvar__2__m__34930,Vvar__4__v__34932)
& Vvar__2__n__34915 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__34930) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists2',axiom,
! [Vvar__0__A__25732,Vvar__1__B__25733,Vvar__2__P__25734,Vvar__3__n__25739,Vvar__4___24Anonymous__25740,Vvar__5___24Anonymous__25741] :
( cType___24t(Vvar__0__A__25732)
=> ( cType___24t(Vvar__1__B__25733)
=> ( c_24__type__25786___24t(Vvar__0__A__25732,Vvar__1__B__25733,Vvar__2__P__25734,Vvar__3__n__25739,Vvar__4___24Anonymous__25740,Vvar__5___24Anonymous__25741,Vvar__2__P__25734)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__25739)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25732,Vvar__3__n__25739,Vvar__4___24Anonymous__25740)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__25733,Vvar__3__n__25739,Vvar__5___24Anonymous__25741)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__25732,Vvar__1__B__25733,Vvar__2__P__25734,Vvar__3__n__25739,Vvar__4___24Anonymous__25740,Vvar__5___24Anonymous__25741)
=> ( ? [Vvar__3__m__25750] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__25750)
& ? [Vvar__4__x1__25751] :
( t(Vvar__4__x1__25751,Vvar__0__A__25732)
& ? [Vvar__5__x2__25752] :
( t(Vvar__5__x2__25752,Vvar__1__B__25733)
& ? [Vvar__6__v1__25753] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25732,Vvar__3__m__25750,Vvar__6__v1__25753)
& ? [Vvar__7__v2__25754] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__25733,Vvar__3__m__25750,Vvar__7__v2__25754)
& p(happ(happ(Vvar__2__P__25734,Vvar__4__x1__25751),Vvar__5__x2__25752))
& Vvar__5___24Anonymous__25741 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__25733,Vvar__5__x2__25752,Vvar__3__m__25750,Vvar__7__v2__25754)
& Vvar__4___24Anonymous__25740 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25732,Vvar__4__x1__25751,Vvar__3__m__25750,Vvar__6__v1__25753)
& Vvar__3__n__25739 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__25750) ) ) ) ) )
| ? [Vvar__3__m__25763] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__25763)
& ? [Vvar__4__x1__25764] :
( t(Vvar__4__x1__25764,Vvar__0__A__25732)
& ? [Vvar__5__x2__25765] :
( t(Vvar__5__x2__25765,Vvar__1__B__25733)
& ? [Vvar__6__v1__25766] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25732,Vvar__3__m__25763,Vvar__6__v1__25766)
& ? [Vvar__7__v2__25767] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__25733,Vvar__3__m__25763,Vvar__7__v2__25767)
& cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__25732,Vvar__1__B__25733,Vvar__2__P__25734,Vvar__3__m__25763,Vvar__6__v1__25766,Vvar__7__v2__25767)
& Vvar__5___24Anonymous__25741 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__25733,Vvar__5__x2__25765,Vvar__3__m__25763,Vvar__7__v2__25767)
& Vvar__4___24Anonymous__25740 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25732,Vvar__4__x1__25764,Vvar__3__m__25763,Vvar__6__v1__25766)
& Vvar__3__n__25739 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__25763) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
! [Vvar__0__A__34884,Vvar__1__P__34885,Vvar__2__n__34888,Vvar__3__v__34889] :
( cType___24t(Vvar__0__A__34884)
=> ( c_24__type__34909___24t(Vvar__0__A__34884,Vvar__1__P__34885,Vvar__2__n__34888,Vvar__3__v__34889,Vvar__1__P__34885)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__34888)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34884,Vvar__2__n__34888,Vvar__3__v__34889)
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__34884,Vvar__1__P__34885,Vvar__2__n__34888,Vvar__3__v__34889)
=> ( ( Vvar__3__v__34889 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__34884)
& Vvar__2__n__34888 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__n__34899] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__34899)
& ? [Vvar__3__x__34900] :
( t(Vvar__3__x__34900,Vvar__0__A__34884)
& ? [Vvar__4__v__34901] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34884,Vvar__2__n__34899,Vvar__4__v__34901)
& p(happ(Vvar__1__P__34885,Vvar__3__x__34900))
& cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__34884,Vvar__1__P__34885,Vvar__2__n__34899,Vvar__4__v__34901)
& Vvar__3__v__34889 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__34884,Vvar__3__x__34900,Vvar__2__n__34899,Vvar__4__v__34901)
& Vvar__2__n__34888 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__34899) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
! [Vvar__0__A__34956,Vvar__1__B__34957,Vvar__2__P__34958,Vvar__3__n__34963,Vvar__4___24Anonymous__34964,Vvar__5___24Anonymous__34965] :
( cType___24t(Vvar__0__A__34956)
=> ( cType___24t(Vvar__1__B__34957)
=> ( c_24__type__35005___24t(Vvar__0__A__34956,Vvar__1__B__34957,Vvar__2__P__34958,Vvar__3__n__34963,Vvar__4___24Anonymous__34964,Vvar__5___24Anonymous__34965,Vvar__2__P__34958)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__34963)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34956,Vvar__3__n__34963,Vvar__4___24Anonymous__34964)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__34957,Vvar__3__n__34963,Vvar__5___24Anonymous__34965)
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__34956,Vvar__1__B__34957,Vvar__2__P__34958,Vvar__3__n__34963,Vvar__4___24Anonymous__34964,Vvar__5___24Anonymous__34965)
=> ( ( Vvar__5___24Anonymous__34965 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__34957)
& Vvar__4___24Anonymous__34964 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__34956)
& Vvar__3__n__34963 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__3__m__34981] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__34981)
& ? [Vvar__4__x1__34982] :
( t(Vvar__4__x1__34982,Vvar__0__A__34956)
& ? [Vvar__5__x2__34983] :
( t(Vvar__5__x2__34983,Vvar__1__B__34957)
& ? [Vvar__6__v1__34984] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34956,Vvar__3__m__34981,Vvar__6__v1__34984)
& ? [Vvar__7__v2__34985] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__34957,Vvar__3__m__34981,Vvar__7__v2__34985)
& p(happ(happ(Vvar__2__P__34958,Vvar__4__x1__34982),Vvar__5__x2__34983))
& cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__34956,Vvar__1__B__34957,Vvar__2__P__34958,Vvar__3__m__34981,Vvar__6__v1__34984,Vvar__7__v2__34985)
& Vvar__5___24Anonymous__34965 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__34957,Vvar__5__x2__34983,Vvar__3__m__34981,Vvar__7__v2__34985)
& Vvar__4___24Anonymous__34964 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__34956,Vvar__4__x1__34982,Vvar__3__m__34981,Vvar__6__v1__34984)
& Vvar__3__n__34963 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__34981) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.In',axiom,
! [Vvar__0__A__34941,Vvar__1__a__34942,Vvar__2__n__34943,Vvar__3___24Anonymous__34944] :
( cType___24t(Vvar__0__A__34941)
=> ( t(Vvar__1__a__34942,Vvar__0__A__34941)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__34943)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34941,Vvar__2__n__34943,Vvar__3___24Anonymous__34944)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__34941,Vvar__1__a__34942,Vvar__2__n__34943,Vvar__3___24Anonymous__34944)
=> ( ? [Vvar__2__m__34948] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__34948)
& ? [Vvar__3__v__34949] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34941,Vvar__2__m__34948,Vvar__3__v__34949)
& Vvar__3___24Anonymous__34944 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__34941,Vvar__1__a__34942,Vvar__2__m__34948,Vvar__3__v__34949)
& Vvar__2__n__34943 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__34948) ) )
| ? [Vvar__2__m__34952] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__34952)
& ? [Vvar__3__x__34953] :
( t(Vvar__3__x__34953,Vvar__0__A__34941)
& ? [Vvar__4__v__34954] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__34941,Vvar__2__m__34952,Vvar__4__v__34954)
& cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__34941,Vvar__1__a__34942,Vvar__2__m__34952,Vvar__4__v__34954)
& Vvar__3___24Anonymous__34944 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__34941,Vvar__3__x__34953,Vvar__2__m__34952,Vvar__4__v__34954)
& Vvar__2__n__34943 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__34952) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__25698,Vvar__1___24Anonymous__25699,VX25700] :
( cType___24t(Vvar__0__A__25698)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__25699)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25698,Vvar__1___24Anonymous__25699,VX25700)
=> ( ( Vvar__1___24Anonymous__25699 = cCoq_2eInit_2eDatatypes_2eO
& VX25700 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__25698) )
| ? [Vvar__1__h__25703] :
( t(Vvar__1__h__25703,Vvar__0__A__25698)
& ? [Vvar__2__n__25704] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__25704)
& ? [Vvar__3___24Anonymous__25705] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__25698,Vvar__2__n__25704,Vvar__3___24Anonymous__25705)
& Vvar__1___24Anonymous__25699 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__25704)
& VX25700 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__25698,Vvar__1__h__25703,Vvar__2__n__25704,Vvar__3___24Anonymous__25705) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__30541,Vvar__1__b__30542,Vvar__2__d__30543] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__30541)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__30542)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__30543)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__30541,Vvar__1__b__30542,Vvar__2__d__30543)
=> ? [Vvar__3__u__30548] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__30548)
& ? [Vvar__4__v__30549] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__30549)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__30548,Vvar__0__a__30541),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__30549,Vvar__1__b__30542)) = Vvar__2__d__30543
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__30516,Vvar__1__b__30517,VX30518] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__30516)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__30517)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__30516,Vvar__1__b__30517,VX30518)
=> ? [Vvar__2__u__30521] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__30521)
& ? [Vvar__3__v__30522] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__30522)
& ? [Vvar__4__d__30523] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__30523)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__30521,Vvar__0__a__30516),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__30522,Vvar__1__b__30517)) = Vvar__4__d__30523
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__30516,Vvar__1__b__30517,Vvar__4__d__30523)
& VX30518 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__30516,Vvar__1__b__30517,Vvar__2__u__30521,Vvar__3__v__30522,Vvar__4__d__30523) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__25950,Vvar__1__b__25951,Vvar__2__g__25952] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__25950)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__25951)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__25952)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__25950,Vvar__1__b__25951,Vvar__2__g__25952)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__25952,Vvar__0__a__25950)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__25952,Vvar__1__b__25951)
& ! [Vvar__var__var__var__var__5__x__25960__25963__25966__25969__25972] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__25960__25963__25966__25969__25972)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__25960__25963__25966__25969__25972,Vvar__0__a__25950)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__25960__25963__25966__25969__25972,Vvar__1__b__25951)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__25960__25963__25966__25969__25972,Vvar__2__g__25952) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__30551] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__30551)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__30551)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__30551))
& ! [Vvar__var__var__2__n__30556__30558__30560] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__30556__30558__30560)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__30556__30558__30560))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__30556__30558__30560,Vvar__0__p__30551)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__30556__30558__30560,Vvar__0__p__30551) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__32219,Vvar__1__p__32220,VX32221] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__32219)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__32220)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__32219,Vvar__1__p__32220,VX32221)
=> ? [Vvar__2__q__32224] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__32224)
& ? [Vvar__3__r__32225] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__32225)
& Vvar__0__x__32219 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__32224,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__32220)),Vvar__3__r__32225)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__32225))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__32225,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__32220)))
& VX32221 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__32219,Vvar__1__p__32220,Vvar__2__q__32224,Vvar__3__r__32225) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__27601,Vvar__1__F__27602] :
( cType___24t(Vvar__0__T__27601)
=> ( t(Vvar__1__F__27602,Vvar__0__T__27601)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__27601,Vvar__1__F__27602)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__30881,Vvar__1__F__30882] :
( cType___24t(Vvar__0__T__30881)
=> ( t(Vvar__1__F__30882,Vvar__0__T__30881)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__30881,Vvar__1__F__30882)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX27606] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX27606)
=> ( VX27606 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__27607] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27607)
& ? [Vvar__1___24Anonymous__27608] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__27608)
& VX27606 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__27607,Vvar__1___24Anonymous__27608) ) )
| ? [Vvar__0___24Anonymous__27609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27609)
& ? [Vvar__1___24Anonymous__27610] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__27610)
& VX27606 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__27609,Vvar__1___24Anonymous__27610) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__14750,VX14751] :
( cType___24t(Vvar__0__C__14750)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,VX14751)
=> ( ? [Vvar__1___24Anonymous__14753] :
( t(Vvar__1___24Anonymous__14753,Vvar__0__C__14750)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14750,Vvar__1___24Anonymous__14753) )
| ? [Vvar__1___24Anonymous__14755] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14755)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14750,Vvar__1___24Anonymous__14755) )
| ? [Vvar__1___24Anonymous__14757] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__1___24Anonymous__14757)
& ? [Vvar__2___24Anonymous__14758] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__2___24Anonymous__14758)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__14750,Vvar__1___24Anonymous__14757,Vvar__2___24Anonymous__14758) ) )
| ? [Vvar__1___24Anonymous__14760] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__1___24Anonymous__14760)
& ? [Vvar__2___24Anonymous__14761] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__2___24Anonymous__14761)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__14750,Vvar__1___24Anonymous__14760,Vvar__2___24Anonymous__14761) ) )
| ? [Vvar__1___24Anonymous__14763] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__1___24Anonymous__14763)
& ? [Vvar__2___24Anonymous__14764] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__2___24Anonymous__14764)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__14750,Vvar__1___24Anonymous__14763,Vvar__2___24Anonymous__14764) ) )
| ? [Vvar__1___24Anonymous__14766] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__1___24Anonymous__14766)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__14750,Vvar__1___24Anonymous__14766) )
| ? [Vvar__1___24Anonymous__14768] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14750,Vvar__1___24Anonymous__14768)
& ? [Vvar__2___24Anonymous__14769] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14769)
& VX14751 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__14750,Vvar__1___24Anonymous__14768,Vvar__2___24Anonymous__14769) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__14914,VX14915] :
( cType___24t(Vvar__0__C__14914)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14914,VX14915)
=> ( ? [Vvar__1___24Anonymous__14917] :
( t(Vvar__1___24Anonymous__14917,Vvar__0__C__14914)
& VX14915 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14914,Vvar__1___24Anonymous__14917) )
| ? [Vvar__1___24Anonymous__14919] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14919)
& ? [Vvar__2___24Anonymous__14920] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14914,Vvar__2___24Anonymous__14920)
& VX14915 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14914,Vvar__1___24Anonymous__14919,Vvar__2___24Anonymous__14920) ) )
| ? [Vvar__1___24Anonymous__14922] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14914,Vvar__1___24Anonymous__14922)
& ? [Vvar__2___24Anonymous__14923] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14923)
& ? [Vvar__3___24Anonymous__14924] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14914,Vvar__3___24Anonymous__14924)
& VX14915 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__14914,Vvar__1___24Anonymous__14922,Vvar__2___24Anonymous__14923,Vvar__3___24Anonymous__14924) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182] :
( cType___24t(Vvar__0__R__11151)
=> ( t(Vvar__1__rO__11152,Vvar__0__R__11151)
=> ( t(Vvar__2__rI__11153,Vvar__0__R__11151)
=> ( c_24__type__11583___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__3__rplus__11154)
=> ( c_24__type__11684___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__4__rtimes__11159)
=> ( c_24__type__11785___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__5__rminus__11164)
=> ( c_24__type__11875___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__6__ropp__11169)
=> ( c_24__type__11976___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__7__req__11172)
=> ( c_24__type__12077___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__8__rle__11177)
=> ( c_24__type__12178___24t(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182,Vvar__9__rlt__11182)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172,Vvar__8__rle__11177,Vvar__9__rlt__11182)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__11151,Vvar__7__req__11172)
& ! [Vvar__var__var__var__var__11__x1__11226__11232__11337__11343__11349] :
( t(Vvar__var__var__var__var__11__x1__11226__11232__11337__11343__11349,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__12__x2__11227__11233__11338__11344__11350] :
( t(Vvar__var__var__var__var__12__x2__11227__11233__11338__11344__11350,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__11__x1__11226__11232__11337__11343__11349),Vvar__var__var__var__var__12__x2__11227__11233__11338__11344__11350))
=> ! [Vvar__var__var__var__var__14__y1__11228__11234__11339__11345__11351] :
( t(Vvar__var__var__var__var__14__y1__11228__11234__11339__11345__11351,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__15__y2__11229__11235__11340__11346__11352] :
( t(Vvar__var__var__var__var__15__y2__11229__11235__11340__11346__11352,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__14__y1__11228__11234__11339__11345__11351),Vvar__var__var__var__var__15__y2__11229__11235__11340__11346__11352))
=> p(happ(happ(Vvar__7__req__11172,happ(happ(Vvar__3__rplus__11154,Vvar__var__var__var__var__11__x1__11226__11232__11337__11343__11349),Vvar__var__var__var__var__14__y1__11228__11234__11339__11345__11351)),happ(happ(Vvar__3__rplus__11154,Vvar__var__var__var__var__12__x2__11227__11233__11338__11344__11350),Vvar__var__var__var__var__15__y2__11229__11235__11340__11346__11352))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__11239__11245__11355__11361__11367] :
( t(Vvar__var__var__var__var__12__x1__11239__11245__11355__11361__11367,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__13__x2__11240__11246__11356__11362__11368] :
( t(Vvar__var__var__var__var__13__x2__11240__11246__11356__11362__11368,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__12__x1__11239__11245__11355__11361__11367),Vvar__var__var__var__var__13__x2__11240__11246__11356__11362__11368))
=> ! [Vvar__var__var__var__var__15__y1__11241__11247__11357__11363__11369] :
( t(Vvar__var__var__var__var__15__y1__11241__11247__11357__11363__11369,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__16__y2__11242__11248__11358__11364__11370] :
( t(Vvar__var__var__var__var__16__y2__11242__11248__11358__11364__11370,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__15__y1__11241__11247__11357__11363__11369),Vvar__var__var__var__var__16__y2__11242__11248__11358__11364__11370))
=> p(happ(happ(Vvar__7__req__11172,happ(happ(Vvar__4__rtimes__11159,Vvar__var__var__var__var__12__x1__11239__11245__11355__11361__11367),Vvar__var__var__var__var__15__y1__11241__11247__11357__11363__11369)),happ(happ(Vvar__4__rtimes__11159,Vvar__var__var__var__var__13__x2__11240__11246__11356__11362__11368),Vvar__var__var__var__var__16__y2__11242__11248__11358__11364__11370))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__11252__11255__11373__11376__11379] :
( t(Vvar__var__var__var__var__13__x1__11252__11255__11373__11376__11379,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__14__x2__11253__11256__11374__11377__11380] :
( t(Vvar__var__var__var__var__14__x2__11253__11256__11374__11377__11380,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__13__x1__11252__11255__11373__11376__11379),Vvar__var__var__var__var__14__x2__11253__11256__11374__11377__11380))
=> p(happ(happ(Vvar__7__req__11172,happ(Vvar__6__ropp__11169,Vvar__var__var__var__var__13__x1__11252__11255__11373__11376__11379)),happ(Vvar__6__ropp__11169,Vvar__var__var__var__var__14__x2__11253__11256__11374__11377__11380))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__11259__11265__11382__11388__11394] :
( t(Vvar__var__var__var__var__14__x1__11259__11265__11382__11388__11394,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__15__x2__11260__11266__11383__11389__11395] :
( t(Vvar__var__var__var__var__15__x2__11260__11266__11383__11389__11395,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__14__x1__11259__11265__11382__11388__11394),Vvar__var__var__var__var__15__x2__11260__11266__11383__11389__11395))
=> ! [Vvar__var__var__var__var__17__y1__11261__11267__11384__11390__11396] :
( t(Vvar__var__var__var__var__17__y1__11261__11267__11384__11390__11396,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__18__y2__11262__11268__11385__11391__11397] :
( t(Vvar__var__var__var__var__18__y2__11262__11268__11385__11391__11397,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__17__y1__11261__11267__11384__11390__11396),Vvar__var__var__var__var__18__y2__11262__11268__11385__11391__11397))
=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__var__14__x1__11259__11265__11382__11388__11394),Vvar__var__var__var__var__17__y1__11261__11267__11384__11390__11396))
<=> p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__var__15__x2__11260__11266__11383__11389__11395),Vvar__var__var__var__var__18__y2__11262__11268__11385__11391__11397)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__11272__11278__11400__11406__11412] :
( t(Vvar__var__var__var__var__15__x1__11272__11278__11400__11406__11412,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__16__x2__11273__11279__11401__11407__11413] :
( t(Vvar__var__var__var__var__16__x2__11273__11279__11401__11407__11413,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__15__x1__11272__11278__11400__11406__11412),Vvar__var__var__var__var__16__x2__11273__11279__11401__11407__11413))
=> ! [Vvar__var__var__var__var__18__y1__11274__11280__11402__11408__11414] :
( t(Vvar__var__var__var__var__18__y1__11274__11280__11402__11408__11414,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__19__y2__11275__11281__11403__11409__11415] :
( t(Vvar__var__var__var__var__19__y2__11275__11281__11403__11409__11415,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__18__y1__11274__11280__11402__11408__11414),Vvar__var__var__var__var__19__y2__11275__11281__11403__11409__11415))
=> ( p(happ(happ(Vvar__9__rlt__11182,Vvar__var__var__var__var__15__x1__11272__11278__11400__11406__11412),Vvar__var__var__var__var__18__y1__11274__11280__11402__11408__11414))
<=> p(happ(happ(Vvar__9__rlt__11182,Vvar__var__var__var__var__16__x2__11273__11279__11401__11407__11413),Vvar__var__var__var__var__19__y2__11275__11281__11403__11409__11415)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__11151,Vvar__1__rO__11152,Vvar__2__rI__11153,Vvar__3__rplus__11154,Vvar__4__rtimes__11159,Vvar__5__rminus__11164,Vvar__6__ropp__11169,Vvar__7__req__11172)
& ! [Vvar__var__var__var__17__n__11286__11287__11418__11419] :
( t(Vvar__var__var__var__17__n__11286__11287__11418__11419,Vvar__0__R__11151)
=> p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__17__n__11286__11287__11418__11419),Vvar__var__var__var__17__n__11286__11287__11418__11419)) )
& ! [Vvar__var__var__var__var__18__n__11289__11293__11420__11424__11428] :
( t(Vvar__var__var__var__var__18__n__11289__11293__11420__11424__11428,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__19__m__11290__11294__11421__11425__11429] :
( t(Vvar__var__var__var__var__19__m__11290__11294__11421__11425__11429,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__var__18__n__11289__11293__11420__11424__11428),Vvar__var__var__var__var__19__m__11290__11294__11421__11425__11429))
=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__var__19__m__11290__11294__11421__11425__11429),Vvar__var__var__var__var__18__n__11289__11293__11420__11424__11428))
=> p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__18__n__11289__11293__11420__11424__11428),Vvar__var__var__var__var__19__m__11290__11294__11421__11425__11429)) ) ) ) )
& ! [Vvar__var__var__var__19__n__11298__11303__11432__11437] :
( t(Vvar__var__var__var__19__n__11298__11303__11432__11437,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__20__m__11299__11304__11433__11438] :
( t(Vvar__var__var__var__20__m__11299__11304__11433__11438,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__21__p__11300__11305__11434__11439] :
( t(Vvar__var__var__var__21__p__11300__11305__11434__11439,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__19__n__11298__11303__11432__11437),Vvar__var__var__var__20__m__11299__11304__11433__11438))
=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__20__m__11299__11304__11433__11438),Vvar__var__var__var__21__p__11300__11305__11434__11439))
=> p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__19__n__11298__11303__11432__11437),Vvar__var__var__var__21__p__11300__11305__11434__11439)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__11309__11311__11442__11444__11446__11448] :
( t(Vvar__var__var__var__var__var__20__n__11309__11311__11442__11444__11446__11448,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__var__21__m__11310__11312__11443__11445__11447__11449] :
( t(Vvar__var__var__var__var__var__21__m__11310__11312__11443__11445__11447__11449,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__9__rlt__11182,Vvar__var__var__var__var__var__20__n__11309__11311__11442__11444__11446__11448),Vvar__var__var__var__var__var__21__m__11310__11312__11443__11445__11447__11449))
<=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__var__var__20__n__11309__11311__11442__11444__11446__11448),Vvar__var__var__var__var__var__21__m__11310__11312__11443__11445__11447__11449))
& ~ p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__var__20__n__11309__11311__11442__11444__11446__11448),Vvar__var__var__var__var__var__21__m__11310__11312__11443__11445__11447__11449)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__11314__11316__11450__11452__11454] :
( t(Vvar__var__var__var__var__21__n__11314__11316__11450__11452__11454,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__22__m__11315__11317__11451__11453__11455] :
( t(Vvar__var__var__var__var__22__m__11315__11317__11451__11453__11455,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__9__rlt__11182,Vvar__var__var__var__var__21__n__11314__11316__11450__11452__11454),Vvar__var__var__var__var__22__m__11315__11317__11451__11453__11455))
| p(happ(happ(Vvar__7__req__11172,Vvar__var__var__var__var__21__n__11314__11316__11450__11452__11454),Vvar__var__var__var__var__22__m__11315__11317__11451__11453__11455))
| p(happ(happ(Vvar__9__rlt__11182,Vvar__var__var__var__var__22__m__11315__11317__11451__11453__11455),Vvar__var__var__var__var__21__n__11314__11316__11450__11452__11454)) ) ) )
& ! [Vvar__var__var__var__var__22__n__11319__11323__11456__11460__11464] :
( t(Vvar__var__var__var__var__22__n__11319__11323__11456__11460__11464,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__23__m__11320__11324__11457__11461__11465] :
( t(Vvar__var__var__var__var__23__m__11320__11324__11457__11461__11465,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__24__p__11321__11325__11458__11462__11466] :
( t(Vvar__var__var__var__var__24__p__11321__11325__11458__11462__11466,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__8__rle__11177,Vvar__var__var__var__var__22__n__11319__11323__11456__11460__11464),Vvar__var__var__var__var__23__m__11320__11324__11457__11461__11465))
=> p(happ(happ(Vvar__8__rle__11177,happ(happ(Vvar__3__rplus__11154,Vvar__var__var__var__var__24__p__11321__11325__11458__11462__11466),Vvar__var__var__var__var__22__n__11319__11323__11456__11460__11464)),happ(happ(Vvar__3__rplus__11154,Vvar__var__var__var__var__24__p__11321__11325__11458__11462__11466),Vvar__var__var__var__var__23__m__11320__11324__11457__11461__11465))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__11328__11332__11468__11472__11476__11480] :
