TPTP Problem File: SEV669+1.p
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%------------------------------------------------------------------------------
% File : SEV669+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - Reduction red par red
% 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 : Reduction.red.par.red.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2955 (1244 unt; 0 def)
% Number of atoms : 9959 (2719 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 7096 ( 92 ~; 782 |;1853 &)
% (1118 <=>;3251 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 6 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 618 ( 617 usr; 0 prp; 1-23 aty)
% Number of functors : 1704 (1704 usr;1135 con; 0-22 aty)
% Number of variables : 9599 (8851 !; 748 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : This is an export from CoqHammer, Naive-Bayes premise selection,
% with 1024 premises.
%------------------------------------------------------------------------------
fof('_HAMMER_COQ_TRUE',axiom,
p(c_24True) ).
fof('_HAMMER_COQ_FALSE',axiom,
~ p(c_24False) ).
fof('_HAMMER_COQ_TYPE_TYPE',axiom,
cType___24t(cType) ).
fof('$_case_Coq.Init.Datatypes.list$29114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( cType___24t(Vv__CANONICAL__0)
=> ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2elist_2429201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429114___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__29118] :
( t(Vvar__1___24Anonymous__29118,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__29119] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__29119)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29118,Vvar__2___24Anonymous__29119)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429114___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29118,c_24__fix__29246__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__29119,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.list$29201',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)) )
| ? [Vvar__1___24Anonymous__29205] :
( t(Vvar__1___24Anonymous__29205,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__29206] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__29206)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29205,Vvar__2___24Anonymous__29206)
& c_24__case__Coq_2eInit_2eDatatypes_2elist_2429201___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29205,c_24__fix__29246__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__29206,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$14819',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2414819___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__14820] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14820)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14820)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2414819___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__14820)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$14841',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__14842] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14842)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14842)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__14842)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$9217',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__9230___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__9222] :
( t(Vvar__2___24Anonymous__9222,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__9223] :
( t(Vvar__3___24Anonymous__9223,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__9222,Vvar__3___24Anonymous__9223)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_249217___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__9222)),Vvar__3___24Anonymous__9223)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$14836',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2414836___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__14837] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14837)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14837)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2414836___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14837) )
| ? [Vvar__0___24Anonymous__14838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14838)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14838)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2414836___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14838) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.positive$27186',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__27187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27187)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27187)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2427186___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__27202__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__27187)) )
| ? [Vvar__0___24Anonymous__27194] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27194)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27194)
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2427186___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27194) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2427186___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_case_Lambda.Terms.lambda$673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__2)
=> ( ? [Vvar__0___24Anonymous__674] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__674)
& Vv__CANONICAL__2 = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__674)
& c_24__case__Lambda_2eTerms_2elambda_24673___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2einsert__Ref___24a3(Vv__CANONICAL__3,Vvar__0___24Anonymous__674,cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__675] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__675)
& Vv__CANONICAL__2 = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__675)
& c_24__case__Lambda_2eTerms_2elambda_24673___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eAbs___24a1(c_24__fix__769__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__675,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) )
| ? [Vvar__0___24Anonymous__688] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__688)
& ? [Vvar__1___24Anonymous__689] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__689)
& Vv__CANONICAL__2 = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__688,Vvar__1___24Anonymous__689)
& c_24__case__Lambda_2eTerms_2elambda_24673___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eApp___24a2(c_24__fix__769__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__688,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eO),c_24__fix__769__v__CANONICAL__0___24a3(Vvar__1___24Anonymous__689,Vv__CANONICAL__3,cCoq_2eInit_2eDatatypes_2eO)) ) ) ) ) ).
fof('$_def_$_let_var_6_p_20711_20714',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20710] : c_24__let__var__6__p__20711__20714___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20710) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20710) ).
fof('$_def_$_let_var_6_p_20713_20715',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20712] : c_24__let__var__6__p__20713__20715___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20712) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20712) ).
fof('$_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)
<=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r))
& cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q) ) ) ).
fof('$_def_Coq.Arith.EqNat.eq_nat',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__25428] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25428)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25428)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__25429] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25429)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25429)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__25432] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25432)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25432)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__25429,Vvar__0___24Anonymous__25432) ) ) ) ) ) ) ) ) ).
fof('$_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__30532___24a1(V0__A)) ).
fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__28348] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__28348)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__28348)
& cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__28348,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_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)
<=> p(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__30474] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30474)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30474)
& 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__22426] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__22426)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__22426) ) ).