( t(Vvar__var__var__var__var__var__23__n__11328__11332__11468__11472__11476__11480,Vvar__0__R__11151)
=> ! [Vvar__var__var__var__var__var__24__m__11329__11333__11469__11473__11477__11481] :
( t(Vvar__var__var__var__var__var__24__m__11329__11333__11469__11473__11477__11481,Vvar__0__R__11151)
=> ( p(happ(happ(Vvar__9__rlt__11182,Vvar__1__rO__11152),Vvar__var__var__var__var__var__23__n__11328__11332__11468__11472__11476__11480))
=> ( p(happ(happ(Vvar__9__rlt__11182,Vvar__1__rO__11152),Vvar__var__var__var__var__var__24__m__11329__11333__11469__11473__11477__11481))
=> p(happ(happ(Vvar__9__rlt__11182,Vvar__1__rO__11152),happ(happ(Vvar__4__rtimes__11159,Vvar__var__var__var__var__var__23__n__11328__11332__11468__11472__11476__11480),Vvar__var__var__var__var__var__24__m__11329__11333__11469__11473__11477__11481))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__11172,Vvar__1__rO__11152),Vvar__2__rI__11153))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX29021] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX29021)
=> ( VX29021 = cCoq_2emicromega_2eRMicromega_2eC0
| VX29021 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__29022] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__29022)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__29022) )
| ? [Vvar__0__r__29023] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__29023)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__29023) )
| ? [Vvar__0__r1__29024] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__29024)
& ? [Vvar__1__r2__29025] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__29025)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__29024,Vvar__1__r2__29025) ) )
| ? [Vvar__0__r1__29026] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__29026)
& ? [Vvar__1__r2__29027] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__29027)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__29026,Vvar__1__r2__29027) ) )
| ? [Vvar__0__r1__29028] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__29028)
& ? [Vvar__1__r2__29029] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__29029)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__29028,Vvar__1__r2__29029) ) )
| ? [Vvar__0__r1__29030] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__29030)
& ? [Vvar__1__z__29031] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__29031)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__29030,Vvar__1__z__29031) ) )
| ? [Vvar__0__r__29032] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__29032)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__29032) )
| ? [Vvar__0__r__29033] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__29033)
& VX29021 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__29033) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__29405,VX29406] :
( cType___24t(Vvar__0__T__29405)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__29405,VX29406)
=> ? [Vvar__1__Flhs__29408] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__29405,Vvar__1__Flhs__29408)
& ? [Vvar__2__Fop__29409] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__29409)
& ? [Vvar__3__Frhs__29410] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__29405,Vvar__3__Frhs__29410)
& VX29406 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__29405,Vvar__1__Flhs__29408,Vvar__2__Fop__29409,Vvar__3__Frhs__29410) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX19988] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX19988)
=> ( VX19988 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX19988 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX19988 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX19988 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX26957] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX26957)
=> ( VX26957 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX26957 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX26957 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX26957 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX26957 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX26957 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__29259,VX29260] :
( cType___24t(Vvar__0__C__29259)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29259,VX29260)
=> ( ? [Vvar__1___24Anonymous__29262] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__29262)
& VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__29259,Vvar__1___24Anonymous__29262) )
| ? [Vvar__1___24Anonymous__29264] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__29259,Vvar__1___24Anonymous__29264)
& VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__29259,Vvar__1___24Anonymous__29264) )
| ? [Vvar__1___24Anonymous__29266] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__29259,Vvar__1___24Anonymous__29266)
& ? [Vvar__2___24Anonymous__29267] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29259,Vvar__2___24Anonymous__29267)
& VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__29259,Vvar__1___24Anonymous__29266,Vvar__2___24Anonymous__29267) ) )
| ? [Vvar__1___24Anonymous__29269] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29259,Vvar__1___24Anonymous__29269)
& ? [Vvar__2___24Anonymous__29270] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29259,Vvar__2___24Anonymous__29270)
& VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__29259,Vvar__1___24Anonymous__29269,Vvar__2___24Anonymous__29270) ) )
| ? [Vvar__1___24Anonymous__29272] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29259,Vvar__1___24Anonymous__29272)
& ? [Vvar__2___24Anonymous__29273] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__29259,Vvar__2___24Anonymous__29273)
& VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__29259,Vvar__1___24Anonymous__29272,Vvar__2___24Anonymous__29273) ) )
| ? [Vvar__1___24Anonymous__29275] :
( t(Vvar__1___24Anonymous__29275,Vvar__0__C__29259)
& VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__29259,Vvar__1___24Anonymous__29275) )
| VX29260 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__29259) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043] :
( cType___24t(Vvar__0__R__1974)
=> ( t(Vvar__1__rO__1975,Vvar__0__R__1974)
=> ( t(Vvar__2__rI__1976,Vvar__0__R__1974)
=> ( c_24__type__2507___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__3__rplus__1977)
=> ( c_24__type__2853___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__4__rtimes__1982)
=> ( c_24__type__3199___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__5__rminus__1987)
=> ( c_24__type__3522___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__6__ropp__1992)
=> ( c_24__type__3868___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__7__req__1995)
=> ( c_24__type__4214___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__8__rle__2000)
=> ( cType___24t(Vvar__9__C__2005)
=> ( t(Vvar__10__cO__2006,Vvar__9__C__2005)
=> ( t(Vvar__11__cI__2007,Vvar__9__C__2005)
=> ( c_24__type__4560___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__12__cplus__2008)
=> ( c_24__type__4906___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__13__ctimes__2013)
=> ( c_24__type__5252___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__14__cminus__2018)
=> ( c_24__type__5575___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__15__copp__2023)
=> ( c_24__type__5921___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__16__ceqb__2026)
=> ( c_24__type__6267___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__17__cleb__2031)
=> ( c_24__type__6590___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__18__phi__2036)
=> ( cType___24t(Vvar__19__E__2039)
=> ( c_24__type__6913___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__20__pow__phi__2040)
=> ( c_24__type__7259___24t(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043,Vvar__21__rpow__2043)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__8__rle__2000,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__17__cleb__2031,Vvar__18__phi__2036,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__1974,Vvar__1__rO__1975,Vvar__2__rI__1976,Vvar__3__rplus__1977,Vvar__4__rtimes__1982,Vvar__5__rminus__1987,Vvar__6__ropp__1992,Vvar__7__req__1995,Vvar__9__C__2005,Vvar__10__cO__2006,Vvar__11__cI__2007,Vvar__12__cplus__2008,Vvar__13__ctimes__2013,Vvar__14__cminus__2018,Vvar__15__copp__2023,Vvar__16__ceqb__2026,Vvar__18__phi__2036)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__1974,Vvar__2__rI__1976,Vvar__4__rtimes__1982,Vvar__7__req__1995,Vvar__19__E__2039,Vvar__20__pow__phi__2040,Vvar__21__rpow__2043)
& ! [Vvar__var__var__var__var__var__24__x__2126__2129__2139__2142__2145__2148] :
( t(Vvar__var__var__var__var__var__24__x__2126__2129__2139__2142__2145__2148,Vvar__9__C__2005)
=> ! [Vvar__var__var__var__var__var__25__y__2127__2130__2140__2143__2146__2149] :
( t(Vvar__var__var__var__var__var__25__y__2127__2130__2140__2143__2146__2149,Vvar__9__C__2005)
=> ( happ(happ(Vvar__16__ceqb__2026,Vvar__var__var__var__var__var__24__x__2126__2129__2139__2142__2145__2148),Vvar__var__var__var__var__var__25__y__2127__2130__2140__2143__2146__2149) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__1995,happ(Vvar__18__phi__2036,Vvar__var__var__var__var__var__24__x__2126__2129__2139__2142__2145__2148)),happ(Vvar__18__phi__2036,Vvar__var__var__var__var__var__25__y__2127__2130__2140__2143__2146__2149))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__2133__2136__2151__2154__2157__2160] :
( t(Vvar__var__var__var__var__var__25__x__2133__2136__2151__2154__2157__2160,Vvar__9__C__2005)
=> ! [Vvar__var__var__var__var__var__26__y__2134__2137__2152__2155__2158__2161] :
( t(Vvar__var__var__var__var__var__26__y__2134__2137__2152__2155__2158__2161,Vvar__9__C__2005)
=> ( happ(happ(Vvar__17__cleb__2031,Vvar__var__var__var__var__var__25__x__2133__2136__2151__2154__2157__2160),Vvar__var__var__var__var__var__26__y__2134__2137__2152__2155__2158__2161) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__2000,happ(Vvar__18__phi__2036,Vvar__var__var__var__var__var__25__x__2133__2136__2151__2154__2157__2160)),happ(Vvar__18__phi__2036,Vvar__var__var__var__var__var__26__y__2134__2137__2152__2155__2158__2161))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,VX30038] :
( cType___24t(Vvar__0__TA__30034)
=> ( cType___24t(Vvar__1__TX__30035)
=> ( cType___24t(Vvar__2__AA__30036)
=> ( cType___24t(Vvar__3__AF__30037)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,VX30038)
=> ( VX30038 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037)
| VX30038 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037)
| ? [Vvar__4___24Anonymous__30051] :
( t(Vvar__4___24Anonymous__30051,Vvar__1__TX__30035)
& VX30038 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30051) )
| ? [Vvar__4___24Anonymous__30056] :
( t(Vvar__4___24Anonymous__30056,Vvar__0__TA__30034)
& ? [Vvar__5___24Anonymous__30057] :
( t(Vvar__5___24Anonymous__30057,Vvar__2__AA__30036)
& VX30038 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30056,Vvar__5___24Anonymous__30057) ) )
| ? [Vvar__4___24Anonymous__30062] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30062)
& ? [Vvar__5___24Anonymous__30063] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__5___24Anonymous__30063)
& VX30038 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30062,Vvar__5___24Anonymous__30063) ) )
| ? [Vvar__4___24Anonymous__30068] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30068)
& ? [Vvar__5___24Anonymous__30069] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__5___24Anonymous__30069)
& VX30038 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30068,Vvar__5___24Anonymous__30069) ) )
| ? [Vvar__4___24Anonymous__30074] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30074)
& VX30038 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30074) )
| ? [Vvar__4___24Anonymous__30079] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30079)
& ? [Vvar__5___24Anonymous__30080] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__30037,Vvar__5___24Anonymous__30080)
& ? [Vvar__6___24Anonymous__30081] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__6___24Anonymous__30081)
& VX30038 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__30034,Vvar__1__TX__30035,Vvar__2__AA__30036,Vvar__3__AF__30037,Vvar__4___24Anonymous__30079,Vvar__5___24Anonymous__30080,Vvar__6___24Anonymous__30081) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__25500,VX25501] :
( cType___24t(Vvar__0__A__25500)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__25500,VX25501)
=> ( VX25501 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25500)
| ? [Vvar__1___24Anonymous__25504] :
( t(Vvar__1___24Anonymous__25504,Vvar__0__A__25500)
& VX25501 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25500,Vvar__1___24Anonymous__25504) )
| ? [Vvar__1___24Anonymous__25506] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__25500,Vvar__1___24Anonymous__25506)
& ? [Vvar__2___24Anonymous__25507] :
( t(Vvar__2___24Anonymous__25507,Vvar__0__A__25500)
& ? [Vvar__3___24Anonymous__25508] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__25500,Vvar__3___24Anonymous__25508)
& VX25501 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__25500,Vvar__1___24Anonymous__25506,Vvar__2___24Anonymous__25507,Vvar__3___24Anonymous__25508) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__30596] :
( cProp___24t(Vvar__0___24Anonymous__30596)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__30596)
=> ( ? [Vvar__0__P__30598] :
( cProp___24t(Vvar__0__P__30598)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30598)
& Vvar__0___24Anonymous__30596 = Vvar__0__P__30598 )
| ? [Vvar__0__s__30600] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__30600)
& Vvar__0___24Anonymous__30596 = c_24__prop__30609___24a2(Vvar__0___24Anonymous__30596,Vvar__0__s__30600) )
| ? [Vvar__0__s1__30602] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__30602)
& ? [Vvar__1__s2__30603] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__30603)
& Vvar__0___24Anonymous__30596 = c_24__prop__30610___24a3(Vvar__0___24Anonymous__30596,Vvar__0__s1__30602,Vvar__1__s2__30603) ) )
| ? [Vvar__0__s1__30606] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__30606)
& ? [Vvar__1__s2__30607] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__30607)
& Vvar__0___24Anonymous__30596 = c_24__prop__30611___24a3(Vvar__0___24Anonymous__30596,Vvar__0__s1__30606,Vvar__1__s2__30607) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__30565] :
( cProp___24t(Vvar__0___24Anonymous__30565)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__30565)
=> ( ? [Vvar__0__S__30567] :
( cType___24t(Vvar__0__S__30567)
& ? [Vvar__1__x__30568] :
( t(Vvar__1__x__30568,Vvar__0__S__30567)
& ? [Vvar__2__y__30569] :
( t(Vvar__2__y__30569,Vvar__0__S__30567)
& Vvar__0___24Anonymous__30565 = c_24__prop__30589___24a4(Vvar__0___24Anonymous__30565,Vvar__0__S__30567,Vvar__1__x__30568,Vvar__2__y__30569) ) ) )
| ? [Vvar__0__x__30570] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__30570)
& ? [Vvar__1__y__30571] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__30571)
& Vvar__0___24Anonymous__30565 = c_24__prop__30590___24a3(Vvar__0___24Anonymous__30565,Vvar__0__x__30570,Vvar__1__y__30571) ) )
| ? [Vvar__0__x__30572] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__30572)
& ? [Vvar__1__s__30573] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__30573)
& Vvar__0___24Anonymous__30565 = c_24__prop__30591___24a3(Vvar__0___24Anonymous__30565,Vvar__0__x__30572,Vvar__1__s__30573) ) )
| Vvar__0___24Anonymous__30565 = c_24True
| Vvar__0___24Anonymous__30565 = c_24False
| ? [Vvar__0__P__30574] :
( cProp___24t(Vvar__0__P__30574)
& ? [Vvar__1__Q__30575] :
( cProp___24t(Vvar__1__Q__30575)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30574)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__30575)
& Vvar__0___24Anonymous__30565 = c_24__prop__30592___24a3(Vvar__0___24Anonymous__30565,Vvar__0__P__30574,Vvar__1__Q__30575) ) )
| ? [Vvar__0__P__30578] :
( cProp___24t(Vvar__0__P__30578)
& ? [Vvar__1__Q__30579] :
( cProp___24t(Vvar__1__Q__30579)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30578)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__30579)
& Vvar__0___24Anonymous__30565 = c_24__prop__30593___24a3(Vvar__0___24Anonymous__30565,Vvar__0__P__30578,Vvar__1__Q__30579) ) )
| ? [Vvar__0__P__30582] :
( cProp___24t(Vvar__0__P__30582)
& ? [Vvar__1__Q__30583] :
( cProp___24t(Vvar__1__Q__30583)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30582)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__30583)
& Vvar__0___24Anonymous__30565 = c_24__prop__30594___24a3(Vvar__0___24Anonymous__30565,Vvar__0__P__30582,Vvar__1__Q__30583) ) )
| ? [Vvar__0__P__30587] :
( cProp___24t(Vvar__0__P__30587)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__30587)
& Vvar__0___24Anonymous__30565 = c_24__prop__30595___24a2(Vvar__0___24Anonymous__30565,Vvar__0__P__30587) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX25874] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX25874)
=> ( VX25874 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__25875] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__25875)
& ? [Vvar__1___24Anonymous__25876] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__25876)
& VX25874 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25875,Vvar__1___24Anonymous__25876) ) )
| ? [Vvar__0___24Anonymous__25877] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__25877)
& ? [Vvar__1___24Anonymous__25878] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__25878)
& VX25874 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__25877,Vvar__1___24Anonymous__25878) ) )
| ? [Vvar__0___24Anonymous__25879] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__25879)
& ? [Vvar__1___24Anonymous__25880] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__25880)
& ? [Vvar__2___24Anonymous__25881] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__25881)
& VX25874 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__25879,Vvar__1___24Anonymous__25880,Vvar__2___24Anonymous__25881) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
! [Vvar__0__x__35146,Vvar__1___24Anonymous__35147] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__35146)
=> ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__35147)
=> ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__35146,Vvar__1___24Anonymous__35147)
=> ( ? [Vvar__1__c__35150] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__35150)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__35146,Vvar__1__c__35150)
& Vvar__1___24Anonymous__35147 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__35150) )
| ? [Vvar__1__p__35153] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__35153)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__35146,Vvar__1__p__35153)
& ? [Vvar__3__j__35155] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__35155)
& Vvar__1___24Anonymous__35147 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__35155,Vvar__1__p__35153) ) )
| ? [Vvar__1__p__35157] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__35157)
& ? [Vvar__2__q__35158] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__35158)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__35146,Vvar__1__p__35157)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__35146,Vvar__2__q__35158)
& ? [Vvar__5__j__35161] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__35161)
& Vvar__1___24Anonymous__35147 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__35157,Vvar__5__j__35161,Vvar__2__q__35158) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__32153,Vvar__1__env__32154,Vvar__2__env_27__32157,Vvar__3__x__32160] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__32153)
=> ( c_24__type__32181___24t(Vvar__0__fr__32153,Vvar__1__env__32154,Vvar__2__env_27__32157,Vvar__3__x__32160,Vvar__1__env__32154)
=> ( c_24__type__32190___24t(Vvar__0__fr__32153,Vvar__1__env__32154,Vvar__2__env_27__32157,Vvar__3__x__32160,Vvar__2__env_27__32157)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__32160)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__32153,Vvar__1__env__32154,Vvar__2__env_27__32157,Vvar__3__x__32160)
=> ( happ(Vvar__1__env__32154,Vvar__3__x__32160) = happ(Vvar__2__env_27__32157,Vvar__3__x__32160)
& happ(Vvar__1__env__32154,Vvar__3__x__32160) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__32157,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__32153,Vvar__3__x__32160))),happ(Vvar__2__env_27__32157,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__32153,Vvar__3__x__32160))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__32157,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__32153,Vvar__3__x__32160))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__32157,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__32153,Vvar__3__x__32160))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__17522,VX17523] :
( cType___24t(Vvar__0__C__17522)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,VX17523)
=> ( VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__17522)
| VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__17522)
| ? [Vvar__1___24Anonymous__17527] :
( t(Vvar__1___24Anonymous__17527,Vvar__0__C__17522)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__17522,Vvar__1___24Anonymous__17527) )
| ? [Vvar__1___24Anonymous__17529] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__17529)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__17522,Vvar__1___24Anonymous__17529) )
| ? [Vvar__1___24Anonymous__17531] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17531)
& ? [Vvar__2___24Anonymous__17532] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__2___24Anonymous__17532)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__17522,Vvar__1___24Anonymous__17531,Vvar__2___24Anonymous__17532) ) )
| ? [Vvar__1___24Anonymous__17534] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17534)
& ? [Vvar__2___24Anonymous__17535] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__2___24Anonymous__17535)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__17522,Vvar__1___24Anonymous__17534,Vvar__2___24Anonymous__17535) ) )
| ? [Vvar__1___24Anonymous__17537] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17537)
& ? [Vvar__2___24Anonymous__17538] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__2___24Anonymous__17538)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__17522,Vvar__1___24Anonymous__17537,Vvar__2___24Anonymous__17538) ) )
| ? [Vvar__1___24Anonymous__17540] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17540)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__17522,Vvar__1___24Anonymous__17540) )
| ? [Vvar__1___24Anonymous__17542] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17542)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__17522,Vvar__1___24Anonymous__17542) )
| ? [Vvar__1___24Anonymous__17544] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17544)
& ? [Vvar__2___24Anonymous__17545] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__2___24Anonymous__17545)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__17522,Vvar__1___24Anonymous__17544,Vvar__2___24Anonymous__17545) ) )
| ? [Vvar__1___24Anonymous__17547] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__17522,Vvar__1___24Anonymous__17547)
& ? [Vvar__2___24Anonymous__17548] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__17548)
& VX17523 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__17522,Vvar__1___24Anonymous__17547,Vvar__2___24Anonymous__17548) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506] :
( cType___24t(Vvar__0__R__15477)
=> ( t(Vvar__1__rO__15478,Vvar__0__R__15477)
=> ( t(Vvar__2__rI__15479,Vvar__0__R__15477)
=> ( c_24__type__15671___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__3__radd__15480)
=> ( c_24__type__15764___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__4__rmul__15485)
=> ( c_24__type__15857___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__5__rsub__15490)
=> ( c_24__type__15939___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__6__ropp__15495)
=> ( c_24__type__16032___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__7__rdiv__15498)
=> ( c_24__type__16114___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__8__rinv__15503)
=> ( c_24__type__16207___24t(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506,Vvar__9__req__15506)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__7__rdiv__15498,Vvar__8__rinv__15503,Vvar__9__req__15506)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__15477,Vvar__1__rO__15478,Vvar__2__rI__15479,Vvar__3__radd__15480,Vvar__4__rmul__15485,Vvar__5__rsub__15490,Vvar__6__ropp__15495,Vvar__9__req__15506)
& ~ p(happ(happ(Vvar__9__req__15506,Vvar__2__rI__15479),Vvar__1__rO__15478))
& ! [Vvar__var__var__var__var__var__var__12__p__15549__15551__15558__15560__15562__15564__15566] :
( t(Vvar__var__var__var__var__var__var__12__p__15549__15551__15558__15560__15562__15564__15566,Vvar__0__R__15477)
=> ! [Vvar__var__var__var__var__var__var__13__q__15550__15552__15559__15561__15563__15565__15567] :
( t(Vvar__var__var__var__var__var__var__13__q__15550__15552__15559__15561__15563__15565__15567,Vvar__0__R__15477)
=> p(happ(happ(Vvar__9__req__15506,happ(happ(Vvar__7__rdiv__15498,Vvar__var__var__var__var__var__var__12__p__15549__15551__15558__15560__15562__15564__15566),Vvar__var__var__var__var__var__var__13__q__15550__15552__15559__15561__15563__15565__15567)),happ(happ(Vvar__4__rmul__15485,Vvar__var__var__var__var__var__var__12__p__15549__15551__15558__15560__15562__15564__15566),happ(Vvar__8__rinv__15503,Vvar__var__var__var__var__var__var__13__q__15550__15552__15559__15561__15563__15565__15567)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__15554__15556__15568__15570__15572__15574__15576__15578] :
( t(Vvar__var__var__var__var__var__var__var__13__p__15554__15556__15568__15570__15572__15574__15576__15578,Vvar__0__R__15477)
=> ( ~ p(happ(happ(Vvar__9__req__15506,Vvar__var__var__var__var__var__var__var__13__p__15554__15556__15568__15570__15572__15574__15576__15578),Vvar__1__rO__15478))
=> p(happ(happ(Vvar__9__req__15506,happ(happ(Vvar__4__rmul__15485,happ(Vvar__8__rinv__15503,Vvar__var__var__var__var__var__var__var__13__p__15554__15556__15568__15570__15572__15574__15576__15578)),Vvar__var__var__var__var__var__var__var__13__p__15554__15556__15568__15570__15572__15574__15576__15578)),Vvar__2__rI__15479)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692] :
( cType___24t(Vvar__0__R__27663)
=> ( t(Vvar__1__rO__27664,Vvar__0__R__27663)
=> ( t(Vvar__2__rI__27665,Vvar__0__R__27663)
=> ( c_24__type__27857___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__3__radd__27666)
=> ( c_24__type__27950___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__4__rmul__27671)
=> ( c_24__type__28043___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__5__rsub__27676)
=> ( c_24__type__28125___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__6__ropp__27681)
=> ( c_24__type__28218___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__7__rdiv__27684)
=> ( c_24__type__28300___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__8__rinv__27689)
=> ( c_24__type__28393___24t(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692,Vvar__9__req__27692)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__7__rdiv__27684,Vvar__8__rinv__27689,Vvar__9__req__27692)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__27663,Vvar__1__rO__27664,Vvar__2__rI__27665,Vvar__3__radd__27666,Vvar__4__rmul__27671,Vvar__5__rsub__27676,Vvar__6__ropp__27681,Vvar__9__req__27692)
& ~ p(happ(happ(Vvar__9__req__27692,Vvar__2__rI__27665),Vvar__1__rO__27664))
& ! [Vvar__var__var__var__var__var__var__12__p__27735__27737__27744__27746__27748__27750__27752] :
( t(Vvar__var__var__var__var__var__var__12__p__27735__27737__27744__27746__27748__27750__27752,Vvar__0__R__27663)
=> ! [Vvar__var__var__var__var__var__var__13__q__27736__27738__27745__27747__27749__27751__27753] :
( t(Vvar__var__var__var__var__var__var__13__q__27736__27738__27745__27747__27749__27751__27753,Vvar__0__R__27663)
=> p(happ(happ(Vvar__9__req__27692,happ(happ(Vvar__7__rdiv__27684,Vvar__var__var__var__var__var__var__12__p__27735__27737__27744__27746__27748__27750__27752),Vvar__var__var__var__var__var__var__13__q__27736__27738__27745__27747__27749__27751__27753)),happ(happ(Vvar__4__rmul__27671,Vvar__var__var__var__var__var__var__12__p__27735__27737__27744__27746__27748__27750__27752),happ(Vvar__8__rinv__27689,Vvar__var__var__var__var__var__var__13__q__27736__27738__27745__27747__27749__27751__27753)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__27740__27742__27754__27756__27758__27760__27762__27764] :
( t(Vvar__var__var__var__var__var__var__var__13__p__27740__27742__27754__27756__27758__27760__27762__27764,Vvar__0__R__27663)
=> ( ~ p(happ(happ(Vvar__9__req__27692,Vvar__var__var__var__var__var__var__var__13__p__27740__27742__27754__27756__27758__27760__27762__27764),Vvar__1__rO__27664))
=> p(happ(happ(Vvar__9__req__27692,happ(happ(Vvar__4__rmul__27671,happ(Vvar__8__rinv__27689,Vvar__var__var__var__var__var__var__var__13__p__27740__27742__27754__27756__27758__27760__27762__27764)),Vvar__var__var__var__var__var__var__var__13__p__27740__27742__27754__27756__27758__27760__27762__27764)),Vvar__2__rI__27665)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__18145,VX18146] :
( cType___24t(Vvar__0__C__18145)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__18145,VX18146)
=> ? [Vvar__1__num__18148] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__18145,Vvar__1__num__18148)
& ? [Vvar__2__denum__18149] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__18145,Vvar__2__denum__18149)
& ? [Vvar__3__condition__18150] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__18145),Vvar__3__condition__18150)
& VX18146 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__18145,Vvar__1__num__18148,Vvar__2__denum__18149,Vvar__3__condition__18150) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__18223,VX18224] :
( cType___24t(Vvar__0__C__18223)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__18223,VX18224)
=> ? [Vvar__1__rsplit__left__18226] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__18223,Vvar__1__rsplit__left__18226)
& ? [Vvar__2__rsplit__common__18227] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__18223,Vvar__2__rsplit__common__18227)
& ? [Vvar__3__rsplit__right__18228] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__18223,Vvar__3__rsplit__right__18228)
& VX18224 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__18223,Vvar__1__rsplit__left__18226,Vvar__2__rsplit__common__18227,Vvar__3__rsplit__right__18228) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420] :
( cType___24t(Vvar__0__R__28399)
=> ( t(Vvar__1__rO__28400,Vvar__0__R__28399)
=> ( t(Vvar__2__rI__28401,Vvar__0__R__28399)
=> ( c_24__type__28547___24t(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420,Vvar__3__radd__28402)
=> ( c_24__type__28610___24t(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420,Vvar__4__rmul__28407)
=> ( c_24__type__28673___24t(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420,Vvar__5__rdiv__28412)
=> ( c_24__type__28727___24t(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420,Vvar__6__rinv__28417)
=> ( c_24__type__28790___24t(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420,Vvar__7__req__28420)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__5__rdiv__28412,Vvar__6__rinv__28417,Vvar__7__req__28420)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__28399,Vvar__1__rO__28400,Vvar__2__rI__28401,Vvar__3__radd__28402,Vvar__4__rmul__28407,Vvar__7__req__28420)
& ~ p(happ(happ(Vvar__7__req__28420,Vvar__2__rI__28401),Vvar__1__rO__28400))
& ! [Vvar__var__var__var__var__var__var__10__p__28455__28457__28464__28466__28468__28470__28472] :
( t(Vvar__var__var__var__var__var__var__10__p__28455__28457__28464__28466__28468__28470__28472,Vvar__0__R__28399)
=> ! [Vvar__var__var__var__var__var__var__11__q__28456__28458__28465__28467__28469__28471__28473] :
( t(Vvar__var__var__var__var__var__var__11__q__28456__28458__28465__28467__28469__28471__28473,Vvar__0__R__28399)
=> p(happ(happ(Vvar__7__req__28420,happ(happ(Vvar__5__rdiv__28412,Vvar__var__var__var__var__var__var__10__p__28455__28457__28464__28466__28468__28470__28472),Vvar__var__var__var__var__var__var__11__q__28456__28458__28465__28467__28469__28471__28473)),happ(happ(Vvar__4__rmul__28407,Vvar__var__var__var__var__var__var__10__p__28455__28457__28464__28466__28468__28470__28472),happ(Vvar__6__rinv__28417,Vvar__var__var__var__var__var__var__11__q__28456__28458__28465__28467__28469__28471__28473)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__28460__28462__28474__28476__28478__28480__28482__28484] :
( t(Vvar__var__var__var__var__var__var__var__11__p__28460__28462__28474__28476__28478__28480__28482__28484,Vvar__0__R__28399)
=> ( ~ p(happ(happ(Vvar__7__req__28420,Vvar__var__var__var__var__var__var__var__11__p__28460__28462__28474__28476__28478__28480__28482__28484),Vvar__1__rO__28400))
=> p(happ(happ(Vvar__7__req__28420,happ(happ(Vvar__4__rmul__28407,happ(Vvar__6__rinv__28417,Vvar__var__var__var__var__var__var__var__11__p__28460__28462__28474__28476__28478__28480__28482__28484)),Vvar__var__var__var__var__var__var__var__11__p__28460__28462__28474__28476__28478__28480__28482__28484)),Vvar__2__rI__28401)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX30949] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX30949)
=> ? [Vvar__0__hypo__type__30950] :
( cType___24t(Vvar__0__hypo__type__30950)
& ? [Vvar__1__hypo__proof__30951] :
( t(Vvar__1__hypo__proof__30951,Vvar__0__hypo__type__30950)
& VX30949 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__30950,Vvar__1__hypo__proof__30951) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX21334] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX21334)
=> ( VX21334 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__21335] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21335)
& ? [Vvar__1___24Anonymous__21336] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__21336)
& VX21334 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__21335,Vvar__1___24Anonymous__21336) ) )
| ? [Vvar__0___24Anonymous__21337] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21337)
& ? [Vvar__1___24Anonymous__21338] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__21338)
& VX21334 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__21337,Vvar__1___24Anonymous__21338) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__12271,VX12272] :
( cType___24t(Vvar__0__C__12271)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,VX12272)
=> ( VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12271)
| VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12271)
| ? [Vvar__1___24Anonymous__12276] :
( t(Vvar__1___24Anonymous__12276,Vvar__0__C__12271)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__12271,Vvar__1___24Anonymous__12276) )
| ? [Vvar__1___24Anonymous__12278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12278)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__12271,Vvar__1___24Anonymous__12278) )
| ? [Vvar__1___24Anonymous__12280] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__1___24Anonymous__12280)
& ? [Vvar__2___24Anonymous__12281] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__2___24Anonymous__12281)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__12271,Vvar__1___24Anonymous__12280,Vvar__2___24Anonymous__12281) ) )
| ? [Vvar__1___24Anonymous__12283] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__1___24Anonymous__12283)
& ? [Vvar__2___24Anonymous__12284] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__2___24Anonymous__12284)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__12271,Vvar__1___24Anonymous__12283,Vvar__2___24Anonymous__12284) ) )
| ? [Vvar__1___24Anonymous__12286] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__1___24Anonymous__12286)
& ? [Vvar__2___24Anonymous__12287] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__2___24Anonymous__12287)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__12271,Vvar__1___24Anonymous__12286,Vvar__2___24Anonymous__12287) ) )
| ? [Vvar__1___24Anonymous__12289] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__1___24Anonymous__12289)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__12271,Vvar__1___24Anonymous__12289) )
| ? [Vvar__1___24Anonymous__12291] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12271,Vvar__1___24Anonymous__12291)
& ? [Vvar__2___24Anonymous__12292] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__12292)
& VX12272 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__12271,Vvar__1___24Anonymous__12291,Vvar__2___24Anonymous__12292) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__20675,VX20676] :
( cType___24t(Vvar__0__C__20675)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20675,VX20676)
=> ( ? [Vvar__1___24Anonymous__20678] :
( t(Vvar__1___24Anonymous__20678,Vvar__0__C__20675)
& VX20676 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__20675,Vvar__1___24Anonymous__20678) )
| ? [Vvar__1___24Anonymous__20680] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__20680)
& ? [Vvar__2___24Anonymous__20681] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20675,Vvar__2___24Anonymous__20681)
& VX20676 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__20675,Vvar__1___24Anonymous__20680,Vvar__2___24Anonymous__20681) ) )
| ? [Vvar__1___24Anonymous__20683] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20675,Vvar__1___24Anonymous__20683)
& ? [Vvar__2___24Anonymous__20684] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__20684)
& ? [Vvar__3___24Anonymous__20685] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__20675,Vvar__3___24Anonymous__20685)
& VX20676 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__20675,Vvar__1___24Anonymous__20683,Vvar__2___24Anonymous__20684,Vvar__3___24Anonymous__20685) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690] :
( cType___24t(Vvar__0__R__12669)
=> ( t(Vvar__1__rO__12670,Vvar__0__R__12669)
=> ( t(Vvar__2__rI__12671,Vvar__0__R__12669)
=> ( c_24__type__12918___24t(Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690,Vvar__3__radd__12672)
=> ( c_24__type__12981___24t(Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690,Vvar__4__rmul__12677)
=> ( c_24__type__13044___24t(Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690,Vvar__5__rsub__12682)
=> ( c_24__type__13098___24t(Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690,Vvar__6__ropp__12687)
=> ( c_24__type__13161___24t(Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690,Vvar__7__req__12690)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__12669,Vvar__1__rO__12670,Vvar__2__rI__12671,Vvar__3__radd__12672,Vvar__4__rmul__12677,Vvar__5__rsub__12682,Vvar__6__ropp__12687,Vvar__7__req__12690)
=> ( ! [Vvar__var__var__var__var__var__8__x__12723__12724__12777__12778__12779__12780] :
( t(Vvar__var__var__var__var__var__8__x__12723__12724__12777__12778__12779__12780,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__3__radd__12672,Vvar__1__rO__12670),Vvar__var__var__var__var__var__8__x__12723__12724__12777__12778__12779__12780)),Vvar__var__var__var__var__var__8__x__12723__12724__12777__12778__12779__12780)) )
& ! [Vvar__var__var__var__var__9__x__12726__12728__12781__12783__12785] :
( t(Vvar__var__var__var__var__9__x__12726__12728__12781__12783__12785,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__10__y__12727__12729__12782__12784__12786] :
( t(Vvar__var__var__var__var__10__y__12727__12729__12782__12784__12786,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__9__x__12726__12728__12781__12783__12785),Vvar__var__var__var__var__10__y__12727__12729__12782__12784__12786)),happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__10__y__12727__12729__12782__12784__12786),Vvar__var__var__var__var__9__x__12726__12728__12781__12783__12785))) ) )
& ! [Vvar__var__var__var__var__10__x__12731__12734__12787__12790__12793] :
( t(Vvar__var__var__var__var__10__x__12731__12734__12787__12790__12793,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__11__y__12732__12735__12788__12791__12794] :
( t(Vvar__var__var__var__var__11__y__12732__12735__12788__12791__12794,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__12__z__12733__12736__12789__12792__12795] :
( t(Vvar__var__var__var__var__12__z__12733__12736__12789__12792__12795,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__10__x__12731__12734__12787__12790__12793),happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__11__y__12732__12735__12788__12791__12794),Vvar__var__var__var__var__12__z__12733__12736__12789__12792__12795))),happ(happ(Vvar__3__radd__12672,happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__10__x__12731__12734__12787__12790__12793),Vvar__var__var__var__var__11__y__12732__12735__12788__12791__12794)),Vvar__var__var__var__var__12__z__12733__12736__12789__12792__12795))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__12738__12739__12796__12797__12798__12799] :
( t(Vvar__var__var__var__var__var__11__x__12738__12739__12796__12797__12798__12799,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__4__rmul__12677,Vvar__2__rI__12671),Vvar__var__var__var__var__var__11__x__12738__12739__12796__12797__12798__12799)),Vvar__var__var__var__var__var__11__x__12738__12739__12796__12797__12798__12799)) )
& ! [Vvar__var__var__var__var__var__12__x__12741__12742__12800__12801__12802__12803] :
( t(Vvar__var__var__var__var__var__12__x__12741__12742__12800__12801__12802__12803,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__4__rmul__12677,Vvar__1__rO__12670),Vvar__var__var__var__var__var__12__x__12741__12742__12800__12801__12802__12803)),Vvar__1__rO__12670)) )
& ! [Vvar__var__var__var__var__13__x__12744__12746__12804__12806__12808] :
( t(Vvar__var__var__var__var__13__x__12744__12746__12804__12806__12808,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__14__y__12745__12747__12805__12807__12809] :
( t(Vvar__var__var__var__var__14__y__12745__12747__12805__12807__12809,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__13__x__12744__12746__12804__12806__12808),Vvar__var__var__var__var__14__y__12745__12747__12805__12807__12809)),happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__14__y__12745__12747__12805__12807__12809),Vvar__var__var__var__var__13__x__12744__12746__12804__12806__12808))) ) )
& ! [Vvar__var__var__var__var__14__x__12749__12752__12810__12813__12816] :
( t(Vvar__var__var__var__var__14__x__12749__12752__12810__12813__12816,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__15__y__12750__12753__12811__12814__12817] :
( t(Vvar__var__var__var__var__15__y__12750__12753__12811__12814__12817,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__16__z__12751__12754__12812__12815__12818] :
( t(Vvar__var__var__var__var__16__z__12751__12754__12812__12815__12818,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__14__x__12749__12752__12810__12813__12816),happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__15__y__12750__12753__12811__12814__12817),Vvar__var__var__var__var__16__z__12751__12754__12812__12815__12818))),happ(happ(Vvar__4__rmul__12677,happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__14__x__12749__12752__12810__12813__12816),Vvar__var__var__var__var__15__y__12750__12753__12811__12814__12817)),Vvar__var__var__var__var__16__z__12751__12754__12812__12815__12818))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__12756__12759__12819__12822__12825__12828] :
( t(Vvar__var__var__var__var__var__15__x__12756__12759__12819__12822__12825__12828,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__var__16__y__12757__12760__12820__12823__12826__12829] :
( t(Vvar__var__var__var__var__var__16__y__12757__12760__12820__12823__12826__12829,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__var__17__z__12758__12761__12821__12824__12827__12830] :
( t(Vvar__var__var__var__var__var__17__z__12758__12761__12821__12824__12827__12830,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__4__rmul__12677,happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__var__15__x__12756__12759__12819__12822__12825__12828),Vvar__var__var__var__var__var__16__y__12757__12760__12820__12823__12826__12829)),Vvar__var__var__var__var__var__17__z__12758__12761__12821__12824__12827__12830)),happ(happ(Vvar__3__radd__12672,happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__var__15__x__12756__12759__12819__12822__12825__12828),Vvar__var__var__var__var__var__17__z__12758__12761__12821__12824__12827__12830)),happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__var__16__y__12757__12760__12820__12823__12826__12829),Vvar__var__var__var__var__var__17__z__12758__12761__12821__12824__12827__12830)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__12763__12765__12831__12833__12835__12837] :
( t(Vvar__var__var__var__var__var__16__x__12763__12765__12831__12833__12835__12837,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__var__17__y__12764__12766__12832__12834__12836__12838] :
( t(Vvar__var__var__var__var__var__17__y__12764__12766__12832__12834__12836__12838,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(Vvar__6__ropp__12687,happ(happ(Vvar__4__rmul__12677,Vvar__var__var__var__var__var__16__x__12763__12765__12831__12833__12835__12837),Vvar__var__var__var__var__var__17__y__12764__12766__12832__12834__12836__12838))),happ(happ(Vvar__4__rmul__12677,happ(Vvar__6__ropp__12687,Vvar__var__var__var__var__var__16__x__12763__12765__12831__12833__12835__12837)),Vvar__var__var__var__var__var__17__y__12764__12766__12832__12834__12836__12838))) ) )
& ! [Vvar__var__var__var__var__var__17__x__12768__12770__12839__12841__12843__12845] :
( t(Vvar__var__var__var__var__var__17__x__12768__12770__12839__12841__12843__12845,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__var__18__y__12769__12771__12840__12842__12844__12846] :
( t(Vvar__var__var__var__var__var__18__y__12769__12771__12840__12842__12844__12846,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(Vvar__6__ropp__12687,happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__var__17__x__12768__12770__12839__12841__12843__12845),Vvar__var__var__var__var__var__18__y__12769__12771__12840__12842__12844__12846))),happ(happ(Vvar__3__radd__12672,happ(Vvar__6__ropp__12687,Vvar__var__var__var__var__var__17__x__12768__12770__12839__12841__12843__12845)),happ(Vvar__6__ropp__12687,Vvar__var__var__var__var__var__18__y__12769__12771__12840__12842__12844__12846)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__12773__12775__12847__12849__12851__12853__12855] :
( t(Vvar__var__var__var__var__var__var__18__x__12773__12775__12847__12849__12851__12853__12855,Vvar__0__R__12669)
=> ! [Vvar__var__var__var__var__var__var__19__y__12774__12776__12848__12850__12852__12854__12856] :
( t(Vvar__var__var__var__var__var__var__19__y__12774__12776__12848__12850__12852__12854__12856,Vvar__0__R__12669)
=> p(happ(happ(Vvar__7__req__12690,happ(happ(Vvar__5__rsub__12682,Vvar__var__var__var__var__var__var__18__x__12773__12775__12847__12849__12851__12853__12855),Vvar__var__var__var__var__var__var__19__y__12774__12776__12848__12850__12852__12854__12856)),happ(happ(Vvar__3__radd__12672,Vvar__var__var__var__var__var__var__18__x__12773__12775__12847__12849__12851__12853__12855),happ(Vvar__6__ropp__12687,Vvar__var__var__var__var__var__var__19__y__12774__12776__12848__12850__12852__12854__12856)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078] :
( cType___24t(Vvar__0__R__24058)
=> ( c_24__type__24198___24t(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078,Vvar__1__req__24059)
=> ( cType___24t(Vvar__2__C__24064)
=> ( c_24__type__24248___24t(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078,Vvar__3__cadd__24065)
=> ( c_24__type__24298___24t(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078,Vvar__4__cmul__24070)
=> ( c_24__type__24340___24t(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078,Vvar__5__phi__24075)
=> ( c_24__type__24390___24t(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078,Vvar__6__cdiv__24078)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__24110__24115__24120__24125__24130__24135__24140__24145] :
( t(Vvar__var__var__var__var__var__var__var__7__a__24110__24115__24120__24125__24130__24135__24140__24145,Vvar__2__C__24064)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__24111__24116__24121__24126__24131__24136__24141__24146] :
( t(Vvar__var__var__var__var__var__var__var__8__b__24111__24116__24121__24126__24131__24136__24141__24146,Vvar__2__C__24064)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2424453___24a9(Vvar__0__R__24058,Vvar__1__req__24059,Vvar__2__C__24064,Vvar__3__cadd__24065,Vvar__4__cmul__24070,Vvar__5__phi__24075,Vvar__6__cdiv__24078,Vvar__var__var__var__var__var__var__var__7__a__24110__24115__24120__24125__24130__24135__24140__24145,Vvar__var__var__var__var__var__var__var__8__b__24111__24116__24121__24126__24131__24136__24141__24146) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__3__req__9831,Vvar__4__Cpow__9836,Vvar__5__Cp__phi__9837,Vvar__6__rpow__9840] :
( cType___24t(Vvar__0__R__9824)
=> ( t(Vvar__1__rI__9825,Vvar__0__R__9824)
=> ( c_24__type__9926___24t(Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__3__req__9831,Vvar__4__Cpow__9836,Vvar__5__Cp__phi__9837,Vvar__6__rpow__9840,Vvar__2__rmul__9826)
=> ( c_24__type__9970___24t(Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__3__req__9831,Vvar__4__Cpow__9836,Vvar__5__Cp__phi__9837,Vvar__6__rpow__9840,Vvar__3__req__9831)
=> ( cType___24t(Vvar__4__Cpow__9836)
=> ( c_24__type__10006___24t(Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__3__req__9831,Vvar__4__Cpow__9836,Vvar__5__Cp__phi__9837,Vvar__6__rpow__9840,Vvar__5__Cp__phi__9837)
=> ( c_24__type__10050___24t(Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__3__req__9831,Vvar__4__Cpow__9836,Vvar__5__Cp__phi__9837,Vvar__6__rpow__9840,Vvar__6__rpow__9840)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__3__req__9831,Vvar__4__Cpow__9836,Vvar__5__Cp__phi__9837,Vvar__6__rpow__9840)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__9868__9870__9872__9874__9876__9878__9880__9882] :
( t(Vvar__var__var__var__var__var__var__var__7__r__9868__9870__9872__9874__9876__9878__9880__9882,Vvar__0__R__9824)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__9869__9871__9873__9875__9877__9879__9881__9883] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__9869__9871__9873__9875__9877__9879__9881__9883)
=> p(happ(happ(Vvar__3__req__9831,happ(happ(Vvar__6__rpow__9840,Vvar__var__var__var__var__var__var__var__7__r__9868__9870__9872__9874__9876__9878__9880__9882),happ(Vvar__5__Cp__phi__9837,Vvar__var__var__var__var__var__var__var__8__n__9869__9871__9873__9875__9877__9879__9881__9883))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__9824,Vvar__1__rI__9825,Vvar__2__rmul__9826,Vvar__var__var__var__var__var__var__var__7__r__9868__9870__9872__9874__9876__9878__9880__9882,Vvar__var__var__var__var__var__var__var__8__n__9869__9871__9873__9875__9877__9879__9881__9883))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225] :
( cType___24t(Vvar__0__R__13211)
=> ( c_24__type__13316___24t(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225,Vvar__1__radd__13212)
=> ( c_24__type__13346___24t(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225,Vvar__2__rmul__13217)
=> ( c_24__type__13370___24t(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225,Vvar__3__ropp__13222)
=> ( c_24__type__13400___24t(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225,Vvar__4__req__13225)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13430___24a5(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__13211,c_24__type__13454___24a5(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225),Vvar__4__req__13225,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__13211,Vvar__0__R__13211,Vvar__4__req__13225,Vvar__4__req__13225)),Vvar__1__radd__13212)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13487___24a5(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__13211,c_24__type__13511___24a5(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225),Vvar__4__req__13225,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__13211,Vvar__0__R__13211,Vvar__4__req__13225,Vvar__4__req__13225)),Vvar__2__rmul__13217)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__13538___24a5(Vvar__0__R__13211,Vvar__1__radd__13212,Vvar__2__rmul__13217,Vvar__3__ropp__13222,Vvar__4__req__13225),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__13211,Vvar__0__R__13211,Vvar__4__req__13225,Vvar__4__req__13225),Vvar__3__ropp__13222)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX29683] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX29683)
=> ( VX29683 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__29684] :
( cType___24t(Vvar__0__R__29684)
& ? [Vvar__1__req__29685] :
( c_24__type__7284___24t(Vvar__0__R__29684,Vvar__1__req__29685)
& ? [Vvar__2__reqb__29690] :
( c_24__type__10937___24t(Vvar__0__R__29684,Vvar__2__reqb__29690)
& ! [Vvar__var__3__x__29696__29699] :
( t(Vvar__var__3__x__29696__29699,Vvar__0__R__29684)
=> ! [Vvar__var__4__y__29697__29700] :
( t(Vvar__var__4__y__29697__29700,Vvar__0__R__29684)
=> ( happ(happ(Vvar__2__reqb__29690,Vvar__var__3__x__29696__29699),Vvar__var__4__y__29697__29700) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__29685,Vvar__var__3__x__29696__29699),Vvar__var__4__y__29697__29700)) ) ) )
& VX29683 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__29684,Vvar__1__req__29685,Vvar__2__reqb__29690) ) ) )
| ? [Vvar__0__R__29702] :
( cType___24t(Vvar__0__R__29702)
& ? [Vvar__1__rO__29703] :
( t(Vvar__1__rO__29703,Vvar__0__R__29702)
& ? [Vvar__2__rI__29704] :
( t(Vvar__2__rI__29704,Vvar__0__R__29702)
& ? [Vvar__3__radd__29705] :
( c_24__type__7270___24t(Vvar__0__R__29702,Vvar__3__radd__29705)
& ? [Vvar__4__rmul__29710] :
( c_24__type__7270___24t(Vvar__0__R__29702,Vvar__4__rmul__29710)
& ? [Vvar__5__rsub__29715] :
( c_24__type__7270___24t(Vvar__0__R__29702,Vvar__5__rsub__29715)
& ? [Vvar__6__ropp__29720] :
( c_24__type__7279___24t(Vvar__0__R__29702,Vvar__6__ropp__29720)
& ? [Vvar__7__req__29723] :
( c_24__type__7284___24t(Vvar__0__R__29702,Vvar__7__req__29723)
& ? [Vvar__8__C__29728] :
( cType___24t(Vvar__8__C__29728)
& ? [Vvar__9__cO__29729] :
( t(Vvar__9__cO__29729,Vvar__8__C__29728)
& ? [Vvar__10__cI__29730] :
( t(Vvar__10__cI__29730,Vvar__8__C__29728)
& ? [Vvar__11__cadd__29731] :
( c_24__type__7294___24t(Vvar__0__R__29702,Vvar__8__C__29728,Vvar__11__cadd__29731)
& ? [Vvar__12__cmul__29736] :
( c_24__type__7294___24t(Vvar__0__R__29702,Vvar__8__C__29728,Vvar__12__cmul__29736)
& ? [Vvar__13__csub__29741] :
( c_24__type__7294___24t(Vvar__0__R__29702,Vvar__8__C__29728,Vvar__13__csub__29741)
& ? [Vvar__14__copp__29746] :
( c_24__type__7308___24t(Vvar__0__R__29702,Vvar__8__C__29728,Vvar__14__copp__29746)
& ? [Vvar__15__ceqb__29749] :
( c_24__type__7315___24t(Vvar__0__R__29702,Vvar__8__C__29728,Vvar__15__ceqb__29749)
& ? [Vvar__16__phi__29754] :
( c_24__type__7324___24t(Vvar__0__R__29702,Vvar__8__C__29728,Vvar__16__phi__29754)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__29702,Vvar__1__rO__29703,Vvar__2__rI__29704,Vvar__3__radd__29705,Vvar__4__rmul__29710,Vvar__5__rsub__29715,Vvar__6__ropp__29720,Vvar__7__req__29723,Vvar__8__C__29728,Vvar__9__cO__29729,Vvar__10__cI__29730,Vvar__11__cadd__29731,Vvar__12__cmul__29736,Vvar__13__csub__29741,Vvar__14__copp__29746,Vvar__15__ceqb__29749,Vvar__16__phi__29754)
& VX29683 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__29702,Vvar__1__rO__29703,Vvar__2__rI__29704,Vvar__3__radd__29705,Vvar__4__rmul__29710,Vvar__5__rsub__29715,Vvar__6__ropp__29720,Vvar__7__req__29723,Vvar__8__C__29728,Vvar__9__cO__29729,Vvar__10__cI__29730,Vvar__11__cadd__29731,Vvar__12__cmul__29736,Vvar__13__csub__29741,Vvar__14__copp__29746,Vvar__15__ceqb__29749,Vvar__16__phi__29754) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392] :
( cType___24t(Vvar__0__R__7340)
=> ( t(Vvar__1__rO__7341,Vvar__0__R__7340)
=> ( t(Vvar__2__rI__7342,Vvar__0__R__7340)
=> ( c_24__type__7736___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__3__radd__7343)
=> ( c_24__type__7949___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__4__rmul__7348)
=> ( c_24__type__8162___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__5__rsub__7353)
=> ( c_24__type__8357___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__6__ropp__7358)
=> ( c_24__type__8570___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__7__req__7361)
=> ( cType___24t(Vvar__8__C__7366)
=> ( t(Vvar__9__cO__7367,Vvar__8__C__7366)
=> ( t(Vvar__10__cI__7368,Vvar__8__C__7366)
=> ( c_24__type__8783___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__11__cadd__7369)
=> ( c_24__type__8996___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__12__cmul__7374)
=> ( c_24__type__9209___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__13__csub__7379)
=> ( c_24__type__9404___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__14__copp__7384)
=> ( c_24__type__9617___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__15__ceqb__7387)
=> ( c_24__type__9812___24t(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392,Vvar__16__phi__7392)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__7340,Vvar__1__rO__7341,Vvar__2__rI__7342,Vvar__3__radd__7343,Vvar__4__rmul__7348,Vvar__5__rsub__7353,Vvar__6__ropp__7358,Vvar__7__req__7361,Vvar__8__C__7366,Vvar__9__cO__7367,Vvar__10__cI__7368,Vvar__11__cadd__7369,Vvar__12__cmul__7374,Vvar__13__csub__7379,Vvar__14__copp__7384,Vvar__15__ceqb__7387,Vvar__16__phi__7392)
=> ( p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,Vvar__9__cO__7367)),Vvar__1__rO__7341))
& p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,Vvar__10__cI__7368)),Vvar__2__rI__7342))
& ! [Vvar__var__var__var__var__var__var__19__x__7454__7456__7478__7480__7482__7484__7486] :
( t(Vvar__var__var__var__var__var__var__19__x__7454__7456__7478__7480__7482__7484__7486,Vvar__8__C__7366)
=> ! [Vvar__var__var__var__var__var__var__20__y__7455__7457__7479__7481__7483__7485__7487] :
( t(Vvar__var__var__var__var__var__var__20__y__7455__7457__7479__7481__7483__7485__7487,Vvar__8__C__7366)
=> p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,happ(happ(Vvar__11__cadd__7369,Vvar__var__var__var__var__var__var__19__x__7454__7456__7478__7480__7482__7484__7486),Vvar__var__var__var__var__var__var__20__y__7455__7457__7479__7481__7483__7485__7487))),happ(happ(Vvar__3__radd__7343,happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__19__x__7454__7456__7478__7480__7482__7484__7486)),happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__20__y__7455__7457__7479__7481__7483__7485__7487)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__7459__7461__7488__7490__7492__7494__7496] :
( t(Vvar__var__var__var__var__var__var__20__x__7459__7461__7488__7490__7492__7494__7496,Vvar__8__C__7366)
=> ! [Vvar__var__var__var__var__var__var__21__y__7460__7462__7489__7491__7493__7495__7497] :
( t(Vvar__var__var__var__var__var__var__21__y__7460__7462__7489__7491__7493__7495__7497,Vvar__8__C__7366)
=> p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,happ(happ(Vvar__13__csub__7379,Vvar__var__var__var__var__var__var__20__x__7459__7461__7488__7490__7492__7494__7496),Vvar__var__var__var__var__var__var__21__y__7460__7462__7489__7491__7493__7495__7497))),happ(happ(Vvar__5__rsub__7353,happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__20__x__7459__7461__7488__7490__7492__7494__7496)),happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__21__y__7460__7462__7489__7491__7493__7495__7497)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__7464__7466__7498__7500__7502__7504__7506] :
( t(Vvar__var__var__var__var__var__var__21__x__7464__7466__7498__7500__7502__7504__7506,Vvar__8__C__7366)
=> ! [Vvar__var__var__var__var__var__var__22__y__7465__7467__7499__7501__7503__7505__7507] :
( t(Vvar__var__var__var__var__var__var__22__y__7465__7467__7499__7501__7503__7505__7507,Vvar__8__C__7366)