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('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
! [V1__i,V2__m] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
=> ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__22471] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__22471)
& ? [Vvar__1___24Anonymous__22472] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__22472)
& ? [Vvar__2___24Anonymous__22473] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__22473)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22471,Vvar__1___24Anonymous__22472,Vvar__2___24Anonymous__22473)
& ( ? [Vvar__0___24Anonymous__22486] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22486)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22486)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__22486,Vvar__2___24Anonymous__22473) )
| ? [Vvar__0___24Anonymous__22487] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22487)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22487)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__22487,Vvar__0___24Anonymous__22471) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__22472 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__9619] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__9619)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__9619) ) ).
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('$_def_Coq.Init.Datatypes.ID',axiom,
! [Vvar__25400] :
( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__25400)
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( t(V1___24Anonymous,V0__A)
=> t(happ(happ(Vvar__25400,V0__A),V1___24Anonymous),V0__A) ) ) ) ).
fof('$_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__1149] :
( t(Vvar__1___24Anonymous__1149,V0__A)
& ? [Vvar__2___24Anonymous__1150] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__1150)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1149,Vvar__2___24Anonymous__1150)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__1149,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__1150,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.fst',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__10488] :
( t(Vvar__2___24Anonymous__10488,V0__A)
& ? [Vvar__3___24Anonymous__10489] :
( t(Vvar__3___24Anonymous__10489,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__10488,Vvar__3___24Anonymous__10489)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__10488 ) ) ) ) ) ).
fof('$_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__10558] :
( t(Vvar__1___24Anonymous__10558,V0__A)
& ? [Vvar__2___24Anonymous__10559] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__10559)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__10558,Vvar__2___24Anonymous__10559)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__10559)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
! [V0__P,V1__f,V2__f,V4__n] :
( c_24__type__27286___24t(V0__P,V0__P)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( ( V4__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = V1__f )
| ? [Vvar__0___24Anonymous__27284] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27284)
& V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27284)
& cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__27284),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__27284)) ) ) ) ) ).
fof('$_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.prod_curry',axiom,
! [V0__A,V1__B,V2__C,V3__f,V4__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cType___24t(V2__C)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
=> ? [Vvar__2___24Anonymous__27332] :
( t(Vvar__2___24Anonymous__27332,V0__A)
& ? [Vvar__3___24Anonymous__27333] :
( t(Vvar__3___24Anonymous__27333,V1__B)
& V4__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__27332,Vvar__3___24Anonymous__27333)
& cCoq_2eInit_2eDatatypes_2eprod__curry___24a5(V0__A,V1__B,V2__C,V3__f,V4__p) = happ(happ(V3__f,Vvar__2___24Anonymous__27332),Vvar__3___24Anonymous__27333) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__27320] :
( t(Vvar__2___24Anonymous__27320,V0__A)
& ? [Vvar__3___24Anonymous__27321] :
( t(Vvar__3___24Anonymous__27321,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__27320,Vvar__3___24Anonymous__27321)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__27321 ) ) ) ) ) ).
fof('$_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__27366] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27366)
& V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__27366)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__27366) )
| ? [Vvar__0___24Anonymous__27367] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27367)
& V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__27367)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27368] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27368)
& V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__27368)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27369] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27369)
& V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__27369)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27370] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27370)
& V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__27370)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27371] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27371)
& V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__27371)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27372] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27372)
& V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__27372)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27373] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27373)
& V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__27373)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27374] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27374)
& V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__27374)
& cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
| ? [Vvar__0___24Anonymous__27375] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__27375)
& V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__27375)
& 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('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__931] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__931)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__931)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__931,V2__m)) ) ) ) ).
fof('$_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__12800] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12800)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12800)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__12801] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12801)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12801)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__12804] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12804)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12804)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__12801,Vvar__0___24Anonymous__12804) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__27759] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27759)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27759)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27759)
& ( ( Vvar__0___24Anonymous__27759 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__27762] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27762)
& Vvar__0___24Anonymous__27759 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27762)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__27762)) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__27711] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27711)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27711)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__27712] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27712)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27712)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__27715] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27715)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27715)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__27712,Vvar__0___24Anonymous__27715) ) ) ) ) ) ) ) ).
fof('$_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__27724] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27724)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27724)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27724)
& ( ( Vvar__0___24Anonymous__27724 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__27727] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27727)
& Vvar__0___24Anonymous__27724 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27727)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__27727) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__27732] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27732)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27732)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27732)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27732)) ) ) ) ).
fof('$_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__12792] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12792)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12792)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__12795] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12795)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12795)
& cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__12792,Vvar__0___24Anonymous__12795) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.log2_iter',axiom,
! [V1__k,V2__p,V3__q,V4__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__27748] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27748)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27748)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__27748,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
| ? [Vvar__0___24Anonymous__27751] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27751)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27751)
& cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__27748,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__27751) ) ) ) ) ) ) ) ).