=> p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,happ(happ(Vvar__12__cmul__7374,Vvar__var__var__var__var__var__var__21__x__7464__7466__7498__7500__7502__7504__7506),Vvar__var__var__var__var__var__var__22__y__7465__7467__7499__7501__7503__7505__7507))),happ(happ(Vvar__4__rmul__7348,happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__21__x__7464__7466__7498__7500__7502__7504__7506)),happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__22__y__7465__7467__7499__7501__7503__7505__7507)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__7469__7470__7508__7509__7510__7511__7512] :
( t(Vvar__var__var__var__var__var__var__22__x__7469__7470__7508__7509__7510__7511__7512,Vvar__8__C__7366)
=> p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,happ(Vvar__14__copp__7384,Vvar__var__var__var__var__var__var__22__x__7469__7470__7508__7509__7510__7511__7512))),happ(Vvar__6__ropp__7358,happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__var__22__x__7469__7470__7508__7509__7510__7511__7512)))) )
& ! [Vvar__var__var__var__var__var__23__x__7472__7475__7513__7516__7519__7522] :
( t(Vvar__var__var__var__var__var__23__x__7472__7475__7513__7516__7519__7522,Vvar__8__C__7366)
=> ! [Vvar__var__var__var__var__var__24__y__7473__7476__7514__7517__7520__7523] :
( t(Vvar__var__var__var__var__var__24__y__7473__7476__7514__7517__7520__7523,Vvar__8__C__7366)
=> ( happ(happ(Vvar__15__ceqb__7387,Vvar__var__var__var__var__var__23__x__7472__7475__7513__7516__7519__7522),Vvar__var__var__var__var__var__24__y__7473__7476__7514__7517__7520__7523) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__7361,happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__23__x__7472__7475__7513__7516__7519__7522)),happ(Vvar__16__phi__7392,Vvar__var__var__var__var__var__24__y__7473__7476__7514__7517__7520__7523))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979] :
( cType___24t(Vvar__0__R__26958)
=> ( t(Vvar__1__rO__26959,Vvar__0__R__26958)
=> ( t(Vvar__2__rI__26960,Vvar__0__R__26958)
=> ( c_24__type__27182___24t(Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979,Vvar__3__radd__26961)
=> ( c_24__type__27245___24t(Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979,Vvar__4__rmul__26966)
=> ( c_24__type__27308___24t(Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979,Vvar__5__rsub__26971)
=> ( c_24__type__27362___24t(Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979,Vvar__6__ropp__26976)
=> ( c_24__type__27425___24t(Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979,Vvar__7__req__26979)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__26958,Vvar__1__rO__26959,Vvar__2__rI__26960,Vvar__3__radd__26961,Vvar__4__rmul__26966,Vvar__5__rsub__26971,Vvar__6__ropp__26976,Vvar__7__req__26979)
=> ( ! [Vvar__var__var__var__var__var__8__x__27012__27013__27056__27057__27058__27059] :
( t(Vvar__var__var__var__var__var__8__x__27012__27013__27056__27057__27058__27059,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__3__radd__26961,Vvar__1__rO__26959),Vvar__var__var__var__var__var__8__x__27012__27013__27056__27057__27058__27059)),Vvar__var__var__var__var__var__8__x__27012__27013__27056__27057__27058__27059)) )
& ! [Vvar__var__var__var__var__9__x__27015__27017__27060__27062__27064] :
( t(Vvar__var__var__var__var__9__x__27015__27017__27060__27062__27064,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__10__y__27016__27018__27061__27063__27065] :
( t(Vvar__var__var__var__var__10__y__27016__27018__27061__27063__27065,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__9__x__27015__27017__27060__27062__27064),Vvar__var__var__var__var__10__y__27016__27018__27061__27063__27065)),happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__10__y__27016__27018__27061__27063__27065),Vvar__var__var__var__var__9__x__27015__27017__27060__27062__27064))) ) )
& ! [Vvar__var__var__var__var__10__x__27020__27023__27066__27069__27072] :
( t(Vvar__var__var__var__var__10__x__27020__27023__27066__27069__27072,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__11__y__27021__27024__27067__27070__27073] :
( t(Vvar__var__var__var__var__11__y__27021__27024__27067__27070__27073,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__12__z__27022__27025__27068__27071__27074] :
( t(Vvar__var__var__var__var__12__z__27022__27025__27068__27071__27074,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__10__x__27020__27023__27066__27069__27072),happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__11__y__27021__27024__27067__27070__27073),Vvar__var__var__var__var__12__z__27022__27025__27068__27071__27074))),happ(happ(Vvar__3__radd__26961,happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__10__x__27020__27023__27066__27069__27072),Vvar__var__var__var__var__11__y__27021__27024__27067__27070__27073)),Vvar__var__var__var__var__12__z__27022__27025__27068__27071__27074))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__27027__27028__27075__27076__27077__27078] :
( t(Vvar__var__var__var__var__var__11__x__27027__27028__27075__27076__27077__27078,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__4__rmul__26966,Vvar__2__rI__26960),Vvar__var__var__var__var__var__11__x__27027__27028__27075__27076__27077__27078)),Vvar__var__var__var__var__var__11__x__27027__27028__27075__27076__27077__27078)) )
& ! [Vvar__var__var__var__var__12__x__27030__27032__27079__27081__27083] :
( t(Vvar__var__var__var__var__12__x__27030__27032__27079__27081__27083,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__13__y__27031__27033__27080__27082__27084] :
( t(Vvar__var__var__var__var__13__y__27031__27033__27080__27082__27084,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__12__x__27030__27032__27079__27081__27083),Vvar__var__var__var__var__13__y__27031__27033__27080__27082__27084)),happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__13__y__27031__27033__27080__27082__27084),Vvar__var__var__var__var__12__x__27030__27032__27079__27081__27083))) ) )
& ! [Vvar__var__var__var__var__13__x__27035__27038__27085__27088__27091] :
( t(Vvar__var__var__var__var__13__x__27035__27038__27085__27088__27091,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__14__y__27036__27039__27086__27089__27092] :
( t(Vvar__var__var__var__var__14__y__27036__27039__27086__27089__27092,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__15__z__27037__27040__27087__27090__27093] :
( t(Vvar__var__var__var__var__15__z__27037__27040__27087__27090__27093,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__13__x__27035__27038__27085__27088__27091),happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__14__y__27036__27039__27086__27089__27092),Vvar__var__var__var__var__15__z__27037__27040__27087__27090__27093))),happ(happ(Vvar__4__rmul__26966,happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__13__x__27035__27038__27085__27088__27091),Vvar__var__var__var__var__14__y__27036__27039__27086__27089__27092)),Vvar__var__var__var__var__15__z__27037__27040__27087__27090__27093))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__27042__27045__27094__27097__27100__27103] :
( t(Vvar__var__var__var__var__var__14__x__27042__27045__27094__27097__27100__27103,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__var__15__y__27043__27046__27095__27098__27101__27104] :
( t(Vvar__var__var__var__var__var__15__y__27043__27046__27095__27098__27101__27104,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__var__16__z__27044__27047__27096__27099__27102__27105] :
( t(Vvar__var__var__var__var__var__16__z__27044__27047__27096__27099__27102__27105,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__4__rmul__26966,happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__var__14__x__27042__27045__27094__27097__27100__27103),Vvar__var__var__var__var__var__15__y__27043__27046__27095__27098__27101__27104)),Vvar__var__var__var__var__var__16__z__27044__27047__27096__27099__27102__27105)),happ(happ(Vvar__3__radd__26961,happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__var__14__x__27042__27045__27094__27097__27100__27103),Vvar__var__var__var__var__var__16__z__27044__27047__27096__27099__27102__27105)),happ(happ(Vvar__4__rmul__26966,Vvar__var__var__var__var__var__15__y__27043__27046__27095__27098__27101__27104),Vvar__var__var__var__var__var__16__z__27044__27047__27096__27099__27102__27105)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__27049__27051__27106__27108__27110__27112__27114] :
( t(Vvar__var__var__var__var__var__var__15__x__27049__27051__27106__27108__27110__27112__27114,Vvar__0__R__26958)
=> ! [Vvar__var__var__var__var__var__var__16__y__27050__27052__27107__27109__27111__27113__27115] :
( t(Vvar__var__var__var__var__var__var__16__y__27050__27052__27107__27109__27111__27113__27115,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__5__rsub__26971,Vvar__var__var__var__var__var__var__15__x__27049__27051__27106__27108__27110__27112__27114),Vvar__var__var__var__var__var__var__16__y__27050__27052__27107__27109__27111__27113__27115)),happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__var__var__15__x__27049__27051__27106__27108__27110__27112__27114),happ(Vvar__6__ropp__26976,Vvar__var__var__var__var__var__var__16__y__27050__27052__27107__27109__27111__27113__27115)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__27054__27055__27116__27117__27118__27119__27120] :
( t(Vvar__var__var__var__var__var__var__16__x__27054__27055__27116__27117__27118__27119__27120,Vvar__0__R__26958)
=> p(happ(happ(Vvar__7__req__26979,happ(happ(Vvar__3__radd__26961,Vvar__var__var__var__var__var__var__16__x__27054__27055__27116__27117__27118__27119__27120),happ(Vvar__6__ropp__26976,Vvar__var__var__var__var__var__var__16__x__27054__27055__27116__27117__27118__27119__27120))),Vvar__1__rO__26959)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055] :
( cType___24t(Vvar__0__R__31019)
=> ( t(Vvar__1__rO__31020,Vvar__0__R__31019)
=> ( t(Vvar__2__rI__31021,Vvar__0__R__31019)
=> ( c_24__type__31272___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__3__radd__31022)
=> ( c_24__type__31397___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__4__rmul__31027)
=> ( c_24__type__31522___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__5__req__31032)
=> ( cType___24t(Vvar__6__C__31037)
=> ( t(Vvar__7__cO__31038,Vvar__6__C__31037)
=> ( t(Vvar__8__cI__31039,Vvar__6__C__31037)
=> ( c_24__type__31647___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__9__cadd__31040)
=> ( c_24__type__31772___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__10__cmul__31045)
=> ( c_24__type__31897___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__11__ceqb__31050)
=> ( c_24__type__32008___24t(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055,Vvar__12__phi__31055)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__31019,Vvar__1__rO__31020,Vvar__2__rI__31021,Vvar__3__radd__31022,Vvar__4__rmul__31027,Vvar__5__req__31032,Vvar__6__C__31037,Vvar__7__cO__31038,Vvar__8__cI__31039,Vvar__9__cadd__31040,Vvar__10__cmul__31045,Vvar__11__ceqb__31050,Vvar__12__phi__31055)
=> ( p(happ(happ(Vvar__5__req__31032,happ(Vvar__12__phi__31055,Vvar__7__cO__31038)),Vvar__1__rO__31020))
& p(happ(happ(Vvar__5__req__31032,happ(Vvar__12__phi__31055,Vvar__8__cI__31039)),Vvar__2__rI__31021))
& ! [Vvar__var__var__var__var__var__var__15__x__31101__31103__31117__31119__31121__31123__31125] :
( t(Vvar__var__var__var__var__var__var__15__x__31101__31103__31117__31119__31121__31123__31125,Vvar__6__C__31037)
=> ! [Vvar__var__var__var__var__var__var__16__y__31102__31104__31118__31120__31122__31124__31126] :
( t(Vvar__var__var__var__var__var__var__16__y__31102__31104__31118__31120__31122__31124__31126,Vvar__6__C__31037)
=> p(happ(happ(Vvar__5__req__31032,happ(Vvar__12__phi__31055,happ(happ(Vvar__9__cadd__31040,Vvar__var__var__var__var__var__var__15__x__31101__31103__31117__31119__31121__31123__31125),Vvar__var__var__var__var__var__var__16__y__31102__31104__31118__31120__31122__31124__31126))),happ(happ(Vvar__3__radd__31022,happ(Vvar__12__phi__31055,Vvar__var__var__var__var__var__var__15__x__31101__31103__31117__31119__31121__31123__31125)),happ(Vvar__12__phi__31055,Vvar__var__var__var__var__var__var__16__y__31102__31104__31118__31120__31122__31124__31126)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__31106__31108__31127__31129__31131__31133__31135] :
( t(Vvar__var__var__var__var__var__var__16__x__31106__31108__31127__31129__31131__31133__31135,Vvar__6__C__31037)
=> ! [Vvar__var__var__var__var__var__var__17__y__31107__31109__31128__31130__31132__31134__31136] :
( t(Vvar__var__var__var__var__var__var__17__y__31107__31109__31128__31130__31132__31134__31136,Vvar__6__C__31037)
=> p(happ(happ(Vvar__5__req__31032,happ(Vvar__12__phi__31055,happ(happ(Vvar__10__cmul__31045,Vvar__var__var__var__var__var__var__16__x__31106__31108__31127__31129__31131__31133__31135),Vvar__var__var__var__var__var__var__17__y__31107__31109__31128__31130__31132__31134__31136))),happ(happ(Vvar__4__rmul__31027,happ(Vvar__12__phi__31055,Vvar__var__var__var__var__var__var__16__x__31106__31108__31127__31129__31131__31133__31135)),happ(Vvar__12__phi__31055,Vvar__var__var__var__var__var__var__17__y__31107__31109__31128__31130__31132__31134__31136)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__31111__31114__31137__31140__31143__31146] :
( t(Vvar__var__var__var__var__var__17__x__31111__31114__31137__31140__31143__31146,Vvar__6__C__31037)
=> ! [Vvar__var__var__var__var__var__18__y__31112__31115__31138__31141__31144__31147] :
( t(Vvar__var__var__var__var__var__18__y__31112__31115__31138__31141__31144__31147,Vvar__6__C__31037)
=> ( happ(happ(Vvar__11__ceqb__31050,Vvar__var__var__var__var__var__17__x__31111__31114__31137__31140__31143__31146),Vvar__var__var__var__var__var__18__y__31112__31115__31138__31141__31144__31147) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__31032,happ(Vvar__12__phi__31055,Vvar__var__var__var__var__var__17__x__31111__31114__31137__31140__31143__31146)),happ(Vvar__12__phi__31055,Vvar__var__var__var__var__var__18__y__31112__31115__31138__31141__31144__31147))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__29419,Vvar__1__rO__29420,Vvar__2__rI__29421,Vvar__3__radd__29422,Vvar__4__rmul__29427,Vvar__5__req__29432] :
( cType___24t(Vvar__0__R__29419)
=> ( t(Vvar__1__rO__29420,Vvar__0__R__29419)
=> ( t(Vvar__2__rI__29421,Vvar__0__R__29419)
=> ( c_24__type__29587___24t(Vvar__0__R__29419,Vvar__1__rO__29420,Vvar__2__rI__29421,Vvar__3__radd__29422,Vvar__4__rmul__29427,Vvar__5__req__29432,Vvar__3__radd__29422)
=> ( c_24__type__29626___24t(Vvar__0__R__29419,Vvar__1__rO__29420,Vvar__2__rI__29421,Vvar__3__radd__29422,Vvar__4__rmul__29427,Vvar__5__req__29432,Vvar__4__rmul__29427)
=> ( c_24__type__29665___24t(Vvar__0__R__29419,Vvar__1__rO__29420,Vvar__2__rI__29421,Vvar__3__radd__29422,Vvar__4__rmul__29427,Vvar__5__req__29432,Vvar__5__req__29432)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__29419,Vvar__1__rO__29420,Vvar__2__rI__29421,Vvar__3__radd__29422,Vvar__4__rmul__29427,Vvar__5__req__29432)
=> ( ! [Vvar__var__var__var__var__var__6__n__29457__29458__29496__29497__29498__29499] :
( t(Vvar__var__var__var__var__var__6__n__29457__29458__29496__29497__29498__29499,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__3__radd__29422,Vvar__1__rO__29420),Vvar__var__var__var__var__var__6__n__29457__29458__29496__29497__29498__29499)),Vvar__var__var__var__var__var__6__n__29457__29458__29496__29497__29498__29499)) )
& ! [Vvar__var__var__var__var__7__n__29460__29462__29500__29502__29504] :
( t(Vvar__var__var__var__var__7__n__29460__29462__29500__29502__29504,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__8__m__29461__29463__29501__29503__29505] :
( t(Vvar__var__var__var__var__8__m__29461__29463__29501__29503__29505,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__3__radd__29422,Vvar__var__var__var__var__7__n__29460__29462__29500__29502__29504),Vvar__var__var__var__var__8__m__29461__29463__29501__29503__29505)),happ(happ(Vvar__3__radd__29422,Vvar__var__var__var__var__8__m__29461__29463__29501__29503__29505),Vvar__var__var__var__var__7__n__29460__29462__29500__29502__29504))) ) )
& ! [Vvar__var__var__var__var__8__n__29465__29468__29506__29509__29512] :
( t(Vvar__var__var__var__var__8__n__29465__29468__29506__29509__29512,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__9__m__29466__29469__29507__29510__29513] :
( t(Vvar__var__var__var__var__9__m__29466__29469__29507__29510__29513,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__10__p__29467__29470__29508__29511__29514] :
( t(Vvar__var__var__var__var__10__p__29467__29470__29508__29511__29514,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__3__radd__29422,Vvar__var__var__var__var__8__n__29465__29468__29506__29509__29512),happ(happ(Vvar__3__radd__29422,Vvar__var__var__var__var__9__m__29466__29469__29507__29510__29513),Vvar__var__var__var__var__10__p__29467__29470__29508__29511__29514))),happ(happ(Vvar__3__radd__29422,happ(happ(Vvar__3__radd__29422,Vvar__var__var__var__var__8__n__29465__29468__29506__29509__29512),Vvar__var__var__var__var__9__m__29466__29469__29507__29510__29513)),Vvar__var__var__var__var__10__p__29467__29470__29508__29511__29514))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__29472__29473__29515__29516__29517__29518] :
( t(Vvar__var__var__var__var__var__9__n__29472__29473__29515__29516__29517__29518,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__4__rmul__29427,Vvar__2__rI__29421),Vvar__var__var__var__var__var__9__n__29472__29473__29515__29516__29517__29518)),Vvar__var__var__var__var__var__9__n__29472__29473__29515__29516__29517__29518)) )
& ! [Vvar__var__var__var__var__var__10__n__29475__29476__29519__29520__29521__29522] :
( t(Vvar__var__var__var__var__var__10__n__29475__29476__29519__29520__29521__29522,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__4__rmul__29427,Vvar__1__rO__29420),Vvar__var__var__var__var__var__10__n__29475__29476__29519__29520__29521__29522)),Vvar__1__rO__29420)) )
& ! [Vvar__var__var__var__var__11__n__29478__29480__29523__29525__29527] :
( t(Vvar__var__var__var__var__11__n__29478__29480__29523__29525__29527,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__12__m__29479__29481__29524__29526__29528] :
( t(Vvar__var__var__var__var__12__m__29479__29481__29524__29526__29528,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__11__n__29478__29480__29523__29525__29527),Vvar__var__var__var__var__12__m__29479__29481__29524__29526__29528)),happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__12__m__29479__29481__29524__29526__29528),Vvar__var__var__var__var__11__n__29478__29480__29523__29525__29527))) ) )
& ! [Vvar__var__var__var__var__12__n__29483__29486__29529__29532__29535] :
( t(Vvar__var__var__var__var__12__n__29483__29486__29529__29532__29535,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__13__m__29484__29487__29530__29533__29536] :
( t(Vvar__var__var__var__var__13__m__29484__29487__29530__29533__29536,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__14__p__29485__29488__29531__29534__29537] :
( t(Vvar__var__var__var__var__14__p__29485__29488__29531__29534__29537,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__12__n__29483__29486__29529__29532__29535),happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__13__m__29484__29487__29530__29533__29536),Vvar__var__var__var__var__14__p__29485__29488__29531__29534__29537))),happ(happ(Vvar__4__rmul__29427,happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__12__n__29483__29486__29529__29532__29535),Vvar__var__var__var__var__13__m__29484__29487__29530__29533__29536)),Vvar__var__var__var__var__14__p__29485__29488__29531__29534__29537))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__29490__29493__29538__29541__29544__29547] :
( t(Vvar__var__var__var__var__var__13__n__29490__29493__29538__29541__29544__29547,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__var__14__m__29491__29494__29539__29542__29545__29548] :
( t(Vvar__var__var__var__var__var__14__m__29491__29494__29539__29542__29545__29548,Vvar__0__R__29419)
=> ! [Vvar__var__var__var__var__var__15__p__29492__29495__29540__29543__29546__29549] :
( t(Vvar__var__var__var__var__var__15__p__29492__29495__29540__29543__29546__29549,Vvar__0__R__29419)
=> p(happ(happ(Vvar__5__req__29432,happ(happ(Vvar__4__rmul__29427,happ(happ(Vvar__3__radd__29422,Vvar__var__var__var__var__var__13__n__29490__29493__29538__29541__29544__29547),Vvar__var__var__var__var__var__14__m__29491__29494__29539__29542__29545__29548)),Vvar__var__var__var__var__var__15__p__29492__29495__29540__29543__29546__29549)),happ(happ(Vvar__3__radd__29422,happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__var__13__n__29490__29493__29538__29541__29544__29547),Vvar__var__var__var__var__var__15__p__29492__29495__29540__29543__29546__29549)),happ(happ(Vvar__4__rmul__29427,Vvar__var__var__var__var__var__14__m__29491__29494__29539__29542__29545__29548),Vvar__var__var__var__var__var__15__p__29492__29495__29540__29543__29546__29549)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__34574,Vvar__1__copp__34575,Vvar__2__ceqb__34578,Vvar__3__get__sign__34583] :
( cType___24t(Vvar__0__C__34574)
=> ( c_24__type__34630___24t(Vvar__0__C__34574,Vvar__1__copp__34575,Vvar__2__ceqb__34578,Vvar__3__get__sign__34583,Vvar__1__copp__34575)
=> ( c_24__type__34649___24t(Vvar__0__C__34574,Vvar__1__copp__34575,Vvar__2__ceqb__34578,Vvar__3__get__sign__34583,Vvar__2__ceqb__34578)
=> ( c_24__type__34663___24t(Vvar__0__C__34574,Vvar__1__copp__34575,Vvar__2__ceqb__34578,Vvar__3__get__sign__34583,Vvar__3__get__sign__34583)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__34574,Vvar__1__copp__34575,Vvar__2__ceqb__34578,Vvar__3__get__sign__34583)
=> ( ! [Vvar__var__var__var__var__var__4__c__34600__34603__34606__34609__34612__34615] :
( t(Vvar__var__var__var__var__var__4__c__34600__34603__34606__34609__34612__34615,Vvar__0__C__34574)
=> ! [Vvar__var__var__var__var__var__5__c_27__34601__34604__34607__34610__34613__34616] :
( t(Vvar__var__var__var__var__var__5__c_27__34601__34604__34607__34610__34613__34616,Vvar__0__C__34574)
=> ( happ(Vvar__3__get__sign__34583,Vvar__var__var__var__var__var__4__c__34600__34603__34606__34609__34612__34615) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__34574,Vvar__var__var__var__var__var__5__c_27__34601__34604__34607__34610__34613__34616)
=> happ(happ(Vvar__2__ceqb__34578,Vvar__var__var__var__var__var__4__c__34600__34603__34606__34609__34612__34615),happ(Vvar__1__copp__34575,Vvar__var__var__var__var__var__5__c_27__34601__34604__34607__34610__34613__34616)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723] :
( cType___24t(Vvar__0__R__23712)
=> ( c_24__type__23798___24t(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723,Vvar__1__radd__23713)
=> ( c_24__type__23821___24t(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723,Vvar__2__rmul__23718)
=> ( c_24__type__23844___24t(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723,Vvar__3__req__23723)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23867___24a4(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23712,c_24__type__23885___24a4(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723),Vvar__3__req__23723,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23712,Vvar__0__R__23712,Vvar__3__req__23723,Vvar__3__req__23723)),Vvar__1__radd__23713)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23911___24a4(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23712,c_24__type__23929___24a4(Vvar__0__R__23712,Vvar__1__radd__23713,Vvar__2__rmul__23718,Vvar__3__req__23723),Vvar__3__req__23723,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23712,Vvar__0__R__23712,Vvar__3__req__23723,Vvar__3__req__23723)),Vvar__2__rmul__23718)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX29166] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX29166)
=> ( VX29166 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX29166 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.mixin_of',axiom,
! [Vvar__0__T__26002,VX26003] :
( cType___24t(Vvar__0__T__26002)
=> ( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__T__26002,VX26003)
=> ? [Vvar__1__op__26005] :
( c_24__type__10937___24t(Vvar__0__T__26002,Vvar__1__op__26005)
& ? [Vvar__2___24Anonymous__26010] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(Vvar__0__T__26002,Vvar__1__op__26005,Vvar__2___24Anonymous__26010)
& VX26003 = chahn_2eHahnBase_2eEquality_2eMixin___24a3(Vvar__0__T__26002,Vvar__1__op__26005,Vvar__2___24Anonymous__26010) ) ) ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.type',axiom,
! [VX26044] :
( chahn_2eHahnBase_2eEquality_2etype___24t(VX26044)
=> ? [Vvar__0__sort__26045] :
( cType___24t(Vvar__0__sort__26045)
& ? [Vvar__1___24Anonymous__26046] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__26045,Vvar__1___24Anonymous__26046)
& ? [Vvar__2___24Anonymous__26047] :
( cType___24t(Vvar__2___24Anonymous__26047)
& VX26044 = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__26045,Vvar__1___24Anonymous__26046,Vvar__2___24Anonymous__26047) ) ) ) ) ).
fof('$_lam_19996',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__19996___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_20004',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20004___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_20012',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20012___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_20020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__20020___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_26198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__26198___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_30905',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__30905___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_30913',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__30913___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_32566',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__32566___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_35184',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__35184___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_35255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__35255___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35256] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35256)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35256)
& c_24__lam__35255___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__35256) ) ) ) ).
fof('$_lam_35262',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__35262___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__35263] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35263)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35263)
& c_24__lam__35262___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__35263) ) ) ) ).
fof('$_lam_35266',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__35266___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__35267] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35267)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35267)
& c_24__lam__35266___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_prop_30589',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__S__30567,Vvar__1__x__30568,Vvar__2__y__30569] :
( p(c_24__prop__30589___24a4(Vvar__0___24Anonymous__30565,Vvar__0__S__30567,Vvar__1__x__30568,Vvar__2__y__30569))
<=> Vvar__1__x__30568 = Vvar__2__y__30569 ) ).
fof('$_prop_30590',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__x__30570,Vvar__1__y__30571] :
( p(c_24__prop__30590___24a3(Vvar__0___24Anonymous__30565,Vvar__0__x__30570,Vvar__1__y__30571))
<=> Vvar__0__x__30570 = Vvar__1__y__30571 ) ).
fof('$_prop_30591',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__x__30572,Vvar__1__s__30573] :
( p(c_24__prop__30591___24a3(Vvar__0___24Anonymous__30565,Vvar__0__x__30572,Vvar__1__s__30573))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__30572,Vvar__1__s__30573) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_30592',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__P__30574,Vvar__1__Q__30575] :
( p(c_24__prop__30592___24a3(Vvar__0___24Anonymous__30565,Vvar__0__P__30574,Vvar__1__Q__30575))
<=> ( p(Vvar__0__P__30574)
& p(Vvar__1__Q__30575) ) ) ).
fof('$_prop_30593',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__P__30578,Vvar__1__Q__30579] :
( p(c_24__prop__30593___24a3(Vvar__0___24Anonymous__30565,Vvar__0__P__30578,Vvar__1__Q__30579))
<=> ( p(Vvar__0__P__30578)
| p(Vvar__1__Q__30579) ) ) ).
fof('$_prop_30594',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__P__30582,Vvar__1__Q__30583] :
( p(c_24__prop__30594___24a3(Vvar__0___24Anonymous__30565,Vvar__0__P__30582,Vvar__1__Q__30583))
<=> ( p(Vvar__0__P__30582)
=> p(Vvar__1__Q__30583) ) ) ).
fof('$_prop_30595',axiom,
! [Vvar__0___24Anonymous__30565,Vvar__0__P__30587] :
( p(c_24__prop__30595___24a2(Vvar__0___24Anonymous__30565,Vvar__0__P__30587))
<=> ~ p(Vvar__0__P__30587) ) ).
fof('$_prop_30609',axiom,
! [Vvar__0___24Anonymous__30596,Vvar__0__s__30600] :
( p(c_24__prop__30609___24a2(Vvar__0___24Anonymous__30596,Vvar__0__s__30600))
<=> ! [Vvar__1__a__30601] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__30601)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__30601,Vvar__0__s__30600) ) ) ).
fof('$_prop_30610',axiom,
! [Vvar__0___24Anonymous__30596,Vvar__0__s1__30602,Vvar__1__s2__30603] :
( p(c_24__prop__30610___24a3(Vvar__0___24Anonymous__30596,Vvar__0__s1__30602,Vvar__1__s2__30603))
<=> ! [Vvar__2__a__30604] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__30604)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30604,Vvar__0__s1__30602)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30604,Vvar__1__s2__30603) ) ) ) ).
fof('$_prop_30611',axiom,
! [Vvar__0___24Anonymous__30596,Vvar__0__s1__30606,Vvar__1__s2__30607] :
( p(c_24__prop__30611___24a3(Vvar__0___24Anonymous__30596,Vvar__0__s1__30606,Vvar__1__s2__30607))
<=> ! [Vvar__2__a__30608] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__30608)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30608,Vvar__0__s1__30606)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__30608,Vvar__1__s2__30607) ) ) ) ).
fof('$_prop_32593',axiom,
! [V1__A] :
( p(c_24__prop__32593___24a1(V1__A))
<=> ( p(V1__A)
=> p(V1__A) ) ) ).
fof('$_prop_32709',axiom,
! [V7__A] :
( p(c_24__prop__32709___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_35346',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__35346___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_type_10006',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10007] :
( c_24__type__10006___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10007)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__10007,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_10050',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10051] :
( c_24__type__10050___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__10051)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__10051,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_10094',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10095] :
( c_24__type__10094___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__10095)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__10095,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_10119',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10120] :
( c_24__type__10119___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10120)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10120,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10123',axiom,
! [Vvar__10124] :
( c_24__type__10123___24t(Vvar__10124)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10124,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10141',axiom,
! [Vvar__10142] :
( c_24__type__10141___24t(Vvar__10142)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___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__10142,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_10401',axiom,
! [Vvar__10402] :
( c_24__type__10401___24t(Vvar__10402)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10402,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10404',axiom,
! [Vvar__10405] :
( c_24__type__10404___24t(Vvar__10405)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__10405,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10408',axiom,
! [Vvar__10409] :
( c_24__type__10408___24t(Vvar__10409)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__10404___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10404___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10409,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10411',axiom,
! [Vvar__10412] :
( c_24__type__10411___24t(Vvar__10412)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__10412,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10432',axiom,
! [Vvar__10433] :
( c_24__type__10432___24t(Vvar__10433)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10433,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10449',axiom,
! [Vvar__10450] :
( c_24__type__10449___24t(Vvar__10450)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__10450,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10455',axiom,
! [Vvar__10456] :
( c_24__type__10455___24t(Vvar__10456)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10456,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10461',axiom,
! [Vvar__10462] :
( c_24__type__10461___24t(Vvar__10462)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__10462,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10464',axiom,
! [Vvar__10465] :
( c_24__type__10464___24t(Vvar__10465)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__10466___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__10465,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10466',axiom,
! [Vvar__10467] :
( c_24__type__10466___24t(Vvar__10467)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10467,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10495',axiom,
! [Vvar__10496] :
( c_24__type__10495___24t(Vvar__10496)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10496,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10511',axiom,
! [Vvar__10512] :
( c_24__type__10511___24t(Vvar__10512)
<=> ! [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__10512,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_10521',axiom,
! [Vvar__10522] :
( c_24__type__10521___24t(Vvar__10522)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__10522,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10533',axiom,
! [Vvar__10534] :
( c_24__type__10533___24t(Vvar__10534)
<=> ! [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__10534,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_10937',axiom,
! [Vv__CANONICAL__0,Vvar__10938] :
( c_24__type__10937___24t(Vv__CANONICAL__0,Vvar__10938)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10938,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_11093',axiom,
! [Vvar__11094] :
( c_24__type__11093___24t(Vvar__11094)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__7279___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__11094,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_11146',axiom,
! [Vvar__11147] :
( c_24__type__11146___24t(Vvar__11147)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__11147,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11583',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__11584] :
( c_24__type__11583___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__11584)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11584,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__11685] :
( c_24__type__11684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__11685)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11685,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11785',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__11786] :
( c_24__type__11785___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__11786)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__11786,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_11875',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__11876] :
( c_24__type__11875___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__11876)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__11876,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_11976',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__11977] :
( c_24__type__11976___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__11977)
<=> ! [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__11977,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_12077',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12078] :
( c_24__type__12077___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__12078)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12078,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_12178',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__12179] :
( c_24__type__12178___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__12179)
<=> ! [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__12179,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_12258',axiom,
! [Vvar__12259] :
( c_24__type__12258___24t(Vvar__12259)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12259,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12264',axiom,
! [Vvar__12265] :
( c_24__type__12264___24t(Vvar__12265)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__12265,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12664',axiom,
! [Vvar__12665] :
( c_24__type__12664___24t(Vvar__12665)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__12665,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12918',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__12919] :
( c_24__type__12918___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__12919)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12919,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12981',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12982] :
( c_24__type__12981___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12982)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12982,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13',axiom,
! [Vvar__14] :
( c_24__type__13___24t(Vvar__14)
<=> ! [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__14,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13044',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13045] :
( c_24__type__13044___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13045)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13045,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13098',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__13099] :
( c_24__type__13098___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__13099)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__13099,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_13161',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13162] :
( c_24__type__13161___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__13162)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13162,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_13316',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13317] :
( c_24__type__13316___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13317)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13317,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13347] :
( c_24__type__13346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13347)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13347,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13370',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13371] :
( c_24__type__13370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13371)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13371,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13401] :
( c_24__type__13400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13401)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13401,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_13430',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13431] :
( c_24__type__13430___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13431)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13431,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13454',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13455] :
( c_24__type__13454___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13455)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13455,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13488] :
( c_24__type__13487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13488)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13488,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13511',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13512] :
( c_24__type__13511___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13512)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13512,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13538',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13539] :
( c_24__type__13538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__13539)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__13539,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_13628',axiom,
! [Vvar__13629] :
( c_24__type__13628___24t(Vvar__13629)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__13629,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13718',axiom,
! [Vvar__13719] :
( c_24__type__13718___24t(Vvar__13719)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__13719,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13758',axiom,
! [Vvar__13759] :
( c_24__type__13758___24t(Vvar__13759)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__13759,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_13763',axiom,
! [Vvar__13764] :
( c_24__type__13763___24t(Vvar__13764)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__13764,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13792',axiom,
! [Vvar__13793] :
( c_24__type__13792___24t(Vvar__13793)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__13793,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13796',axiom,
! [Vvar__13797] :
( c_24__type__13796___24t(Vvar__13797)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__13797,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13907',axiom,
! [Vvar__13908] :
( c_24__type__13907___24t(Vvar__13908)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__13908,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14576] :
( c_24__type__14575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14576)
<=> ! [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__14576,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14595',axiom,
! [Vvar__14596] :
( c_24__type__14595___24t(Vvar__14596)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__14596,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14621',axiom,
! [Vvar__14622] :
( c_24__type__14621___24t(Vvar__14622)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__14622,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14634',axiom,
! [Vvar__14635] :
( c_24__type__14634___24t(Vvar__14635)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__14635,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14636',axiom,
! [Vvar__14637] :
( c_24__type__14636___24t(Vvar__14637)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__14637,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14697',axiom,
! [Vvar__14698] :
( c_24__type__14697___24t(Vvar__14698)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__14698,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_14728',axiom,
! [Vvar__14729] :
( c_24__type__14728___24t(Vvar__14729)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14729,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14732',axiom,
! [Vv__CANONICAL__0,Vvar__14733] :
( c_24__type__14732___24t(Vv__CANONICAL__0,Vvar__14733)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__14733,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_14962',axiom,
! [Vvar__14963] :
( c_24__type__14962___24t(Vvar__14963)
<=> ! [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__14963,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14967',axiom,
! [Vvar__14968] :
( c_24__type__14967___24t(Vvar__14968)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__14968,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14975',axiom,
! [Vvar__14976] :
( c_24__type__14975___24t(Vvar__14976)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__14976,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15',axiom,
! [Vvar__16] :
( c_24__type__15___24t(Vvar__16)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__16,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15475',axiom,
! [Vv__CANONICAL__0,Vvar__15476] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vvar__15476)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15476,Vv__CANONICAL__1)) ) ) ).
fof('$_type_15671',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15672] :
( c_24__type__15671___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15672)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15672,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15764',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__15765] :
( c_24__type__15764___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__15765)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15765,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15858] :
( c_24__type__15857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15858)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15858,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15939',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__15940] :
( c_24__type__15939___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__15940)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__15940,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_16032',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__16033] :
( c_24__type__16032___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__16033)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16033,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16114',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__16115] :
( c_24__type__16114___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__16115)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__16115,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_16207',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__16208] :
( c_24__type__16207___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__16208)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__16208,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1728',axiom,
! [Vvar__1729] :
( c_24__type__1728___24t(Vvar__1729)
<=> ! [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__1729,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1745',axiom,
! [Vvar__1746] :
( c_24__type__1745___24t(Vvar__1746)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1746,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1771',axiom,
! [Vvar__1772] :
( c_24__type__1771___24t(Vvar__1772)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1772,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1775',axiom,
! [Vvar__1776] :
( c_24__type__1775___24t(Vvar__1776)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__1776,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1782',axiom,
! [Vvar__1783] :
( c_24__type__1782___24t(Vvar__1783)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__1783,Vv__CANONICAL__0)) ) ) ).
fof('$_type_17850',axiom,
! [Vvar__17851] :
( c_24__type__17850___24t(Vvar__17851)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__17851,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_17855',axiom,
! [Vvar__17856] :
( c_24__type__17855___24t(Vvar__17856)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__17856,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17858',axiom,
! [Vvar__17859] :
( c_24__type__17858___24t(Vvar__17859)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__17859,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1790',axiom,
! [Vvar__1791] :
( c_24__type__1790___24t(Vvar__1791)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1791,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1804',axiom,
! [Vvar__1805] :
( c_24__type__1804___24t(Vvar__1805)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1805,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1809',axiom,
! [Vvar__1810] :
( c_24__type__1809___24t(Vvar__1810)
<=> ! [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__1810,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1869',axiom,
! [Vvar__1870] :
( c_24__type__1869___24t(Vvar__1870)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1870,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18813',axiom,
! [Vvar__18814] :
( c_24__type__18813___24t(Vvar__18814)
<=> ! [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__18814,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18837',axiom,
! [Vvar__18838] :
( c_24__type__18837___24t(Vvar__18838)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__18844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__18838,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_18844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18845] :
( c_24__type__18844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__18845)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__18845,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_18903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18904] :
( c_24__type__18903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__18904)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__18904,Vv__CANONICAL__3)) ) ) ).
fof('$_type_19',axiom,
! [Vvar__20] :
( c_24__type__19___24t(Vvar__20)
<=> ! [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__20,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19038',axiom,
! [Vvar__19039] :
( c_24__type__19038___24t(Vvar__19039)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__19039,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19066',axiom,
! [Vvar__19067] :
( c_24__type__19066___24t(Vvar__19067)
<=> ! [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__19067,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19156',axiom,
! [Vvar__19157] :
( c_24__type__19156___24t(Vvar__19157)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__19157,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19161',axiom,
! [Vvar__19162] :
( c_24__type__19161___24t(Vvar__19162)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__19162,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19166',axiom,
! [Vvar__19167] :
( c_24__type__19166___24t(Vvar__19167)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__19167,Vv__CANONICAL__0)) ) ) ).
fof('$_type_19361',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__19362] :
( c_24__type__19361___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__19362)
<=> ! [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__19362,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_1938',axiom,
! [Vvar__1939] :
( c_24__type__1938___24t(Vvar__1939)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__1939,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1962',axiom,
! [Vvar__1963] :
( c_24__type__1962___24t(Vvar__1963)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1969___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__1963,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_1969',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1970] :
( c_24__type__1969___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1970)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1970,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1972',axiom,
! [Vvar__1973] :
( c_24__type__1972___24t(Vvar__1973)
<=> ! [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__1973,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20063',axiom,
! [Vvar__20064] :
( c_24__type__20063___24t(Vvar__20064)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__20064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_20723',axiom,
! [Vvar__20724] :
( c_24__type__20723___24t(Vvar__20724)
<=> ! [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__20724,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20852',axiom,
! [Vvar__20853] :
( c_24__type__20852___24t(Vvar__20853)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10937___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__20853,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21671',axiom,
! [Vvar__21672] :
( c_24__type__21671___24t(Vvar__21672)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__21672,Vv__CANONICAL__0)) ) ) ).
fof('$_type_21674',axiom,
! [Vvar__21675] :
( c_24__type__21674___24t(Vvar__21675)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__21675,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21677',axiom,
! [Vvar__21678] :
( c_24__type__21677___24t(Vvar__21678)
<=> ! [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__21678,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21682',axiom,
! [Vvar__21683] :
( c_24__type__21682___24t(Vvar__21683)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__21683,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_21691',axiom,
! [Vvar__21692] :
( c_24__type__21691___24t(Vvar__21692)
<=> ! [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__21692,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21696',axiom,
! [Vvar__21697] :
( c_24__type__21696___24t(Vvar__21697)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__21697,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23',axiom,
! [Vvar__24] :
( c_24__type__23___24t(Vvar__24)
<=> ! [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__24,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23629',axiom,
! [Vvar__23630] :
( c_24__type__23629___24t(Vvar__23630)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__23630,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_23798',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23799] :
( c_24__type__23798___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23799)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23799,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23821',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23822] :
( c_24__type__23821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23822)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23822,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23844',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23845] :
( c_24__type__23844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23845)
<=> ! [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__23845,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_23867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23868] :
( c_24__type__23867___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23868)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23868,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23885',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23886] :
( c_24__type__23885___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23886)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__23886,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_23911',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23912] :
( c_24__type__23911___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23912)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23912,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23930] :
( c_24__type__23929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__23930)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__23930,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_24198',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24199] :
( c_24__type__24198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24199)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24199,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_24248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24249] :
( c_24__type__24248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24249)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__24249,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_24298',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24299] :
( c_24__type__24298___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24299)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__24299,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_24340',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24341] :
( c_24__type__24340___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24341)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__24341,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_24390',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24391] :
( c_24__type__24390___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__24391)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__24391,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_24466',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24467] :
( c_24__type__24466___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24467)
<=> ! [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__24467,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_24573',axiom,
! [Vvar__24574] :
( c_24__type__24573___24t(Vvar__24574)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24642',axiom,
! [Vvar__24643] :
( c_24__type__24642___24t(Vvar__24643)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7270___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__24643,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_24731',axiom,
! [Vvar__24732] :
( c_24__type__24731___24t(Vvar__24732)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__24732,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24774',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24775] :
( c_24__type__24774___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24775)
<=> ! [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__24775,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_24833',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24834] :
( c_24__type__24833___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__24834)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24834,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_24874',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24875] :
( c_24__type__24874___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24875)
<=> ! [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__24875,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_24908',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24909] :
( c_24__type__24908___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24909)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24909,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24912',axiom,
! [Vvar__24913] :
( c_24__type__24912___24t(Vvar__24913)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__24913,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24930',axiom,
! [Vvar__24931] :
( c_24__type__24930___24t(Vvar__24931)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__24931,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_24947',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24948] :
( c_24__type__24947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__24948)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24948,Vv__CANONICAL__2)) ) ) ).
fof('$_type_24953',axiom,
! [Vvar__24954] :
( c_24__type__24953___24t(Vvar__24954)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__24954,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_2507',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__2508] :
( c_24__type__2507___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__2508)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2508,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25707',axiom,
! [Vvar__25708] :
( c_24__type__25707___24t(Vvar__25708)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__25708,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25786',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__25787] :
( c_24__type__25786___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__25787)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__25787,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_25797',axiom,
! [Vvar__25798] :
( c_24__type__25797___24t(Vvar__25798)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__25798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25865',axiom,
! [Vv__CANONICAL__0,Vvar__25866] :
( c_24__type__25865___24t(Vv__CANONICAL__0,Vvar__25866)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__25866,Vv__CANONICAL__1)) ) ) ).
fof('$_type_26',axiom,
! [Vvar__27] :
( c_24__type__26___24t(Vvar__27)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__27,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26210',axiom,
! [Vvar__26211] :
( c_24__type__26210___24t(Vvar__26211)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__26215___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__26211,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_26215',axiom,
! [Vv__CANONICAL__0,Vvar__26216] :
( c_24__type__26215___24t(Vv__CANONICAL__0,Vvar__26216)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26216,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26282',axiom,
! [Vvar__26283] :
( c_24__type__26282___24t(Vvar__26283)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__26283,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_26290',axiom,
! [Vvar__26291] :
( c_24__type__26290___24t(Vvar__26291)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__19038___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__19038___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__26291,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26323',axiom,
! [Vvar__26324] :
( c_24__type__26323___24t(Vvar__26324)
<=> ! [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__26324,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26334',axiom,
! [Vvar__26335] :
( c_24__type__26334___24t(Vvar__26335)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__26335,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26390',axiom,
! [Vvar__26391] :
( c_24__type__26390___24t(Vvar__26391)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__26391,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26423',axiom,
! [Vvar__26424] :
( c_24__type__26423___24t(Vvar__26424)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26424,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26675',axiom,
! [Vvar__26676] :
( c_24__type__26675___24t(Vvar__26676)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__26676,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26679',axiom,
! [Vvar__26680] :
( c_24__type__26679___24t(Vvar__26680)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__26680,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26682',axiom,
! [Vvar__26683] :
( c_24__type__26682___24t(Vvar__26683)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__26683,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26749',axiom,
! [Vvar__26750] :
( c_24__type__26749___24t(Vvar__26750)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__26750,Vv__CANONICAL__0)) ) ) ).
fof('$_type_26955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26956] :
( c_24__type__26955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__26956)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__26956,Vv__CANONICAL__6)) ) ) ).
fof('$_type_27182',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27183] :
( c_24__type__27182___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27183)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27183,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27245',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__27246] :
( c_24__type__27245___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__27246)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27246,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27309] :
( c_24__type__27308___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27309)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27309,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27362',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__27363] :
( c_24__type__27362___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__27363)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__27363,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_27425',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27426] :
( c_24__type__27425___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__27426)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27426,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_27455',axiom,
! [Vvar__27456] :
( c_24__type__27455___24t(Vvar__27456)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__27456,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27503',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27504] :
( c_24__type__27503___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27504)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__27504,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_27653',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27654] :
( c_24__type__27653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__27654)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__27654,Vv__CANONICAL__6)) ) ) ).
fof('$_type_27857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27858] :
( c_24__type__27857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__27858)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27858,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27950',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__27951] :
( c_24__type__27950___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__27951)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27951,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28044] :
( c_24__type__28043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28044)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28044,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28125',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__28126] :
( c_24__type__28125___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__28126)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__28126,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_28218',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28219] :
( c_24__type__28218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28219)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28219,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28300',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__28301] :
( c_24__type__28300___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__28301)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__28301,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_28393',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28394] :
( c_24__type__28393___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__28394)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28394,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_2853',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__2854] :
( c_24__type__2853___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__2854)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__2854,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__28548] :
( c_24__type__28547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__28548)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28548,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28610',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__28611] :
( c_24__type__28610___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__28611)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28611,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__28674] :
( c_24__type__28673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__28674)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__28674,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_28727',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__28728] :
( c_24__type__28727___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__28728)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__28728,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_28790',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__28791] :
( c_24__type__28790___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__28791)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28791,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_28821',axiom,
! [Vvar__28822] :
( c_24__type__28821___24t(Vvar__28822)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__7270___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__28822,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_28902',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__28903] :
( c_24__type__28902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__28903)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28903,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_28921',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__28922] :
( c_24__type__28921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__28922)
<=> ! [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__28922,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_28941',axiom,
! [Vvar__28942] :
( c_24__type__28941___24t(Vvar__28942)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__28942,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_29225',axiom,
! [Vvar__29226] :
( c_24__type__29225___24t(Vvar__29226)
<=> ! [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__29226,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__29588] :
( c_24__type__29587___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__29588)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29588,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29626',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__29627] :
( c_24__type__29626___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__29627)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29627,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_29665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__29666] :
( c_24__type__29665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__29666)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29666,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_29910',axiom,
! [Vvar__29911] :
( c_24__type__29910___24t(Vvar__29911)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7284___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__29920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__29911,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_29920',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29921] :
( c_24__type__29920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29921)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__29921,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_29946',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29947] :
( c_24__type__29946___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29947)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__29947,Vv__CANONICAL__3)) ) ) ).
fof('$_type_29954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29955] :
( c_24__type__29954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29955)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__29955,Vv__CANONICAL__3)) ) ) ).
fof('$_type_29962',axiom,
! [Vvar__29963] :
( c_24__type__29962___24t(Vvar__29963)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__29963,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30002',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30003] :
( c_24__type__30002___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30003)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30003,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30010',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30011] :
( c_24__type__30010___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30011)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30011,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30018',axiom,
! [Vvar__30019] :
( c_24__type__30018___24t(Vvar__30019)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__30019,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30088',axiom,
! [Vvar__30089] :
( c_24__type__30088___24t(Vvar__30089)
<=> ! [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__30089,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30512',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30513] :
( c_24__type__30512___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30513)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30513,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_30624',axiom,
! [Vvar__30625] :
( c_24__type__30624___24t(Vvar__30625)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7279___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__30625,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_30647',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30648] :
( c_24__type__30647___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30648)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__30648,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30668',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30669] :
( c_24__type__30668___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30669)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__30669,Vv__CANONICAL__3)) ) ) ).
fof('$_type_30703',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30704] :
( c_24__type__30703___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30704)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__30704,Vv__CANONICAL__5)) ) ) ).
fof('$_type_30711',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30712] :
( c_24__type__30711___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__30712)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__30712,Vv__CANONICAL__5)) ) ) ).
fof('$_type_30713',axiom,
! [Vvar__30714] :
( c_24__type__30713___24t(Vvar__30714)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30714,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30718',axiom,
! [Vvar__30719] :
( c_24__type__30718___24t(Vvar__30719)
<=> ! [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__30719,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30732',axiom,
! [Vvar__30733] :
( c_24__type__30732___24t(Vvar__30733)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__30733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30745',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30746] :
( c_24__type__30745___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30746)
<=> ! [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__30746,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_30752',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30753] :
( c_24__type__30752___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30753)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__30753,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30756',axiom,
! [Vvar__30757] :
( c_24__type__30756___24t(Vvar__30757)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30757,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30762',axiom,
! [Vv__CANONICAL__0,Vvar__30763] :
( c_24__type__30762___24t(Vv__CANONICAL__0,Vvar__30763)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30763,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_30767',axiom,
! [Vv__CANONICAL__0,Vvar__30768] :
( c_24__type__30767___24t(Vv__CANONICAL__0,Vvar__30768)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__30768,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_30769',axiom,
! [Vvar__30770] :
( c_24__type__30769___24t(Vvar__30770)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30770,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30809',axiom,
! [Vvar__30810] :
( c_24__type__30809___24t(Vvar__30810)
<=> ! [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__30810,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30897',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30898] :
( c_24__type__30897___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30898)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__30898,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30993',axiom,
! [Vvar__30994] :
( c_24__type__30993___24t(Vvar__30994)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__30994,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30996',axiom,
! [Vvar__30997] :
( c_24__type__30996___24t(Vvar__30997)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__30997,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31014',axiom,
! [Vvar__31015] :
( c_24__type__31014___24t(Vvar__31015)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7270___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__31015,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_31272',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31273] :
( c_24__type__31272___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31273)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31273,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31397',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__31398] :
( c_24__type__31397___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__31398)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__31398,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31522',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31523] :
( c_24__type__31522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31523)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31523,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_31647',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__31648] :
( c_24__type__31647___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__31648)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__31648,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_31772',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31773] :
( c_24__type__31772___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__31773)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__31773,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_31897',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__31898] :
( c_24__type__31897___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__31898)
<=> ! [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__31898,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_3199',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__3200] :
( c_24__type__3199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__3200)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3200,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32008',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__32009] :
( c_24__type__32008___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__32009)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__32009,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_32050',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32051] :
( c_24__type__32050___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32051)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32051,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_32083',axiom,
! [Vvar__32084] :
( c_24__type__32083___24t(Vvar__32084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7284___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__29920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__32084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_32093',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32094] :
( c_24__type__32093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32094)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32094,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_32150',axiom,
! [Vvar__32151] :
( c_24__type__32150___24t(Vvar__32151)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__32151,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32181',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32182] :
( c_24__type__32181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32182)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__32182,Vv__CANONICAL__4)) ) ) ).
fof('$_type_32190',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32191] :
( c_24__type__32190___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32191)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__32191,Vv__CANONICAL__4)) ) ) ).
fof('$_type_32241',axiom,
! [Vvar__32242] :
( c_24__type__32241___24t(Vvar__32242)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__32242,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32351',axiom,
! [Vvar__32352] :
( c_24__type__32351___24t(Vvar__32352)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__32352,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32360',axiom,
! [Vvar__32361] :
( c_24__type__32360___24t(Vvar__32361)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__32361,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32383',axiom,
! [Vvar__32384] :
( c_24__type__32383___24t(Vvar__32384)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__14575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__32384,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_32406',axiom,
! [Vvar__32407] :
( c_24__type__32406___24t(Vvar__32407)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__27503___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__32407,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_32412',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32413] :
( c_24__type__32412___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32413)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__32413,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32429',axiom,
! [Vvar__32430] :
( c_24__type__32429___24t(Vvar__32430)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__32430,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32471',axiom,
! [Vvar__32472] :
( c_24__type__32471___24t(Vvar__32472)
<=> ! [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__32472,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('$_type_32478',axiom,
! [Vvar__32479] :
( c_24__type__32478___24t(Vvar__32479)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__32479,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32517] :
( c_24__type__32516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32517)
<=> ! [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__32517,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_32559',axiom,
! [Vv__CANONICAL__0,Vvar__32560] :
( c_24__type__32559___24t(Vv__CANONICAL__0,Vvar__32560)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( ? [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
& p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) )
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__32566___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__32560,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32613',axiom,
! [Vv__CANONICAL__0,Vvar__32614] :
( c_24__type__32613___24t(Vv__CANONICAL__0,Vvar__32614)
<=> ( p(Vv__CANONICAL__0)
=> cProp___24t(Vvar__32614) ) ) ).
fof('$_type_32621',axiom,
! [Vvar__32622] :
( c_24__type__32621___24t(Vvar__32622)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__32622,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32685] :
( c_24__type__32684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__32685)
<=> ( p(happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2))
=> cProp___24t(Vvar__32685) ) ) ).
fof('$_type_32732',axiom,
! [Vv__CANONICAL__0,Vvar__32733] :
( c_24__type__32732___24t(Vv__CANONICAL__0,Vvar__32733)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__32733,Vv__CANONICAL__1)) ) ) ).
fof('$_type_32745',axiom,
! [Vvar__32746] :
( c_24__type__32745___24t(Vvar__32746)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__1869___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO))
=> ! [Vv__CANONICAL__2] :
( c_24__type__32750___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__32746,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32750',axiom,
! [Vv__CANONICAL__0,Vvar__32751] :
( c_24__type__32750___24t(Vv__CANONICAL__0,Vvar__32751)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__32751,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_32755',axiom,
! [Vvar__32756] :
( c_24__type__32755___24t(Vvar__32756)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__32756,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32760',axiom,
! [Vvar__32761] :
( c_24__type__32760___24t(Vvar__32761)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__32761,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32772',axiom,
! [Vvar__32773] :
( c_24__type__32772___24t(Vvar__32773)
<=> ! [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__32773,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_32774',axiom,
! [Vvar__32775] :
( c_24__type__32774___24t(Vvar__32775)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__32775,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32776',axiom,
! [Vvar__32777] :
( c_24__type__32776___24t(Vvar__32777)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__32777,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32778',axiom,
! [Vvar__32779] :
( c_24__type__32778___24t(Vvar__32779)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__32779,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32791',axiom,
! [Vvar__32792] :
( c_24__type__32791___24t(Vvar__32792)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__32792,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32794',axiom,
! [Vvar__32795] :
( c_24__type__32794___24t(Vvar__32795)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__32795,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32797',axiom,
! [Vvar__32798] :
( c_24__type__32797___24t(Vvar__32798)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__32798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32800',axiom,
! [Vvar__32801] :
( c_24__type__32800___24t(Vvar__32801)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__32801,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32811',axiom,
! [Vvar__32812] :
( c_24__type__32811___24t(Vvar__32812)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__15475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(happ(happ(Vvar__32812,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_32820',axiom,
! [Vvar__32821] :
( c_24__type__32820___24t(Vvar__32821)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(happ(happ(Vvar__32821,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_32822',axiom,
! [Vvar__32823] :
( c_24__type__32822___24t(Vvar__32823)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__32823,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32825',axiom,
! [Vvar__32826] :
( c_24__type__32825___24t(Vvar__32826)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__32826,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32835',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32836] :
( c_24__type__32835___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32836)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__32836,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32840',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32841] :
( c_24__type__32840___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32841)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__32841,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32847] :
( c_24__type__32846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32847)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__32847,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32852] :
( c_24__type__32851___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32852)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__32852,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).
fof('$_type_32862',axiom,
! [Vv__CANONICAL__0,Vvar__32863] :
( c_24__type__32862___24t(Vv__CANONICAL__0,Vvar__32863)
<=> ! [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__32863,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_32873',axiom,
! [Vvar__32874] :
( c_24__type__32873___24t(Vvar__32874)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__32862___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__32874,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_32899',axiom,
! [Vvar__32900] :
( c_24__type__32899___24t(Vvar__32900)
<=> ! [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__32900,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32910',axiom,
! [Vvar__32911] :
( c_24__type__32910___24t(Vvar__32911)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__32911,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_32942',axiom,
! [Vvar__32943] :
( c_24__type__32942___24t(Vvar__32943)
<=> ! [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__32943,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_32966',axiom,
! [Vvar__32967] :
( c_24__type__32966___24t(Vvar__32967)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__32967,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_33013',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33014] :
( c_24__type__33013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33014)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__33014,Vv__CANONICAL__3)) ) ) ).