fof('$_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__12809] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12809)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12809)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__12812] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12812)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12812)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__12809,Vvar__0___24Anonymous__12812)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__27718] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27718)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27718)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__27721] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27721)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27721)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__27718,Vvar__0___24Anonymous__27721)) ) ) ) ) ) ) ) ).
fof('$_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__12789] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12789)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12789)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__12789,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__12817] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12817)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12817)
& 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__12817)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__8] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__8 ) ) ) ).
fof('$_def_Coq.Init.Nat.sqrt_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_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
| ? [Vvar__0___24Anonymous__27735] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27735)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
=> ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27735)
& ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__27735,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q)),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q))) )
| ? [Vvar__0___24Anonymous__27738] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27738)
& V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27738)
& cCoq_2eInit_2eNat_2esqrt__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(Vvar__0___24Anonymous__27735,V2__p,V3__q,Vvar__0___24Anonymous__27738) ) ) ) ) ) ) ) ).
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__23698] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23698)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23698)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__23701] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__23701)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__23701)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__23698,Vvar__0___24Anonymous__23701) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.succ',axiom,
cCoq_2eInit_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).
fof('$_def_Coq.Init.Nat.t',axiom,
! [Vvar__25539] :
( cCoq_2eInit_2eNat_2et___24t(Vvar__25539)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__25539) ) ).
fof('$_def_Coq.Init.Nat.tail_add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__27729] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27729)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27729)
& cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__27729,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).
fof('$_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__27764] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__27764)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__27764)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__27764) ) ) ) ).
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__25540] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25540)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25540)
& ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_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__30015___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__30009] :
( t(Vvar__2__x__30009,V0__A)
& p(happ(V1__P,Vvar__2__x__30009))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__30009)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__30009 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__30038___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__30032] :
( t(Vvar__2__x__30032,V0__A)
& ? [Vvar__3___24Anonymous__30033] :
( t(Vvar__3___24Anonymous__30033,happ(V1__P,Vvar__2__x__30032))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__30032,Vvar__3___24Anonymous__30033)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__30032 ) ) ) ) ) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__12615] :
( t(Vvar__1___24Anonymous__12615,V0__A)
& ? [Vvar__2___24Anonymous__12616] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12616)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12615,Vvar__2___24Anonymous__12616)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__12615 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__12616) ) ) ) ) ) ) ) ).
fof('$_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__27508] :
( t(Vvar__1___24Anonymous__27508,V1__B)
& ? [Vvar__2___24Anonymous__27509] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__27509)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__27508,Vvar__2___24Anonymous__27509)
& 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__27509,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__27508)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__27537] :
( t(Vvar__1___24Anonymous__27537,V1__B)
& ? [Vvar__2___24Anonymous__27538] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__27538)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__27537,Vvar__2___24Anonymous__27538)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__27537),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__27538)) ) ) ) ) ) ) ).
fof('$_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__27463] :
( t(Vvar__1___24Anonymous__27463,V0__A)
& ? [Vvar__2___24Anonymous__27464] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__27464)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__27463,Vvar__2___24Anonymous__27464)
& cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__27463 ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__27484] :
( t(Vvar__1___24Anonymous__27484,V0__A)
& ? [Vvar__2___24Anonymous__27485] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__27485)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__27485)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__27484,Vvar__2___24Anonymous__27485)
& ( ( Vvar__2___24Anonymous__27485 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__27484 )
| ? [Vvar__1___24Anonymous__27496] :
( t(Vvar__1___24Anonymous__27496,V0__A)
& ? [Vvar__2___24Anonymous__27497] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__27497)
& Vvar__2___24Anonymous__27485 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__27496,Vvar__2___24Anonymous__27497)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__27485,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_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__12627] :
( t(Vvar__1___24Anonymous__12627,V0__A)
& ? [Vvar__2___24Anonymous__12628] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12628)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12627,Vvar__2___24Anonymous__12628)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__12627 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12630] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12630)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12630)
& ( ( 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__12637] :
( t(Vvar__1___24Anonymous__12637,V0__A)
& ? [Vvar__2___24Anonymous__12638] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__12638)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__12637,Vvar__2___24Anonymous__12638)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__12630,Vvar__2___24Anonymous__12638,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.tl',axiom,
! [V0__A,V1__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ( ( V1__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__27474] :
( t(Vvar__1___24Anonymous__27474,V0__A)
& ? [Vvar__2___24Anonymous__27475] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__27475)
& V1__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__27474,Vvar__2___24Anonymous__27475)
& cCoq_2eLists_2eList_2etl___24a2(V0__A,V1__l) = Vvar__2___24Anonymous__27475 ) ) ) ) ) ).