fof('$_type_33060',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__33061] :
( c_24__type__33060___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__33061)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__33061,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_33095',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33096] :
( c_24__type__33095___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__33096)
<=> ! [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__33096,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_33117',axiom,
! [Vvar__33118] :
( c_24__type__33117___24t(Vvar__33118)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__33118,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33139',axiom,
! [Vvar__33140] :
( c_24__type__33139___24t(Vvar__33140)
<=> ! [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__33140,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33752',axiom,
! [Vvar__33753] :
( c_24__type__33752___24t(Vvar__33753)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__33753,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33754',axiom,
! [Vvar__33755] :
( c_24__type__33754___24t(Vvar__33755)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__33755,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33757',axiom,
! [Vvar__33758] :
( c_24__type__33757___24t(Vvar__33758)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__33758,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33761',axiom,
! [Vvar__33762] :
( c_24__type__33761___24t(Vvar__33762)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__33762,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33779',axiom,
! [Vvar__33780] :
( c_24__type__33779___24t(Vvar__33780)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__33780,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33805',axiom,
! [Vvar__33806] :
( c_24__type__33805___24t(Vvar__33806)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___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__33806,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34017',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34018] :
( c_24__type__34017___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34018)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34018,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34043] :
( c_24__type__34042___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34043)
<=> ! [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__34043,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34124',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34125] :
( c_24__type__34124___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34125)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__34125,Vv__CANONICAL__6)) ) ) ).
fof('$_type_34153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34154] :
( c_24__type__34153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34154)
<=> ! [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__34154,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34190',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34191] :
( c_24__type__34190___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34191)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
=> cProp___24t(happ(happ(happ(Vvar__34191,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).
fof('$_type_34262',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34263] :
( c_24__type__34262___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34263)
<=> ! [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__34263,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34287',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34288] :
( c_24__type__34287___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34288)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__34288,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_34329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34330] :
( c_24__type__34329___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34330)
<=> ! [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__34330,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34380',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34381] :
( c_24__type__34380___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34381)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34381,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34422',axiom,
! [Vvar__34423] :
( c_24__type__34422___24t(Vvar__34423)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10937___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__34423,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34428',axiom,
! [Vvar__34429] :
( c_24__type__34428___24t(Vvar__34429)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(happ(Vvar__34429,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34430',axiom,
! [Vvar__34431] :
( c_24__type__34430___24t(Vvar__34431)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__34431,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34443',axiom,
! [Vvar__34444] :
( c_24__type__34443___24t(Vvar__34444)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__34444,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34451',axiom,
! [Vvar__34452] :
( c_24__type__34451___24t(Vvar__34452)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__34452,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34454',axiom,
! [Vvar__34455] :
( c_24__type__34454___24t(Vvar__34455)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__34455,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34630',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34631] :
( c_24__type__34630___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34631)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__34631,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_34649',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34650] :
( c_24__type__34649___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34650)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__34650,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34663',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34664] :
( c_24__type__34663___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34664)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__34664,Vv__CANONICAL__4)) ) ) ).
fof('$_type_34706',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34707] :
( c_24__type__34706___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34707)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34707,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_34746',axiom,
! [Vvar__34747] :
( c_24__type__34746___24t(Vvar__34747)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__32516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__29920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__34747,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34794',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34795] :
( c_24__type__34794___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34795)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__34795,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_34810',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34811] :
( c_24__type__34810___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34811)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__34811,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34816',axiom,
! [Vvar__34817] :
( c_24__type__34816___24t(Vvar__34817)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__34817,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_34822',axiom,
! [Vvar__34823] :
( c_24__type__34822___24t(Vvar__34823)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__34823,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_34827',axiom,
! [Vvar__34828] :
( c_24__type__34827___24t(Vvar__34828)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__34828,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_34830',axiom,
! [Vvar__34831] :
( c_24__type__34830___24t(Vvar__34831)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__34831,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34838',axiom,
! [Vvar__34839] :
( c_24__type__34838___24t(Vvar__34839)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__34839,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34856',axiom,
! [Vvar__34857] :
( c_24__type__34856___24t(Vvar__34857)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__34857,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_34873',axiom,
! [Vvar__34874] :
( c_24__type__34873___24t(Vvar__34874)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__34874,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_34882',axiom,
! [Vvar__34883] :
( c_24__type__34882___24t(Vvar__34883)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__34883,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34909',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34910] :
( c_24__type__34909___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34910)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__34910,Vv__CANONICAL__4)) ) ) ).
fof('$_type_34939',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34940] :
( c_24__type__34939___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34940)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__34940,Vv__CANONICAL__4)) ) ) ).
fof('$_type_35005',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__35006] :
( c_24__type__35005___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__35006)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35006,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_35014',axiom,
! [Vvar__35015] :
( c_24__type__35014___24t(Vvar__35015)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__25865___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__35015,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_35168',axiom,
! [Vvar__35169] :
( c_24__type__35168___24t(Vvar__35169)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__35169,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35172',axiom,
! [Vvar__35173] :
( c_24__type__35172___24t(Vvar__35173)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__35173,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35196',axiom,
! [Vvar__35197] :
( c_24__type__35196___24t(Vvar__35197)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__35201___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__35197,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_35201',axiom,
! [Vv__CANONICAL__0,Vvar__35202] :
( c_24__type__35201___24t(Vv__CANONICAL__0,Vvar__35202)
<=> ! [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__35202,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35206',axiom,
! [Vvar__35207] :
( c_24__type__35206___24t(Vvar__35207)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__35207,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35209',axiom,
! [Vvar__35210] :
( c_24__type__35209___24t(Vvar__35210)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__35210,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3522',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__3523] :
( c_24__type__3522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__3523)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__3523,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_35220',axiom,
! [Vvar__35221] :
( c_24__type__35220___24t(Vvar__35221)
<=> ! [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__35221,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35239',axiom,
! [Vvar__35240] :
( c_24__type__35239___24t(Vvar__35240)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__35240,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35269',axiom,
! [Vvar__35270] :
( c_24__type__35269___24t(Vvar__35270)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__35270,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35276',axiom,
! [Vvar__35277] :
( c_24__type__35276___24t(Vvar__35277)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__35277,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35301',axiom,
! [Vvar__35302] :
( c_24__type__35301___24t(Vvar__35302)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__35302,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35306',axiom,
! [Vvar__35307] :
( c_24__type__35306___24t(Vvar__35307)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__35307,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35313',axiom,
! [Vvar__35314] :
( c_24__type__35313___24t(Vvar__35314)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35314,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35354',axiom,
! [Vvar__35355] :
( c_24__type__35354___24t(Vvar__35355)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__35355,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35358',axiom,
! [Vvar__35359] :
( c_24__type__35358___24t(Vvar__35359)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__26749___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__26749___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35359,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35378',axiom,
! [Vvar__35379] :
( c_24__type__35378___24t(Vvar__35379)
<=> ! [Vv__CANONICAL__0] :
( cA___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__35379,Vv__CANONICAL__0)) ) ) ).
fof('$_type_36',axiom,
! [Vv__CANONICAL__0,Vvar__37] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vvar__37)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__37,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3868',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__3869] :
( c_24__type__3868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__3869)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__3869,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_4214',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__4215] :
( c_24__type__4214___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__4215)
<=> ! [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__4215,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_44',axiom,
! [Vvar__45] :
( c_24__type__44___24t(Vvar__45)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__36___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__45,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4560',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__4561] :
( c_24__type__4560___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__4561)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__4561,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_4906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__4907] :
( c_24__type__4906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__4907)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__4907,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_52',axiom,
! [Vvar__53] :
( c_24__type__52___24t(Vvar__53)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__53,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5252',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__5253] :
( c_24__type__5252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__5253)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__5253,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_54',axiom,
! [Vvar__55] :
( c_24__type__54___24t(Vvar__55)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__55,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5575',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__5576] :
( c_24__type__5575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__5576)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__5576,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_5921',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__5922] :
( c_24__type__5921___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__5922)
<=> ! [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__5922,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_6267',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__6268] :
( c_24__type__6267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__6268)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__6268,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_6590',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__6591] :
( c_24__type__6590___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__6591)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__6591,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_66',axiom,
! [Vvar__67] :
( c_24__type__66___24t(Vvar__67)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__67,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6913',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__6914] :
( c_24__type__6913___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__6914)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__6914,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_7259',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__7260] :
( c_24__type__7259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__7260)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__7260,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7270',axiom,
! [Vv__CANONICAL__0,Vvar__7271] :
( c_24__type__7270___24t(Vv__CANONICAL__0,Vvar__7271)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7271,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7279',axiom,
! [Vv__CANONICAL__0,Vvar__7280] :
( c_24__type__7279___24t(Vv__CANONICAL__0,Vvar__7280)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__7280,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_7284',axiom,
! [Vv__CANONICAL__0,Vvar__7285] :
( c_24__type__7284___24t(Vv__CANONICAL__0,Vvar__7285)
<=> ! [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__7285,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_7294',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7295] :
( c_24__type__7294___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7295)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__7295,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_7308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7309] :
( c_24__type__7308___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7309)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__7309,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_7315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7316] :
( c_24__type__7315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7316)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__7316,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_7324',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7325] :
( c_24__type__7324___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__7325)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__7325,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_7736',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7737] :
( c_24__type__7736___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7737)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7737,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7949',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__7950] :
( c_24__type__7949___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__7950)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7950,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8163] :
( c_24__type__8162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8163)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8163,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8357',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__8358] :
( c_24__type__8357___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__8358)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__8358,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_8570',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8571] :
( c_24__type__8570___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8571)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8571,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_8783',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__8784] :
( c_24__type__8783___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__8784)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__8784,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_89',axiom,
! [Vvar__90] :
( c_24__type__89___24t(Vvar__90)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__90,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_8996',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__8997] :
( c_24__type__8996___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__8997)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__8997,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_9209',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__9210] :
( c_24__type__9209___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__9210)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__9210,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_94',axiom,
! [Vvar__95] :
( c_24__type__94___24t(Vvar__95)
<=> ! [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__95,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_9404',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__9405] :
( c_24__type__9404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__9405)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__9405,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_9617',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__9618] :
( c_24__type__9617___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__9618)
<=> ! [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__9618,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_9812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__9813] :
( c_24__type__9812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__9813)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__9813,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_9926',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9927] :
( c_24__type__9926___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9927)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9927,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9970',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9971] :
( c_24__type__9970___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9971)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9971,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_B',axiom,
cType___24t(cB) ).
fof('$_typeof_C',axiom,
cType___24t(cC) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__26282___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__1972___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__35206___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__1972___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__1972___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__26290___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__1972___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__1972___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__35196___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__11146___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.gtof',axiom,
c_24__type__35014___24t(cCoq_2eArith_2eWf__nat_2egtof) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__35014___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__30713___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__1775___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__30718___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__13907___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__1869___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__19038___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__13792___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__10432___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
c_24__type__35306___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__13792___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_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__13792___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__26423___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Byte.byte_of_byte',axiom,
c_24__type__32478___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).
fof('$_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__32774___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__30809___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_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__14636___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__1782___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__14634___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__1775___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__10533___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__1809___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__32772___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__1775___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__32755___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__32760___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__10521___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__1790___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__32745___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__14621___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__1804___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__1790___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__1775___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__10511___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__10495___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__14697___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__10495___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__1775___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.D1',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD1) ).
fof('$_typeof_Coq.Init.Decimal.D2',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD2) ).
fof('$_typeof_Coq.Init.Decimal.D3',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD3) ).
fof('$_typeof_Coq.Init.Decimal.D4',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD4) ).
fof('$_typeof_Coq.Init.Decimal.D5',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD5) ).
fof('$_typeof_Coq.Init.Decimal.D6',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD6) ).
fof('$_typeof_Coq.Init.Decimal.D7',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD7) ).
fof('$_typeof_Coq.Init.Decimal.D8',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD8) ).
fof('$_typeof_Coq.Init.Decimal.D9',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2eD9) ).
fof('$_typeof_Coq.Init.Decimal.Neg',axiom,
c_24__type__32778___24t(cCoq_2eInit_2eDecimal_2eNeg) ).
fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).
fof('$_typeof_Coq.Init.Decimal.Pos',axiom,
c_24__type__32778___24t(cCoq_2eInit_2eDecimal_2ePos) ).
fof('$_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.int_of_int',axiom,
c_24__type__32791___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).
fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2enzhead) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
c_24__type__32776___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__30769___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__33117___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__1782___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__1782___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__19066___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__19038___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__19066___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__33139___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.one',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2eone) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__1782___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.square',axiom,
c_24__type__1782___24t(cCoq_2eInit_2eNat_2esquare) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__1782___24t(cCoq_2eInit_2eNat_2esucc) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__11146___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__19066___24t(cCoq_2eInit_2eNat_2etestbit) ).
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__10466___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__1972___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__1972___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__1972___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.Exc',axiom,
c_24__type__1790___24t(cCoq_2eInit_2eSpecif_2eExc) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__32150___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__10141___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__24930___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__34822___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__34827___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__89___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__34816___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__24953___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__94___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__10123___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__29962___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__24912___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__30018___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__66___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__27455___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__25797___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__18813___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__18837___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__1962___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__32910___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__32966___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__32942___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__1938___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__34746___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__29910___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__29910___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__32083___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__32083___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ConstructiveIndefiniteDescription_on',axiom,
c_24__type__1790___24t(cCoq_2eLogic_2eChoiceFacts_2eConstructiveIndefiniteDescription__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on',axiom,
c_24__type__30756___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__14595___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on_rel',axiom,
c_24__type__30732___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on',axiom,
c_24__type__30769___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.GeneralizedSetoidFunctionalChoice_on',axiom,
c_24__type__14595___24t(cCoq_2eLogic_2eChoiceFacts_2eGeneralizedSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.GuardedFunctionalChoice_on',axiom,
c_24__type__14595___24t(cCoq_2eLogic_2eChoiceFacts_2eGuardedFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.IndependenceOfGeneralPremises',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eIndependenceOfGeneralPremises) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.OmniscientFunctionalChoice_on',axiom,
c_24__type__14595___24t(cCoq_2eLogic_2eChoiceFacts_2eOmniscientFunctionalChoice__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__30769___24t(cCoq_2eLogic_2eChoiceFacts_2eRepresentativeFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SetoidFunctionalChoice_on',axiom,
c_24__type__14595___24t(cCoq_2eLogic_2eChoiceFacts_2eSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on',axiom,
c_24__type__14595___24t(cCoq_2eLogic_2eChoiceFacts_2eSimpleSetoidFunctionalChoice__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.SmallDrinker\'sParadox',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eSmallDrinker_27sParadox) ).
fof('$_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__10464___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimal) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.RightDistributivityImplicationOverDisjunction',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.provable_prop_extensionality',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eprovable__prop__extensionality) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.weak_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__excluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.weak_generalized_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__14728___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__32811___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__32820___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__19___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__19___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__10408___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__19___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__19___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__26210___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__1728___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__10411___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__10411___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__10401___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__10404___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__1728___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__1728___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__1728___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__1728___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__10411___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__10411___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_pos',axiom,
c_24__type__35172___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__10401___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__13718___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__26290___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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__10461___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__52___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__52___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__1771___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__1771___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__26390___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__26334___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__26334___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__35301___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__35209___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__35220___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__1771___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__35239___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__30624___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__13758___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__26323___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__26323___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__26323___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__35276___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__35276___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
c_24__type__1771___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__13763___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__26323___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__1771___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
c_24__type__35269___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
c_24__type__19166___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__19156___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__19161___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__15___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__12264___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__12258___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__12258___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__15___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__12258___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__12258___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__13___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__15___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__13___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__30993___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__29225___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__24731___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__24731___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__24731___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__1790___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__24731___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__24731___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__24731___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__1790___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__32471___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).
fof('$_typeof_Coq.Strings.String.String',axiom,
c_24__type__34830___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
c_24__type__32873___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
c_24__type__32873___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__28941___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__19___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__19___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.eq',axiom,
c_24__type__1972___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__1972___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__26334___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__26334___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__26334___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__26334___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__26334___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__35313___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__23___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__23___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__1869___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__34882___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__25707___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__35354___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__23___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__23___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__35358___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__23___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__23___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__23___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__23___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__1745___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__26679___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__26675___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__10449___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__26749___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__13628___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__26749___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__13796___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__26682___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__1745___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__1745___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__26___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__1745___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__26679___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__26675___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__32351___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__13628___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__54___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__54___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__10455___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
c_24__type__52___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__29225___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__32241___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__32797___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__32794___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__14975___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__14962___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__14967___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
c_24__type__32800___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__32800___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).
fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).
fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).
fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__33761___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
c_24__type__33757___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__33757___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
c_24__type__33761___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).
fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
c_24__type__33757___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).
fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
c_24__type__33752___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__33754___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__33805___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__33779___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__1790___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('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__34428___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__34430___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__34422___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__20063___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__19066___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__34873___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__34838___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__30088___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
c_24__type__30088___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__34838___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__34856___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__10495___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__1790___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
c_24__type__11093___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__35168___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).
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__13796___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__26682___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__52___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__52___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
c_24__type__13718___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__32822___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__32822___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__17850___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__32825___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__17858___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__17855___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__1790___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__1790___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__1790___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__10411___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
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('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__28821___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__28821___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__11093___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.mkhypo',axiom,
c_24__type__32899___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
c_24__type__21671___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__21671___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__21677___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__21682___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__21674___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__21682___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__21691___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__21696___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__21682___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__1790___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__34451___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__20723___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__20852___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__34443___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__1790___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__31014___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_polynom.vmon',axiom,
c_24__type__34454___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__34454___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).
fof('$_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__24573___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__24573___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__24642___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__10411___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__23629___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__12664___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_HahnSets.set_bunion',axiom,
c_24__type__32383___24t(cHahnSets_2eset__bunion) ).
fof('$_typeof_HahnSets.set_collect',axiom,
c_24__type__32406___24t(cHahnSets_2eset__collect) ).
fof('$_typeof_HahnSets.set_compl',axiom,
c_24__type__44___24t(cHahnSets_2eset__compl) ).
fof('$_typeof_HahnSets.set_disjoint',axiom,
c_24__type__32360___24t(cHahnSets_2eset__disjoint) ).
fof('$_typeof_HahnSets.set_empty',axiom,
c_24__type__30996___24t(cHahnSets_2eset__empty) ).
fof('$_typeof_HahnSets.set_equiv',axiom,
c_24__type__32360___24t(cHahnSets_2eset__equiv) ).
fof('$_typeof_HahnSets.set_full',axiom,
c_24__type__30996___24t(cHahnSets_2eset__full) ).
fof('$_typeof_HahnSets.set_inter',axiom,
c_24__type__32429___24t(cHahnSets_2eset__inter) ).
fof('$_typeof_HahnSets.set_minus',axiom,
c_24__type__32429___24t(cHahnSets_2eset__minus) ).
fof('$_typeof_HahnSets.set_subset',axiom,
c_24__type__32360___24t(cHahnSets_2eset__subset) ).
fof('$_typeof_HahnSets.set_union',axiom,
c_24__type__32429___24t(cHahnSets_2eset__union) ).
fof('$_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('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__30996___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__30996___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_hahn.HahnBase.Equality.mixin_of',axiom,
c_24__type__1790___24t(chahn_2eHahnBase_2eEquality_2emixin__of) ).
fof('$_typeof_hahn.HahnBase.Equality.type',axiom,
cType___24t(chahn_2eHahnBase_2eEquality_2etype) ).
fof('$_typeof_hahn.HahnBase.eqn_rec',axiom,
c_24__type__19066___24t(chahn_2eHahnBase_2eeqn__rec) ).
fof('$_typeof_hahn.HahnBase.is_true',axiom,
c_24__type__30713___24t(chahn_2eHahnBase_2eis__true) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_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.divide_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_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_1',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
! [V0__P] :
( c_24__type__1972___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ! [V3__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
=> ! [V4__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__q)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V3__p,V1__n)
=> p(happ(happ(V0__P,V3__p),V4__q)) ) ) )
=> ( ! [V4__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V4__p,V2__m)
=> p(happ(happ(V0__P,V1__n),V4__p)) ) )
=> p(happ(happ(V0__P,V1__n),V2__m)) ) ) ) )
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> p(happ(happ(V0__P,V2__n),V3__m)) ) ) ) ) ).
fof('Coq.Arith.Wf_nat.lt_wf_ind',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__10466___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__10466___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_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__1972___24t(V0__R)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
=> ( ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( p(happ(happ(V0__R,V3__n),V4__m))
=> p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ! [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
=> p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).
fof('Coq.Logic.ChoiceFacts.proj1_inf',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
& p(V1__B) )
=> p(V0__A) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.BoolP_elim',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ( p(V0__C)
=> ( p(V0__C)
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eBoolP)
=> p(V0__C) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.FalseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.TrueP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eBoolP) ).
fof('Coq.Logic.ClassicalFacts.aux',axiom,
! [V0__bool] :
( cProp___24t(V0__bool)
=> ( p(V0__bool)
=> ( p(V0__bool)
=> ( ! [V3__C] :
( cProp___24t(V3__C)
=> ( p(V3__C)
=> ( p(V3__C)
=> ( p(V0__bool)
=> p(V3__C) ) ) ) )
=> ( ! [V4__C] :
( cProp___24t(V4__C)
=> ( p(V4__C)
=> ( p(V4__C)
=> c_24Proof = c_24Proof ) ) )
=> ( ! [V5__C] :
( cProp___24t(V5__C)
=> ( p(V5__C)
=> ( p(V5__C)
=> c_24Proof = c_24Proof ) ) )
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
=> ( ! [V7__P] :
( c_24__type__32613___24t(V0__bool,V7__P)
=> ( p(V7__P)
=> ( p(V7__P)
=> ( p(V0__bool)
=> p(V7__P) ) ) ) )
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.boolP_ind',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(V0__P) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.boolP_sind',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eboolP)
=> p(V0__P) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.falseP',axiom,
p(cCoq_2eLogic_2eClassicalFacts_2eboolP) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__32621___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__C] :
( cProp___24t(V7__C)
=> ( ( p(V5__A)
=> p(V7__C) )
=> ( ( p(V6__B)
=> p(V7__C) )
=> ( p(V6__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ! [V8__P] :
( c_24__type__32684___24t(V0__or,V6__A,V7__B,V8__P)
=> ( ( p(V6__A)
=> p(V8__P) )
=> ( ( p(V7__B)
=> p(V8__P) )
=> ( p(happ(happ(V0__or,V6__A),V7__B))
=> p(V8__P) ) ) ) ) ) )
=> ( ! [V7__A] :
( cProp___24t(V7__A)
=> p(happ(happ(V0__or,V7__A),c_24__prop__32709___24a1(V7__A))) )
=> ! [V8__B] :
( cProp___24t(V8__B)
=> ( p(V8__B)
=> ( p(V8__B)
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cci',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V1__B)
=> ( p(V1__B)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.prop_ext_A_eq_A_imp_A',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ( p(V1__A)
=> c_24__prop__32593___24a1(V1__A) = V1__A ) ) ) ).
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__36___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__36___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__36___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> ~ p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.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_false_iff',axiom,
( ( p(c_24False)
=> p(c_24False) )
<=> p(c_24True) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_true_iff',axiom,
( ( p(c_24True)
=> p(c_24False) )
<=> p(c_24False) ) ).
fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__15475___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).
fof('Coq.Logic.FunctionalExtensionality.equal_f',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__27503___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__27503___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__15475___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__32835___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__32840___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__27503___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__30913___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__15475___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__30897___24t(V0__A,V1__B,V2__f)
=> V2__f = c_24__lam__30905___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__27503___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__27503___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__15475___24t(V0__A,V1__B)
=> ! [V2__f] :
( c_24__type__32846___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__32851___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.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.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.NArith.BinNat.N.le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.iter_invariant',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__f] :
( c_24__type__7279___24t(V1__A,V2__f)
=> ! [V3__Inv] :
( c_24__type__36___24t(V1__A,V3__Inv)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> ( p(happ(V3__Inv,V4__x))
=> p(happ(V3__Inv,happ(V2__f,V4__x))) ) )
=> ! [V5__x] :
( t(V5__x,V1__A)
=> ( p(happ(V3__Inv,V5__x))
=> p(happ(V3__Inv,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V5__x,V0__p))) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.le_refl',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V0__p) ) ).
fof('Coq.Reals.RIneq.Rle_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r) ) ).
fof('Coq.Relations.Relation_Definitions.Build_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_antisym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.Z_as_OT.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.A\'A_left',axiom,
! [V0__A] :
( c_24__type__54___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [Vvar__4__m__35347] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__35347)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__4__m__35347,V1__z))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,Vvar__4__m__35347))
=> p(happ(V0__A,Vvar__4__m__35347)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V3__n,V1__z))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__35346___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).
fof('Coq.ZArith.BinInt.Z.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> p(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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m
| p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_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.DeclConstant.Build_DeclaredConstant',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( t(V1__F,V0__T)
=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V0__T,V1__F) ) ) ).
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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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__7270___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__7270___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__7270___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__7284___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__7284___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.micromega.ZMicromega.Vars.Facts.MP.equal_refl',axiom,
! [V0__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V0__s)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V0__s) ) ).
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.ARadd_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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V2__rI)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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_add',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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(V3__radd,V9__x),V10__y))),happ(happ(V3__radd,happ(V6__ropp,V9__x)),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_art',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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( ! [V8__x] :
( t(V8__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
=> ( ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
=> ( ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
=> ( ! [V12__x] :
( t(V12__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V12__x)),V1__rO)) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),V14__y)),happ(happ(V4__rmul,V14__y),V13__x))) ) )
=> ( ! [V14__x] :
( t(V14__x,V0__R)
=> ! [V15__y] :
( t(V15__y,V0__R)
=> ! [V16__z] :
( t(V16__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V14__x),happ(happ(V4__rmul,V15__y),V16__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V14__x),V15__y)),V16__z))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> ! [V17__z] :
( t(V17__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V15__x),V16__y)),V17__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V15__x),V17__z)),happ(happ(V4__rmul,V16__y),V17__z)))) ) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> ! [V17__y] :
( t(V17__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V16__x),V17__y))),happ(happ(V4__rmul,happ(V6__ropp,V16__x)),V17__y))) ) )
=> ( ! [V17__x] :
( t(V17__x,V0__R)
=> ! [V18__y] :
( t(V18__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V3__radd,V17__x),V18__y))),happ(happ(V3__radd,happ(V6__ropp,V17__x)),happ(V6__ropp,V18__y)))) ) )
=> ( ! [V18__x] :
( t(V18__x,V0__R)
=> ! [V19__y] :
( t(V19__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V18__x),V19__y)),happ(happ(V3__radd,V18__x),happ(V6__ropp,V19__y)))) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_rt',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__7270___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__7279___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__7284___24t(V0__R,V7__req)
=> ( ! [V8__x] :
( t(V8__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
=> ( ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
=> ( ! [V10__x] :
( t(V10__x,V0__R)
=> ! [V11__y] :
( t(V11__y,V0__R)
=> ! [V12__z] :
( t(V12__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
=> ( ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
=> ( ! [V12__x] :
( t(V12__x,V0__R)
=> ! [V13__y] :
( t(V13__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ! [V15__z] :
( t(V15__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
=> ( ! [V14__x] :
( t(V14__x,V0__R)
=> ! [V15__y] :
( t(V15__y,V0__R)
=> ! [V16__z] :
( t(V16__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
=> ( ! [V15__x] :
( t(V15__x,V0__R)
=> ! [V16__y] :
( t(V16__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
=> ( ! [V16__x] :
( t(V16__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_srt',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__7270___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__7270___24t(V0__R,V4__rmul)
=> ! [V5__req] :
( c_24__type__7284___24t(V0__R,V5__req)
=> ( ! [V6__n] :
( t(V6__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V1__rO),V6__n)),V6__n)) )
=> ( ! [V7__n] :
( t(V7__n,V0__R)
=> ! [V8__m] :
( t(V8__m,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V7__n),V8__m)),happ(happ(V3__radd,V8__m),V7__n))) ) )
=> ( ! [V8__n] :
( t(V8__n,V0__R)
=> ! [V9__m] :
( t(V9__m,V0__R)
=> ! [V10__p] :
( t(V10__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V3__radd,V8__n),happ(happ(V3__radd,V9__m),V10__p))),happ(happ(V3__radd,happ(happ(V3__radd,V8__n),V9__m)),V10__p))) ) ) )
=> ( ! [V9__n] :
( t(V9__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V2__rI),V9__n)),V9__n)) )
=> ( ! [V10__n] :
( t(V10__n,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V1__rO),V10__n)),V1__rO)) )
=> ( ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V11__n),V12__m)),happ(happ(V4__rmul,V12__m),V11__n))) ) )
=> ( ! [V12__n] :
( t(V12__n,V0__R)
=> ! [V13__m] :
( t(V13__m,V0__R)
=> ! [V14__p] :
( t(V14__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,V12__n),happ(happ(V4__rmul,V13__m),V14__p))),happ(happ(V4__rmul,happ(happ(V4__rmul,V12__n),V13__m)),V14__p))) ) ) )
=> ( ! [V13__n] :
( t(V13__n,V0__R)
=> ! [V14__m] :
( t(V14__m,V0__R)
=> ! [V15__p] :
( t(V15__p,V0__R)
=> p(happ(happ(V5__req,happ(happ(V4__rmul,happ(happ(V3__radd,V13__n),V14__m)),V15__p)),happ(happ(V3__radd,happ(happ(V4__rmul,V13__n),V15__p)),happ(happ(V4__rmul,V14__m),V15__p)))) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('HahnSets.SetProperties.set_subsetE',axiom,
! [V0__s] :
( c_24__type__35378___24t(V0__s)
=> ! [V1__s_27] :
( c_24__type__35378___24t(V1__s_27)
=> ( cHahnSets_2eset__subset___24a3(cA,V0__s,V1__s_27)
<=> cHahnSets_2eset__equiv___24a3(cA,cHahnSets_2eset__minus___24a3(cA,V0__s,V1__s_27),cHahnSets_2eset__empty___24a1(cA)) ) ) ) ).
fof('HahnSets.SetProperties.set_subset_eq',axiom,
! [V0__P] :
( c_24__type__35378___24t(V0__P)
=> ! [V1__a] :
( cA___24t(V1__a)
=> ( p(happ(V0__P,V1__a))
=> cHahnSets_2eset__subset___24a3(cA,c_3d___24a2(cA,V1__a),V0__P) ) ) ) ).
fof('$adef_HahnSets.set_empty_$a1',axiom,
! [V_24X1] : happ(cHahnSets_2eset__empty,V_24X1) = cHahnSets_2eset__empty___24a1(V_24X1) ).
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('$adef_Coq.Logic.ChoiceFacts.FunctionalChoice_on_$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('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
<=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
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('$adef_Coq.Arith.Even.even_$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('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$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('$adef_$_case_Coq.Numbers.BinNums.Z$29213_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2429213,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2429213___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.le_AsB_$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_2ele__AsB,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$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('$adef_Coq.NArith.BinNatDef.N.testbit_$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('$adef_$_lam_20012_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20012,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20012___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.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.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_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_$_lam_32566_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__32566,V_24X1),V_24X2) = c_24__lam__32566___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('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$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('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).
fof('$adef_$_lam_35262_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__35262,V_24X1),V_24X2) = c_24__lam__35262___24a2(V_24X1,V_24X2) ).
fof('$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.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.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.Init.Decimal.nzhead_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).
fof('$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.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.NArith.BinNatDef.N.succ_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V_24X1) ).
fof('$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.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_$_lam_26198_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__26198,V_24X1),V_24X2) = c_24__lam__26198___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$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('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).
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('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.Forall_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eVectors_2eVectorDef_2eForall___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_HahnSets.set_compl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnSets_2eset__compl,V_24X1),V_24X2),V_24X3))
<=> cHahnSets_2eset__compl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZCoeff.gen_order_phi_Z_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.Cj_$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('$adef_HahnSets.set_disjoint_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnSets_2eset__disjoint,V_24X1),V_24X2),V_24X3))
<=> cHahnSets_2eset__disjoint___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('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$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('$adef_$_case_Coq.Init.Datatypes.list$19559_$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_2419559,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419559___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_var_6_p_12650_12653_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__12650__12653,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__12650__12653___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_fix_19691_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__19691__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__19691__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_30905_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__30905,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__30905___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.setoid_ring.InitialRing.gen_phiZ_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_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_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_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.Sets.Relations_1.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_35255_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35255,V_24X1) = c_24__lam__35255___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.D_$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('$adef_Coq.Arith.Between.P_nth_$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('$adef_Coq.Init.Datatypes.prod_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$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('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.Exc_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___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('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.Vectors.VectorDef.Forall2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_HahnSets.set_minus_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnSets_2eset__minus,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnSets_2eset__minus___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('$adef_Coq.setoid_ring.Field_theory.FEdiv_$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('$adef_Coq.ZArith.BinIntDef.Z.compare_$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('$adef_Coq.Logic.ChoiceFacts.SimpleSetoidFunctionalChoice_on_$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('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$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_32593_$a1',axiom,
! [V_24X1] : happ(c_24__prop__32593,V_24X1) = c_24__prop__32593___24a1(V_24X1) ).
fof('$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_HahnSets.set_subset_$a1',axiom,
! [V_24X1] : happ(cHahnSets_2eset__subset,V_24X1) = cHahnSets_2eset__subset___24a1(V_24X1) ).
fof('$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.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.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.setoid_ring.InitialRing.gen_phiZ_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.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_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_$_prop_30595_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__30595,V_24X1),V_24X2) = c_24__prop__30595___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.Decimal_$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('$adef_$_prop_30609_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__30609,V_24X1),V_24X2) = c_24__prop__30609___24a2(V_24X1,V_24X2) ).
fof('$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.ZArith.BinIntDef.Z.leb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.lexprod_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2elexprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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_$_lam_20004_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20004,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20004___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Numbers.BinNums.positive$32314_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2432314,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2432314___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$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('$adef_Coq.Bool.Bool.eqb_$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('$adef_Coq.Relations.Relation_Operators.symprod_$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('$adef_hahn.HahnBase.is_true_$a1',axiom,
! [V_24X1] :
( p(happ(chahn_2eHahnBase_2eis__true,V_24X1))
<=> chahn_2eHahnBase_2eis__true___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.compat_op_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__op,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2ecompat__op___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$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('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_$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('$adef_HahnSets.set_union_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnSets_2eset__union,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnSets_2eset__union___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Logic.ChoiceFacts.DependentFunctionalChoice_on_$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('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.last_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$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('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$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('$adef_Coq.Vectors.VectorDef.Exists_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eExists,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eVectors_2eVectorDef_2eExists___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_20012_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20012,V_24X1),V_24X2),V_24X3) = c_24__lam__20012___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_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.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.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.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_$_prop_30589_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__30589,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__30589___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$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('$adef_Coq.Arith.Between.between_$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('$adef_$_lam_30905_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__30905,V_24X1),V_24X2),V_24X3) = c_24__lam__30905___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_prop_30592_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30592,V_24X1),V_24X2),V_24X3) = c_24__prop__30592___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Vectors.VectorDef.t_$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('$adef_HahnSets.set_inter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cHahnSets_2eset__inter,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cHahnSets_2eset__inter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$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('$adef_Coq.Arith.Plus.tail_plus_$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('$adef_Coq.setoid_ring.Field_theory.FEopp_$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('$adef_HahnSets.set_collect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnSets_2eset__collect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnSets_2eset__collect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.RingMicromega.cneqb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecneqb,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$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('$adef_Coq.Init.Specif.exist2_$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('$adef_Coq.Sets.Relations_1.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.micromega.RingMicromega.SORaddon_$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('$adef_Coq.Strings.String.String_$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('$adef_$_lam_30913_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__30913,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__30913___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_30913_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__30913,V_24X1),V_24X2),V_24X3) = c_24__lam__30913___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Nat.square_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esquare,V_24X1) = cCoq_2eInit_2eNat_2esquare___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$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('$adef_Coq.Classes.Morphisms.respectful_$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('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
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('$adef_$_prop_30590_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30590,V_24X1),V_24X2),V_24X3) = c_24__prop__30590___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.Sets.Relations_1.Preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2ePreorder,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2ePreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.GuardedFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eGuardedFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eGuardedFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_fix_32330_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__32330__v__CANONICAL__0,V_24X1) = c_24__fix__32330__v__CANONICAL__0___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('$adef_Coq.Init.Nat.leb_$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('$adef_Coq.Init.Datatypes.id_$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('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$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('$adef_Coq.Reals.Rdefinitions.Rle_$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('$adef_hahn.HahnBase.Equality.Pack_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnBase_2eEquality_2ePack,V_24X1),V_24X2),V_24X3) = chahn_2eHahnBase_2eEquality_2ePack___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_26198_$a1',axiom,
! [V_24X1] : happ(c_24__lam__26198,V_24X1) = c_24__lam__26198___24a1(V_24X1) ).
fof('$adef_$_lam_35266_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35266,V_24X1) = c_24__lam__35266___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.TFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_35184_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35184,V_24X1) = c_24__lam__35184___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_$_lam_20020_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__20020,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__20020___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.eqb_$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('$adef_Coq.Setoids.Setoid.Setoid_Theory_$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('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Peano.ge_$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('$adef_Hammer.Tactics.Reconstr.rdone_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.In_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eIn,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eVectors_2eVectorDef_2eIn___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('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_prop_30594_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30594,V_24X1),V_24X2),V_24X3) = c_24__prop__30594___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_prop_30610_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30610,V_24X1),V_24X2),V_24X3) = c_24__prop__30610___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Subset_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$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('$adef_Coq.ZArith.BinInt.Z.b2z_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinInt_2eZ_2eb2z,V_24X1) = cCoq_2eZArith_2eBinInt_2eZ_2eb2z___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.Tauto.A_$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('$adef_Coq.micromega.ZMicromega.Zdivide_pol_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eZdivide__pol,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.Relations.Relation_Definitions.reflexive_$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('$adef_$_lam_35255_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__35255,V_24X1),V_24X2) = c_24__lam__35255___24a2(V_24X1,V_24X2) ).
fof('$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.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.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.Init.Logic.inhabited_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic_2einhabited,V_24X1))
<=> cCoq_2eInit_2eLogic_2einhabited___24a1(V_24X1) ) ).
fof('$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.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.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.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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.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.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.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_$_lam_19996_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__19996,V_24X1),V_24X2),V_24X3) = c_24__lam__19996___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$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('$adef_Coq.micromega.Tauto.GFormula_$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('$adef_Coq.Numbers.BinNums.Npos_$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('$adef_Coq.Init.Specif.exist_$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] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35346_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35346,V_24X1),V_24X2) = c_24__prop__35346___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_35184_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__35184,V_24X1),V_24X2) = c_24__lam__35184___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('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
<=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.inleft_$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('$adef_Coq.Structures.GenericMinMax.gmax_$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('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Wf_nat.gtof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2egtof,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eArith_2eWf__nat_2egtof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.CPlus_$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('$adef_Coq.Init.Datatypes.cons_$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('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.equiv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequiv,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$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('$adef_Coq.Logic.ChoiceFacts.OmniscientFunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eOmniscientFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eOmniscientFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$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('$adef_Coq.Init.Decimal.int_of_int_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eint__of__int,V_24X1) = cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_19996_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__19996,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__19996___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_32566_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__32566,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__32566___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.max_$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('$adef_Coq.Vectors.VectorDef.Exists2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eExists2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eVectors_2eVectorDef_2eExists2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.Some_$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('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_hahn.HahnBase.Equality.mixin_of_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eEquality_2emixin__of,V_24X1) = chahn_2eHahnBase_2eEquality_2emixin__of___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Even.odd_$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('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
<=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.add_$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('$adef_HahnSets.set_bunion_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnSets_2eset__bunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnSets_2eset__bunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_Coq.Structures.OrderedType.Compare_$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('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$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('$adef_hahn.HahnBase.Equality.Mixin_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnBase_2eEquality_2eMixin,V_24X1),V_24X2),V_24X3) = chahn_2eHahnBase_2eEquality_2eMixin___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$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('$adef_$_case_Coq.Init.Datatypes.list$19646_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2419646,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2419646___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
<=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$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('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$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('$adef_Coq.Bool.Bool.ReflectT_$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('$adef_Coq.Init.Specif.right_$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('$adef_Coq.Lists.List.Forall_$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('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Add_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CMinus_$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('$adef_Coq.ZArith.Zlogarithm.log_inf_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___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('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$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('$adef_Coq.setoid_ring.Field_theory.FEadd_$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('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalFacts.has_fixpoint_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint,V_24X1))
<=> cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.S_$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('$adef_Coq.micromega.VarMap.Empty_$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('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.DecimalExp_$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('$adef_hahn.HahnBase.eqn_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnBase_2eeqn__rec,V_24X1),V_24X2) = chahn_2eHahnBase_2eeqn__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_HahnSets.set_equiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnSets_2eset__equiv,V_24X1),V_24X2),V_24X3))
<=> cHahnSets_2eset__equiv___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('$adef_$_case_Coq.Init.Datatypes.nat$29196_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2429196,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2429196___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).
fof('$adef_$_prop_32709_$a1',axiom,
! [V_24X1] : happ(c_24__prop__32709,V_24X1) = c_24__prop__32709___24a1(V_24X1) ).
fof('$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.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.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_HahnSets.set_empty_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnSets_2eset__empty,V_24X1),V_24X2))
<=> cHahnSets_2eset__empty___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_35262_$a1',axiom,
! [V_24X1] : happ(c_24__lam__35262,V_24X1) = c_24__lam__35262___24a1(V_24X1) ).
fof('$adef_$_lam_20020_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20020,V_24X1),V_24X2),V_24X3) = c_24__lam__20020___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.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.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.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.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_$_prop_30593_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30593,V_24X1),V_24X2),V_24X3) = c_24__prop__30593___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('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$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('$adef_$_case_Coq.Init.Datatypes.nat$29218_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2429218___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('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Lists.List.tl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eLists_2eList_2etl,V_24X1),V_24X2) = cCoq_2eLists_2eList_2etl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalCountableChoice_on_$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('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_HahnSets.set_minus_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnSets_2eset__minus,V_24X1),V_24X2),V_24X3) = cHahnSets_2eset__minus___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_20004_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__20004,V_24X1),V_24X2),V_24X3) = c_24__lam__20004___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_var_6_p_12652_12654_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__12652__12654,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__12652__12654___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Init.Specif.left_$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('$adef_Coq.setoid_ring.Field_theory.FEinv_$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('$adef_Coq.Init.Specif.sigT_$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('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$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('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_HahnSets.set_full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHahnSets_2eset__full,V_24X1),V_24X2))
<=> cHahnSets_2eset__full___24a2(V_24X1,V_24X2) ) ).
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('$adef_Coq.ZArith.BinInt.Z.ge_$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('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$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('$adef_HahnSets.set_subset_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cHahnSets_2eset__subset,V_24X1),V_24X2),V_24X3))
<=> cHahnSets_2eset__subset___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_prop_30591_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30591,V_24X1),V_24X2),V_24X3) = c_24__prop__30591___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Relations_1.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2ePER,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.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.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.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.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$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.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.Init.Datatypes.length_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.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.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.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.Vectors.Fin.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).
fof('$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.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_$_case_Coq.Init.Datatypes.prod$24453_$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_2424453,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_2424453___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_30611_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__30611,V_24X1),V_24X2),V_24X3) = c_24__prop__30611___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.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.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.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_16207',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__16207___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__16207___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30762',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30762___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30762___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35306',axiom,
! [V_24Y] :
( c_24__type__35306___24t(V_24Y)
<=> t(V_24Y,c_24__type__35306) ) ).
fof('$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('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24947',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24947___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24947___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34882',axiom,
! [V_24Y] :
( c_24__type__34882___24t(V_24Y)
<=> t(V_24Y,c_24__type__34882) ) ).
fof('$tdef_$_type_26423',axiom,
! [V_24Y] :
( c_24__type__26423___24t(V_24Y)
<=> t(V_24Y,c_24__type__26423) ) ).
fof('$tdef_$_type_35201',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35201___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35201___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21674',axiom,
! [V_24Y] :
( c_24__type__21674___24t(V_24Y)
<=> t(V_24Y,c_24__type__21674) ) ).
fof('$tdef_$_type_20723',axiom,
! [V_24Y] :
( c_24__type__20723___24t(V_24Y)
<=> t(V_24Y,c_24__type__20723) ) ).
fof('$tdef_$_type_2853',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__2853___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__2853___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_12077',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__12077___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__12077___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_10408',axiom,
! [V_24Y] :
( c_24__type__10408___24t(V_24Y)
<=> t(V_24Y,c_24__type__10408) ) ).
fof('$tdef_$_type_24874',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24874___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24874___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34663',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34663___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34663___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30624',axiom,
! [V_24Y] :
( c_24__type__30624___24t(V_24Y)
<=> t(V_24Y,c_24__type__30624) ) ).
fof('$tdef_$_type_19038',axiom,
! [V_24Y] :
( c_24__type__19038___24t(V_24Y)
<=> t(V_24Y,c_24__type__19038) ) ).
fof('$tdef_$_type_24390',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24390___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24390___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_2507',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__2507___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__2507___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_29665',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__29665___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__29665___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_15671',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15671___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15671___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_28218',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__28218___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__28218___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.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_$_type_23798',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23798___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23798___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10141',axiom,
! [V_24Y] :
( c_24__type__10141___24t(V_24Y)
<=> t(V_24Y,c_24__type__10141) ) ).
fof('$tdef_$_type_34706',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34706___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34706___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_14575',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14575___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14575___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29962',axiom,
! [V_24Y] :
( c_24__type__29962___24t(V_24Y)
<=> t(V_24Y,c_24__type__29962) ) ).
fof('$tdef_$_type_20852',axiom,
! [V_24Y] :
( c_24__type__20852___24t(V_24Y)
<=> t(V_24Y,c_24__type__20852) ) ).
fof('$tdef_$_type_26282',axiom,
! [V_24Y] :
( c_24__type__26282___24t(V_24Y)
<=> t(V_24Y,c_24__type__26282) ) ).
fof('$tdef_$_type_23',axiom,
! [V_24Y] :
( c_24__type__23___24t(V_24Y)
<=> t(V_24Y,c_24__type__23) ) ).
fof('$tdef_$_type_27245',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27245___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__27245___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_14697',axiom,
! [V_24Y] :
( c_24__type__14697___24t(V_24Y)
<=> t(V_24Y,c_24__type__14697) ) ).
fof('$tdef_$_type_9617',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__9617___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__9617___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_19',axiom,
! [V_24Y] :
( c_24__type__19___24t(V_24Y)
<=> t(V_24Y,c_24__type__19) ) ).
fof('$tdef_$_type_9209',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__9209___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__9209___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('$tdef_hahn.HahnBase.Equality.axiom',axiom,
! [V_24X1,V_24X2,V_24Y] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2eaxiom___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13316',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13316___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13316___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_24198',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24198___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24198___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_12178',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__12178___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__12178___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25786',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__25786___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__25786___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Init.Datatypes.list',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13430',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13430___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13430___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_10050',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__10050___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__10050___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_32406',axiom,
! [V_24Y] :
( c_24__type__32406___24t(V_24Y)
<=> t(V_24Y,c_24__type__32406) ) ).
fof('$tdef_$_type_28902',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__28902___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__28902___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
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_7279',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7279___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7279___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29910',axiom,
! [V_24Y] :
( c_24__type__29910___24t(V_24Y)
<=> t(V_24Y,c_24__type__29910) ) ).
fof('$tdef_$_type_36',axiom,
! [V_24X1,V_24Y] :
( c_24__type__36___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__36___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32820',axiom,
! [V_24Y] :
( c_24__type__32820___24t(V_24Y)
<=> t(V_24Y,c_24__type__32820) ) ).
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_$_type_18813',axiom,
! [V_24Y] :
( c_24__type__18813___24t(V_24Y)
<=> t(V_24Y,c_24__type__18813) ) ).
fof('$tdef_$_type_23844',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23844___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23844___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_$_type_32093',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32093___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32093___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28547',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__28547___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__28547___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_33095',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33095___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33095___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32050',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__32050___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__32050___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_32559',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32559___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32559___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23629',axiom,
! [V_24Y] :
( c_24__type__23629___24t(V_24Y)
<=> t(V_24Y,c_24__type__23629) ) ).
fof('$tdef_$_type_10495',axiom,
! [V_24Y] :
( c_24__type__10495___24t(V_24Y)
<=> t(V_24Y,c_24__type__10495) ) ).
fof('$tdef_$_type_10404',axiom,
! [V_24Y] :
( c_24__type__10404___24t(V_24Y)
<=> t(V_24Y,c_24__type__10404) ) ).
fof('$tdef_$_type_10006',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__10006___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__10006___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_13098',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13098___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__13098___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30647',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30647___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30647___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32760',axiom,
! [V_24Y] :
( c_24__type__32760___24t(V_24Y)
<=> t(V_24Y,c_24__type__32760) ) ).
fof('$tdef_$_type_13161',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13161___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__13161___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_$_type_35172',axiom,
! [V_24Y] :
( c_24__type__35172___24t(V_24Y)
<=> t(V_24Y,c_24__type__35172) ) ).
fof('$tdef_$_type_26215',axiom,
! [V_24X1,V_24Y] :
( c_24__type__26215___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__26215___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24642',axiom,
! [V_24Y] :
( c_24__type__24642___24t(V_24Y)
<=> t(V_24Y,c_24__type__24642) ) ).
fof('$tdef_$_type_4214',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__4214___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__4214___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_28821',axiom,
! [V_24Y] :
( c_24__type__28821___24t(V_24Y)
<=> t(V_24Y,c_24__type__28821) ) ).
fof('$tdef_$_type_1782',axiom,
! [V_24Y] :
( c_24__type__1782___24t(V_24Y)
<=> t(V_24Y,c_24__type__1782) ) ).
fof('$tdef_$_type_32846',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32846___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32846___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32008',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__32008___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__32008___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_30668',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30668___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30668___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_34454',axiom,
! [V_24Y] :
( c_24__type__34454___24t(V_24Y)
<=> t(V_24Y,c_24__type__34454) ) ).
fof('$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_26749',axiom,
! [V_24Y] :
( c_24__type__26749___24t(V_24Y)
<=> t(V_24Y,c_24__type__26749) ) ).
fof('$tdef_$_type_24912',axiom,
! [V_24Y] :
( c_24__type__24912___24t(V_24Y)
<=> t(V_24Y,c_24__type__24912) ) ).
fof('$tdef_$_type_1938',axiom,
! [V_24Y] :
( c_24__type__1938___24t(V_24Y)
<=> t(V_24Y,c_24__type__1938) ) ).
fof('$tdef_$_type_12258',axiom,
! [V_24Y] :
( c_24__type__12258___24t(V_24Y)
<=> t(V_24Y,c_24__type__12258) ) ).
fof('$tdef_$_type_19361',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__19361___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__19361___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_7949',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__7949___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__7949___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_34124',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34124___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34124___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
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_$_type_32794',axiom,
! [V_24Y] :
( c_24__type__32794___24t(V_24Y)
<=> t(V_24Y,c_24__type__32794) ) ).
fof('$tdef_$_type_32383',axiom,
! [V_24Y] :
( c_24__type__32383___24t(V_24Y)
<=> t(V_24Y,c_24__type__32383) ) ).
fof('$tdef_$_type_35378',axiom,
! [V_24Y] :
( c_24__type__35378___24t(V_24Y)
<=> t(V_24Y,c_24__type__35378) ) ).
fof('$tdef_$_type_34451',axiom,
! [V_24Y] :
( c_24__type__34451___24t(V_24Y)
<=> t(V_24Y,c_24__type__34451) ) ).
fof('$tdef_$_type_23867',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23867___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23867___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30745',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30745___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30745___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__32684___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__32684___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30732',axiom,
! [V_24Y] :
( c_24__type__30732___24t(V_24Y)
<=> t(V_24Y,c_24__type__30732) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_$_type_29920',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29920___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29920___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_hahn.HahnBase.Equality.mixin_of',axiom,
! [V_24X1,V_24Y] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2emixin__of___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21696',axiom,
! [V_24Y] :
( c_24__type__21696___24t(V_24Y)
<=> t(V_24Y,c_24__type__21696) ) ).
fof('$tdef_$_type_26675',axiom,
! [V_24Y] :
( c_24__type__26675___24t(V_24Y)
<=> t(V_24Y,c_24__type__26675) ) ).
fof('$tdef_$_type_10094',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__10094___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__10094___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_26',axiom,
! [V_24Y] :
( c_24__type__26___24t(V_24Y)
<=> t(V_24Y,c_24__type__26) ) ).
fof('$tdef_$_type_1728',axiom,
! [V_24Y] :
( c_24__type__1728___24t(V_24Y)
<=> t(V_24Y,c_24__type__1728) ) ).
fof('$tdef_$_type_10455',axiom,
! [V_24Y] :
( c_24__type__10455___24t(V_24Y)
<=> t(V_24Y,c_24__type__10455) ) ).
fof('$tdef_$_type_13370',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13370___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13370___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_26290',axiom,
! [V_24Y] :
( c_24__type__26290___24t(V_24Y)
<=> t(V_24Y,c_24__type__26290) ) ).
fof('$tdef_$_type_1804',axiom,
! [V_24Y] :
( c_24__type__1804___24t(V_24Y)
<=> t(V_24Y,c_24__type__1804) ) ).
fof('$tdef_$_type_28673',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__28673___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__28673___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_33013',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__33013___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__33013___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_30769',axiom,
! [V_24Y] :
( c_24__type__30769___24t(V_24Y)
<=> t(V_24Y,c_24__type__30769) ) ).
fof('$tdef_$_type_1745',axiom,
! [V_24Y] :
( c_24__type__1745___24t(V_24Y)
<=> t(V_24Y,c_24__type__1745) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32732',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32732___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32732___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29626',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__29626___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__29626___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
! [V_24Y] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).
fof('$tdef_$_type_17858',axiom,
! [V_24Y] :
( c_24__type__17858___24t(V_24Y)
<=> t(V_24Y,c_24__type__17858) ) ).
fof('$tdef_$_type_14636',axiom,
! [V_24Y] :
( c_24__type__14636___24t(V_24Y)
<=> t(V_24Y,c_24__type__14636) ) ).
fof('$tdef_$_type_9812',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__9812___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__9812___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_34909',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34909___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34909___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_33805',axiom,
! [V_24Y] :
( c_24__type__33805___24t(V_24Y)
<=> t(V_24Y,c_24__type__33805) ) ).
fof('$tdef_$_type_12664',axiom,
! [V_24Y] :
( c_24__type__12664___24t(V_24Y)
<=> t(V_24Y,c_24__type__12664) ) ).
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_$_type_30018',axiom,
! [V_24Y] :
( c_24__type__30018___24t(V_24Y)
<=> t(V_24Y,c_24__type__30018) ) ).
fof('$tdef_$_type_35220',axiom,
! [V_24Y] :
( c_24__type__35220___24t(V_24Y)
<=> t(V_24Y,c_24__type__35220) ) ).
fof('$tdef_$_type_32776',axiom,
! [V_24Y] :
( c_24__type__32776___24t(V_24Y)
<=> t(V_24Y,c_24__type__32776) ) ).
fof('$tdef_$_type_30703',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__30703___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__30703___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_7259',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__7259___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__7259___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_10511',axiom,
! [V_24Y] :
( c_24__type__10511___24t(V_24Y)
<=> t(V_24Y,c_24__type__10511) ) ).
fof('$tdef_$_type_9926',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9926___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9926___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_34856',axiom,
! [V_24Y] :
( c_24__type__34856___24t(V_24Y)
<=> t(V_24Y,c_24__type__34856) ) ).
fof('$tdef_$_type_32910',axiom,
! [V_24Y] :
( c_24__type__32910___24t(V_24Y)
<=> t(V_24Y,c_24__type__32910) ) ).
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_$_type_13454',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13454___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13454___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9970',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9970___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9970___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_13487',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13487___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13487___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32083',axiom,
! [V_24Y] :
( c_24__type__32083___24t(V_24Y)
<=> t(V_24Y,c_24__type__32083) ) ).
fof('$tdef_$_type_33754',axiom,
! [V_24Y] :
( c_24__type__33754___24t(V_24Y)
<=> t(V_24Y,c_24__type__33754) ) ).
fof('$tdef_$_type_7294',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7294___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7294___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29225',axiom,
! [V_24Y] :
( c_24__type__29225___24t(V_24Y)
<=> t(V_24Y,c_24__type__29225) ) ).
fof('$tdef_$_type_32360',axiom,
! [V_24Y] :
( c_24__type__32360___24t(V_24Y)
<=> t(V_24Y,c_24__type__32360) ) ).
fof('$tdef_$_type_34830',axiom,
! [V_24Y] :
( c_24__type__34830___24t(V_24Y)
<=> t(V_24Y,c_24__type__34830) ) ).
fof('$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_3199',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__3199___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__3199___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_13907',axiom,
! [V_24Y] :
( c_24__type__13907___24t(V_24Y)
<=> t(V_24Y,c_24__type__13907) ) ).
fof('$tdef_$_type_8783',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__8783___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__8783___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).
fof('$tdef_$_type_35014',axiom,
! [V_24Y] :
( c_24__type__35014___24t(V_24Y)
<=> t(V_24Y,c_24__type__35014) ) ).
fof('$tdef_$_type_32412',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32412___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32412___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_14621',axiom,
! [V_24Y] :
( c_24__type__14621___24t(V_24Y)
<=> t(V_24Y,c_24__type__14621) ) ).
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_35239',axiom,
! [V_24Y] :
( c_24__type__35239___24t(V_24Y)
<=> t(V_24Y,c_24__type__35239) ) ).
fof('$tdef_$_type_24298',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24298___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24298___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_23821',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23821___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23821___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_33761',axiom,
! [V_24Y] :
( c_24__type__33761___24t(V_24Y)
<=> t(V_24Y,c_24__type__33761) ) ).
fof('$tdef_$_type_13792',axiom,
! [V_24Y] :
( c_24__type__13792___24t(V_24Y)
<=> t(V_24Y,c_24__type__13792) ) ).
fof('$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_35313',axiom,
! [V_24Y] :
( c_24__type__35313___24t(V_24Y)
<=> t(V_24Y,c_24__type__35313) ) ).
fof('$tdef_$_type_32851',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32851___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32851___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_$_type_35168',axiom,
! [V_24Y] :
( c_24__type__35168___24t(V_24Y)
<=> t(V_24Y,c_24__type__35168) ) ).
fof('$tdef_$_type_19161',axiom,
! [V_24Y] :
( c_24__type__19161___24t(V_24Y)
<=> t(V_24Y,c_24__type__19161) ) ).
fof('$tdef_$_type_15764',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15764___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15764___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_5252',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__5252___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__5252___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_32862',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32862___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32862___24a1(V_24X1)) ) ).
fof('$tdef_$_type_5575',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__5575___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__5575___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_34017',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34017___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34017___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_17855',axiom,
! [V_24Y] :
( c_24__type__17855___24t(V_24Y)
<=> t(V_24Y,c_24__type__17855) ) ).
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_$_type_32181',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32181___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32181___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_34262',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34262___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34262___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_15',axiom,
! [V_24Y] :
( c_24__type__15___24t(V_24Y)
<=> t(V_24Y,c_24__type__15) ) ).
fof('$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('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_30713',axiom,
! [V_24Y] :
( c_24__type__30713___24t(V_24Y)
<=> t(V_24Y,c_24__type__30713) ) ).
fof('$tdef_$_type_9404',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__9404___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__9404___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_7270',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7270___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7270___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13400___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_30711',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__30711___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__30711___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32942',axiom,
! [V_24Y] :
( c_24__type__32942___24t(V_24Y)
<=> t(V_24Y,c_24__type__32942) ) ).
fof('$tdef_$_type_10464',axiom,
! [V_24Y] :
( c_24__type__10464___24t(V_24Y)
<=> t(V_24Y,c_24__type__10464) ) ).
fof('$tdef_$_type_27857',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__27857___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__27857___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_89',axiom,
! [V_24Y] :
( c_24__type__89___24t(V_24Y)
<=> t(V_24Y,c_24__type__89) ) ).
fof('$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_24833',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__24833___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__24833___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_33139',axiom,
! [V_24Y] :
( c_24__type__33139___24t(V_24Y)
<=> t(V_24Y,c_24__type__33139) ) ).
fof('$tdef_$_type_32800',axiom,
! [V_24Y] :
( c_24__type__32800___24t(V_24Y)
<=> t(V_24Y,c_24__type__32800) ) ).
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_34430',axiom,
! [V_24Y] :
( c_24__type__34430___24t(V_24Y)
<=> t(V_24Y,c_24__type__34430) ) ).
fof('$tdef_$_type_33779',axiom,
! [V_24Y] :
( c_24__type__33779___24t(V_24Y)
<=> t(V_24Y,c_24__type__33779) ) ).
fof('$tdef_$_type_35005',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__35005___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__35005___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_33752',axiom,
! [V_24Y] :
( c_24__type__33752___24t(V_24Y)
<=> t(V_24Y,c_24__type__33752) ) ).
fof('$tdef_$_type_10123',axiom,
! [V_24Y] :
( c_24__type__10123___24t(V_24Y)
<=> t(V_24Y,c_24__type__10123) ) ).
fof('$tdef_$_type_7308',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7308___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7308___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35301',axiom,
! [V_24Y] :
( c_24__type__35301___24t(V_24Y)
<=> t(V_24Y,c_24__type__35301) ) ).
fof('$tdef_$_type_24248',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24248___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24248___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_24573',axiom,
! [V_24Y] :
( c_24__type__24573___24t(V_24Y)
<=> t(V_24Y,c_24__type__24573) ) ).
fof('$tdef_$_type_31522',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__31522___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__31522___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('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_$_type_1972',axiom,
! [V_24Y] :
( c_24__type__1972___24t(V_24Y)
<=> t(V_24Y,c_24__type__1972) ) ).
fof('$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_24774',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24774___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24774___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_11146',axiom,
! [V_24Y] :
( c_24__type__11146___24t(V_24Y)
<=> t(V_24Y,c_24__type__11146) ) ).
fof('$tdef_$_type_6913',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__6913___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__6913___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_34822',axiom,
! [V_24Y] :
( c_24__type__34822___24t(V_24Y)
<=> t(V_24Y,c_24__type__34822) ) ).
fof('$tdef_$_type_32241',axiom,
! [V_24Y] :
( c_24__type__32241___24t(V_24Y)
<=> t(V_24Y,c_24__type__32241) ) ).
fof('$tdef_$_type_26390',axiom,
! [V_24Y] :
( c_24__type__26390___24t(V_24Y)
<=> t(V_24Y,c_24__type__26390) ) ).
fof('$tdef_$_type_27950',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__27950___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__27950___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_26334',axiom,
! [V_24Y] :
( c_24__type__26334___24t(V_24Y)
<=> t(V_24Y,c_24__type__26334) ) ).
fof('$tdef_$_type_32750',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32750___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32750___24a1(V_24X1)) ) ).
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_$_type_34873',axiom,
! [V_24Y] :
( c_24__type__34873___24t(V_24Y)
<=> t(V_24Y,c_24__type__34873) ) ).
fof('$tdef_$_type_21691',axiom,
! [V_24Y] :
( c_24__type__21691___24t(V_24Y)
<=> t(V_24Y,c_24__type__21691) ) ).
fof('$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_$_type_30718',axiom,
! [V_24Y] :
( c_24__type__30718___24t(V_24Y)
<=> t(V_24Y,c_24__type__30718) ) ).
fof('$tdef_$_type_34428',axiom,
! [V_24Y] :
( c_24__type__34428___24t(V_24Y)
<=> t(V_24Y,c_24__type__34428) ) ).
fof('$tdef_$_type_28300',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__28300___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__28300___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32150',axiom,
! [V_24Y] :
( c_24__type__32150___24t(V_24Y)
<=> t(V_24Y,c_24__type__32150) ) ).
fof('$tdef_$_type_27362',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27362___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27362___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_$_type_19066',axiom,
! [V_24Y] :
( c_24__type__19066___24t(V_24Y)
<=> t(V_24Y,c_24__type__19066) ) ).
fof('$tdef_$_type_28043',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__28043___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__28043___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32840',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32840___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32840___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26679',axiom,
! [V_24Y] :
( c_24__type__26679___24t(V_24Y)
<=> t(V_24Y,c_24__type__26679) ) ).
fof('$tdef_$_type_28610',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__28610___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__28610___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21682',axiom,
! [V_24Y] :
( c_24__type__21682___24t(V_24Y)
<=> t(V_24Y,c_24__type__21682) ) ).
fof('$tdef_$_type_21677',axiom,
! [V_24Y] :
( c_24__type__21677___24t(V_24Y)
<=> t(V_24Y,c_24__type__21677) ) ).
fof('$tdef_$_type_34630',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34630___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34630___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29587',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__29587___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__29587___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_31272',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__31272___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__31272___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_32791',axiom,
! [V_24Y] :
( c_24__type__32791___24t(V_24Y)
<=> t(V_24Y,c_24__type__32791) ) ).
fof('$tdef_$_type_35196',axiom,
! [V_24Y] :
( c_24__type__35196___24t(V_24Y)
<=> t(V_24Y,c_24__type__35196) ) ).
fof('$tdef_$_type_13538',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13538___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13538___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32755',axiom,
! [V_24Y] :
( c_24__type__32755___24t(V_24Y)
<=> t(V_24Y,c_24__type__32755) ) ).
fof('$tdef_$_type_13044',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__13044___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__13044___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_6267',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__6267___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__6267___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.micromega.ZMicromega.coneMember',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32835',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32835___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32835___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31897',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__31897___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__31897___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_32351',axiom,
! [V_24Y] :
( c_24__type__32351___24t(V_24Y)
<=> t(V_24Y,c_24__type__32351) ) ).
fof('$tdef_$_type_24466',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24466___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24466___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30010',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30010___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30010___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_13346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13346___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15939',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15939___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15939___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_A',axiom,
! [V_24Y] :
( cA___24t(V_24Y)
<=> t(V_24Y,cA) ) ).
fof('$tdef_$_type_32429',axiom,
! [V_24Y] :
( c_24__type__32429___24t(V_24Y)
<=> t(V_24Y,c_24__type__32429) ) ).
fof('$tdef_$_type_27653',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__27653___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__27653___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_32613',axiom,
! [V_24X1,V_24Y] :
( c_24__type__32613___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__32613___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24340',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__24340___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__24340___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_11583',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__11583___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__11583___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34746',axiom,
! [V_24Y] :
( c_24__type__34746___24t(V_24Y)
<=> t(V_24Y,c_24__type__34746) ) ).
fof('$tdef_$_type_44',axiom,
! [V_24Y] :
( c_24__type__44___24t(V_24Y)
<=> t(V_24Y,c_24__type__44) ) ).
fof('$tdef_$_type_30996',axiom,
! [V_24Y] :
( c_24__type__30996___24t(V_24Y)
<=> t(V_24Y,c_24__type__30996) ) ).
fof('$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_34287',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34287___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34287___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_27503',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27503___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27503___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32825',axiom,
! [V_24Y] :
( c_24__type__32825___24t(V_24Y)
<=> t(V_24Y,c_24__type__32825) ) ).
fof('$tdef_$_type_11785',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__11785___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__11785___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34422',axiom,
! [V_24Y] :
( c_24__type__34422___24t(V_24Y)
<=> t(V_24Y,c_24__type__34422) ) ).
fof('$tdef_$_type_30088',axiom,
! [V_24Y] :
( c_24__type__30088___24t(V_24Y)
<=> t(V_24Y,c_24__type__30088) ) ).
fof('$tdef_$_type_10411',axiom,
! [V_24Y] :
( c_24__type__10411___24t(V_24Y)
<=> t(V_24Y,c_24__type__10411) ) ).
fof('$tdef_$_type_16114',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__16114___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__16114___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25707',axiom,
! [V_24Y] :
( c_24__type__25707___24t(V_24Y)
<=> t(V_24Y,c_24__type__25707) ) ).
fof('$tdef_$_type_33117',axiom,
! [V_24Y] :
( c_24__type__33117___24t(V_24Y)
<=> t(V_24Y,c_24__type__33117) ) ).
fof('$tdef_$_type_17850',axiom,
! [V_24Y] :
( c_24__type__17850___24t(V_24Y)
<=> t(V_24Y,c_24__type__17850) ) ).
fof('$tdef_$_type_4560',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__4560___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__4560___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_34153',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34153___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34153___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_26955',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__26955___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__26955___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23929',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23929___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23929___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1962',axiom,
! [V_24Y] :
( c_24__type__1962___24t(V_24Y)
<=> t(V_24Y,c_24__type__1962) ) ).
fof('$tdef_$_type_31397',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__31397___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__31397___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_34939',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34939___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34939___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_33757',axiom,
! [V_24Y] :
( c_24__type__33757___24t(V_24Y)
<=> t(V_24Y,c_24__type__33757) ) ).
fof('$tdef_$_type_29954',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29954___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29954___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32899',axiom,
! [V_24Y] :
( c_24__type__32899___24t(V_24Y)
<=> t(V_24Y,c_24__type__32899) ) ).
fof('$tdef_$_type_10461',axiom,
! [V_24Y] :
( c_24__type__10461___24t(V_24Y)
<=> t(V_24Y,c_24__type__10461) ) ).
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_$_type_30993',axiom,
! [V_24Y] :
( c_24__type__30993___24t(V_24Y)
<=> t(V_24Y,c_24__type__30993) ) ).
fof('$tdef_$_type_7284',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7284___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7284___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14962',axiom,
! [V_24Y] :
( c_24__type__14962___24t(V_24Y)
<=> t(V_24Y,c_24__type__14962) ) ).
fof('$tdef_$_type_32778',axiom,
! [V_24Y] :
( c_24__type__32778___24t(V_24Y)
<=> t(V_24Y,c_24__type__32778) ) ).
fof('$tdef_$_type_7324',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7324___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7324___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_94',axiom,
! [V_24Y] :
( c_24__type__94___24t(V_24Y)
<=> t(V_24Y,c_24__type__94) ) ).
fof('$tdef_$_type_31014',axiom,
! [V_24Y] :
( c_24__type__31014___24t(V_24Y)
<=> t(V_24Y,c_24__type__31014) ) ).
fof('$tdef_$_type_32190',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32190___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32190___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_24930',axiom,
! [V_24Y] :
( c_24__type__24930___24t(V_24Y)
<=> t(V_24Y,c_24__type__24930) ) ).
fof('$tdef_$_type_13763',axiom,
! [V_24Y] :
( c_24__type__13763___24t(V_24Y)
<=> t(V_24Y,c_24__type__13763) ) ).
fof('$tdef_$_type_34794',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34794___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34794___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_14728',axiom,
! [V_24Y] :
( c_24__type__14728___24t(V_24Y)
<=> t(V_24Y,c_24__type__14728) ) ).
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_$_type_32621',axiom,
! [V_24Y] :
( c_24__type__32621___24t(V_24Y)
<=> t(V_24Y,c_24__type__32621) ) ).
fof('$tdef_$_type_13796',axiom,
! [V_24Y] :
( c_24__type__13796___24t(V_24Y)
<=> t(V_24Y,c_24__type__13796) ) ).
fof('$tdef_$_type_35276',axiom,
! [V_24Y] :
( c_24__type__35276___24t(V_24Y)
<=> t(V_24Y,c_24__type__35276) ) ).
fof('$tdef_$_type_32811',axiom,
! [V_24Y] :
( c_24__type__32811___24t(V_24Y)
<=> t(V_24Y,c_24__type__32811) ) ).
fof('$tdef_$_type_30809',axiom,
! [V_24Y] :
( c_24__type__30809___24t(V_24Y)
<=> t(V_24Y,c_24__type__30809) ) ).
fof('$tdef_$_type_5921',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__5921___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__5921___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_25865',axiom,
! [V_24X1,V_24Y] :
( c_24__type__25865___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__25865___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34190',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34190___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34190___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_1771',axiom,
! [V_24Y] :
( c_24__type__1771___24t(V_24Y)
<=> t(V_24Y,c_24__type__1771) ) ).
fof('$tdef_$_type_33060',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__33060___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__33060___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_24731',axiom,
! [V_24Y] :
( c_24__type__24731___24t(V_24Y)
<=> t(V_24Y,c_24__type__24731) ) ).
fof('$tdef_$_type_12918',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12918___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__12918___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_13758',axiom,
! [V_24Y] :
( c_24__type__13758___24t(V_24Y)
<=> t(V_24Y,c_24__type__13758) ) ).
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_hahn.HahnBase.Equality.type',axiom,
! [V_24Y] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2etype) ) ).
fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [V_24X1,V_24Y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_7736',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__7736___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__7736___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_11976',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__11976___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__11976___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_25797',axiom,
! [V_24Y] :
( c_24__type__25797___24t(V_24Y)
<=> t(V_24Y,c_24__type__25797) ) ).
fof('$tdef_$_type_14595',axiom,
! [V_24Y] :
( c_24__type__14595___24t(V_24Y)
<=> t(V_24Y,c_24__type__14595) ) ).
fof('$tdef_$_type_34380',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34380___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34380___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_11093',axiom,
! [V_24Y] :
( c_24__type__11093___24t(V_24Y)
<=> t(V_24Y,c_24__type__11093) ) ).
fof('$tdef_$_type_30002',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30002___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30002___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32745',axiom,
! [V_24Y] :
( c_24__type__32745___24t(V_24Y)
<=> t(V_24Y,c_24__type__32745) ) ).
fof('$tdef_$_type_34827',axiom,
! [V_24Y] :
( c_24__type__34827___24t(V_24Y)
<=> t(V_24Y,c_24__type__34827) ) ).
fof('$tdef_$_type_26210',axiom,
! [V_24Y] :
( c_24__type__26210___24t(V_24Y)
<=> t(V_24Y,c_24__type__26210) ) ).
fof('$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_14975',axiom,
! [V_24Y] :
( c_24__type__14975___24t(V_24Y)
<=> t(V_24Y,c_24__type__14975) ) ).
fof('$tdef_$_type_28727',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__28727___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__28727___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30756',axiom,
! [V_24Y] :
( c_24__type__30756___24t(V_24Y)
<=> t(V_24Y,c_24__type__30756) ) ).
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_$_type_8162',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8162___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8162___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_32772',axiom,
! [V_24Y] :
( c_24__type__32772___24t(V_24Y)
<=> t(V_24Y,c_24__type__32772) ) ).
fof('$tdef_$_type_28393',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__28393___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__28393___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_52',axiom,
! [V_24Y] :
( c_24__type__52___24t(V_24Y)
<=> t(V_24Y,c_24__type__52) ) ).
fof('$tdef_$_type_27455',axiom,
! [V_24Y] :
( c_24__type__27455___24t(V_24Y)
<=> t(V_24Y,c_24__type__27455) ) ).
fof('$tdef_$_type_10466',axiom,
! [V_24Y] :
( c_24__type__10466___24t(V_24Y)
<=> t(V_24Y,c_24__type__10466) ) ).
fof('$tdef_$_type_35209',axiom,
! [V_24Y] :
( c_24__type__35209___24t(V_24Y)
<=> t(V_24Y,c_24__type__35209) ) ).
fof('$tdef_$_type_14634',axiom,
! [V_24Y] :
( c_24__type__14634___24t(V_24Y)
<=> t(V_24Y,c_24__type__14634) ) ).
fof('$tdef_$_type_27182',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27182___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__27182___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_15475',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15475___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15475___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8357',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__8357___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__8357___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$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_21671',axiom,
! [V_24Y] :
( c_24__type__21671___24t(V_24Y)
<=> t(V_24Y,c_24__type__21671) ) ).
fof('$tdef_$_type_28921',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__28921___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__28921___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35269',axiom,
! [V_24Y] :
( c_24__type__35269___24t(V_24Y)
<=> t(V_24Y,c_24__type__35269) ) ).
fof('$tdef_$_type_10937',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10937___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10937___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_$_type_30752',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30752___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30752___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_$_type_35358',axiom,
! [V_24Y] :
( c_24__type__35358___24t(V_24Y)
<=> t(V_24Y,c_24__type__35358) ) ).
fof('$tdef_$_type_18837',axiom,
! [V_24Y] :
( c_24__type__18837___24t(V_24Y)
<=> t(V_24Y,c_24__type__18837) ) ).
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_$_type_1869',axiom,
! [V_24Y] :
( c_24__type__1869___24t(V_24Y)
<=> t(V_24Y,c_24__type__1869) ) ).
fof('$tdef_$_type_1809',axiom,
! [V_24Y] :
( c_24__type__1809___24t(V_24Y)
<=> t(V_24Y,c_24__type__1809) ) ).
fof('$tdef_$_type_31772',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__31772___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__31772___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_27308',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27308___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__27308___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_10401',axiom,
! [V_24Y] :
( c_24__type__10401___24t(V_24Y)
<=> t(V_24Y,c_24__type__10401) ) ).
fof('$tdef_$_type_29946',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29946___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29946___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32797',axiom,
! [V_24Y] :
( c_24__type__32797___24t(V_24Y)
<=> t(V_24Y,c_24__type__32797) ) ).
fof('$tdef_$_type_24953',axiom,
! [V_24Y] :
( c_24__type__24953___24t(V_24Y)
<=> t(V_24Y,c_24__type__24953) ) ).
fof('$tdef_$_type_34810',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34810___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34810___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24908',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__24908___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__24908___24a2(V_24X1,V_24X2)) ) ).
fof('$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_10521',axiom,
! [V_24Y] :
( c_24__type__10521___24t(V_24Y)
<=> t(V_24Y,c_24__type__10521) ) ).
fof('$tdef_$_type_13511',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__13511___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__13511___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_66',axiom,
! [V_24Y] :
( c_24__type__66___24t(V_24Y)
<=> t(V_24Y,c_24__type__66) ) ).
fof('$tdef_$_type_54',axiom,
! [V_24Y] :
( c_24__type__54___24t(V_24Y)
<=> t(V_24Y,c_24__type__54) ) ).
fof('$tdef_$_type_35354',axiom,
! [V_24Y] :
( c_24__type__35354___24t(V_24Y)
<=> t(V_24Y,c_24__type__35354) ) ).
fof('$tdef_$_type_28790',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__28790___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__28790___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_$_type_19166',axiom,
! [V_24Y] :
( c_24__type__19166___24t(V_24Y)
<=> t(V_24Y,c_24__type__19166) ) ).
fof('$tdef_$_type_31647',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__31647___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__31647___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_11875',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__11875___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__11875___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Sets.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_32516',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32516___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32516___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13',axiom,
! [V_24Y] :
( c_24__type__13___24t(V_24Y)
<=> t(V_24Y,c_24__type__13) ) ).
fof('$tdef_$_type_34649',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34649___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34649___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3868',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__3868___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__3868___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_3522',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__3522___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__3522___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_13628',axiom,
! [V_24Y] :
( c_24__type__13628___24t(V_24Y)
<=> t(V_24Y,c_24__type__13628) ) ).
fof('$tdef_$_type_35206',axiom,
! [V_24Y] :
( c_24__type__35206___24t(V_24Y)
<=> t(V_24Y,c_24__type__35206) ) ).
fof('$tdef_$_type_1775',axiom,
! [V_24Y] :
( c_24__type__1775___24t(V_24Y)
<=> t(V_24Y,c_24__type__1775) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$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_32478',axiom,
! [V_24Y] :
( c_24__type__32478___24t(V_24Y)
<=> t(V_24Y,c_24__type__32478) ) ).
fof('$tdef_$_type_10533',axiom,
! [V_24Y] :
( c_24__type__10533___24t(V_24Y)
<=> t(V_24Y,c_24__type__10533) ) ).
fof('$tdef_$_type_7315',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__7315___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__7315___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26682',axiom,
! [V_24Y] :
( c_24__type__26682___24t(V_24Y)
<=> t(V_24Y,c_24__type__26682) ) ).
fof('$tdef_$_type_19156',axiom,
! [V_24Y] :
( c_24__type__19156___24t(V_24Y)
<=> t(V_24Y,c_24__type__19156) ) ).
fof('$tdef_$_type_13718',axiom,
! [V_24Y] :
( c_24__type__13718___24t(V_24Y)
<=> t(V_24Y,c_24__type__13718) ) ).
fof('$tdef_$_type_28125',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__28125___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__28125___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_11684',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__11684___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__11684___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1969',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1969___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1969___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_18844',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__18844___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__18844___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_10432',axiom,
! [V_24Y] :
( c_24__type__10432___24t(V_24Y)
<=> t(V_24Y,c_24__type__10432) ) ).
fof('$tdef_$_type_18903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__18903___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__18903___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_14732',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14732___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14732___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27425',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__27425___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__27425___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_34838',axiom,
! [V_24Y] :
( c_24__type__34838___24t(V_24Y)
<=> t(V_24Y,c_24__type__34838) ) ).
fof('$tdef_$_type_23885',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23885___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23885___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34329',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__34329___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__34329___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_30512',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__30512___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__30512___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32822',axiom,
! [V_24Y] :
( c_24__type__32822___24t(V_24Y)
<=> t(V_24Y,c_24__type__32822) ) ).
fof('$tdef_$_type_32774',axiom,
! [V_24Y] :
( c_24__type__32774___24t(V_24Y)
<=> t(V_24Y,c_24__type__32774) ) ).
fof('$tdef_$_type_32471',axiom,
! [V_24Y] :
( c_24__type__32471___24t(V_24Y)
<=> t(V_24Y,c_24__type__32471) ) ).
fof('$tdef_$_type_1790',axiom,
! [V_24Y] :
( c_24__type__1790___24t(V_24Y)
<=> t(V_24Y,c_24__type__1790) ) ).
fof('$tdef_$_type_28941',axiom,
! [V_24Y] :
( c_24__type__28941___24t(V_24Y)
<=> t(V_24Y,c_24__type__28941) ) ).
fof('$tdef_$_type_26323',axiom,
! [V_24Y] :
( c_24__type__26323___24t(V_24Y)
<=> t(V_24Y,c_24__type__26323) ) ).
fof('$tdef_$_type_16032',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__16032___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__16032___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_34443',axiom,
! [V_24Y] :
( c_24__type__34443___24t(V_24Y)
<=> t(V_24Y,c_24__type__34443) ) ).
fof('$tdef_$_type_4906',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__4906___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__4906___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_30767',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30767___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30767___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23911',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__23911___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__23911___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_$_type_20063',axiom,
! [V_24Y] :
( c_24__type__20063___24t(V_24Y)
<=> t(V_24Y,c_24__type__20063) ) ).
fof('$tdef_$_type_8570',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8570___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8570___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_15857',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15857___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15857___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_34816',axiom,
! [V_24Y] :
( c_24__type__34816___24t(V_24Y)
<=> t(V_24Y,c_24__type__34816) ) ).
fof('$tdef_$_type_30897',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30897___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30897___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34042',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34042___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34042___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_6590',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__6590___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__6590___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_8996',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__8996___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__8996___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_12981',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12981___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__12981___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_10119',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10119___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10119___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32873',axiom,
! [V_24Y] :
( c_24__type__32873___24t(V_24Y)
<=> t(V_24Y,c_24__type__32873) ) ).
fof('$tdef_$_type_14967',axiom,
! [V_24Y] :
( c_24__type__14967___24t(V_24Y)
<=> t(V_24Y,c_24__type__14967) ) ).
fof('$tdef_$_type_12264',axiom,
! [V_24Y] :
( c_24__type__12264___24t(V_24Y)
<=> t(V_24Y,c_24__type__12264) ) ).
fof('$tdef_$_type_10449',axiom,
! [V_24Y] :
( c_24__type__10449___24t(V_24Y)
<=> t(V_24Y,c_24__type__10449) ) ).
fof('$tdef_$_type_32966',axiom,
! [V_24Y] :
( c_24__type__32966___24t(V_24Y)
<=> t(V_24Y,c_24__type__32966) ) ).
fof('_HAMMER_GOAL',conjecture,
cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(c_24__type__35378,cHahnSets_2eset__subset___24a1(cA)) ).
%------------------------------------------------------------------------------