fof('$_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__21043___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__3025___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('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_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('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V0__U)
<=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__14753___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x) ) ) ) ) ).
fof('$_def_Coq.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__30510___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__971] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__971)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__971)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__974] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__974)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__974)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__971,Vvar__0___24Anonymous__974)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__22289] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22289)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22289)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__22290] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22290)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22290)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__22293] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22293)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22293)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__22290,Vvar__0___24Anonymous__22293) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__22310] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22310)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22310)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22310)
& ( ? [Vvar__0___24Anonymous__22314] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22314)
& Vvar__0___24Anonymous__22310 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22314)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22314) )
| ? [Vvar__0___24Anonymous__22315] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22315)
& Vvar__0___24Anonymous__22310 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22315)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22315) )
| ( Vvar__0___24Anonymous__22310 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_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__22274] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22274)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22274)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22274)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__22298] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22298)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22298)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__22299] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22299)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22299)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__22302] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22302)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22302)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__22299,Vvar__0___24Anonymous__22302) ) ) ) ) ) ) ) ).
fof('$_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__30487] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30487)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30487)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30487)
& ( ? [Vvar__0___24Anonymous__30491] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30491)
& Vvar__0___24Anonymous__30487 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30491)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30492] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30492)
& Vvar__0___24Anonymous__30487 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30492)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__30487 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.land',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__30493] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30493)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30493)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__30496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30496)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30496)
& cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(Vvar__0___24Anonymous__30493,Vvar__0___24Anonymous__30496) ) ) ) ) ) ) ) ).
fof('$_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__30504] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30504)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30504)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__30507] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30507)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30507)
& cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__30504,Vvar__0___24Anonymous__30507) ) ) ) ) ) ) ) ).
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('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__978] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__978)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__978)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__981] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__981)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__981)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__978,Vvar__0___24Anonymous__981)) ) ) ) ) ) ) ) ).
fof('$_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__22278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22278)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22278)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__22278) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__22277] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22277)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22277)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__22277)) ) ) ) ).
fof('$_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__30484] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30484)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30484)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__pos___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__30484) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
! [Vvar__27110] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__27110)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__27110) ) ).
fof('$_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__22341] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22341)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22341)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__22341,V1__n) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__22343] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22343)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22343)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__22343) ) ) ) ).
fof('$_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('$_def_Coq.PArith.BinPos.Pos.le',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y)
<=> cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
! [V0__c,V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = V0__c )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eLt )
| ( V1__c_27 = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V0__c,V1__c_27) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__27129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27129)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27129)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__27129 )
| ? [Vvar__0___24Anonymous__27130] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27130)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27130)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__27130 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.div2_up',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ( ? [Vvar__0___24Anonymous__30569] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30569)
& V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30569)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__30569) )
| ? [Vvar__0___24Anonymous__30570] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30570)
& V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30570)
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V0__p) = Vvar__0___24Anonymous__30570 )
| ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___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__30605] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30605)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30605)
& ( ? [Vvar__0___24Anonymous__30609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30609)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30609)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__30605,Vvar__0___24Anonymous__30609) )
| ? [Vvar__0___24Anonymous__30610] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30610)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30610)
& 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__30611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30611)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30611)
& ( ? [Vvar__0___24Anonymous__30615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30615)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30615)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30616] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30616)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30616)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__30611,Vvar__0___24Anonymous__30616) )
| ( 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__30617] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30617)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30617)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30618] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30618)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30618)
& 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__27117] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27117)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27117)
& 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__27117),Vvar__0___24Anonymous__27117)) )
| ? [Vvar__0___24Anonymous__27118] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27118)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27118)
& 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__27118),Vvar__0___24Anonymous__27118) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__27132] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27132)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27132)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__27132,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__27133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27133)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27133)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__27133,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_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__9601] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9601)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__9601)
& 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__9601,V2__y))) )
| ? [Vvar__0___24Anonymous__9602] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9602)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__9602)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__9602,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__30653] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30653)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30653)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30653)
& ( ( Vvar__0___24Anonymous__30653 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__30656] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30656)
& Vvar__0___24Anonymous__30653 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30656)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__30653)) ) ) ) ) ) ) ) ).
fof('$_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__30660] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30660)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30660)
& 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__30660)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30577] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30577)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30577)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__30577)) )
| ? [Vvar__0___24Anonymous__30578] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30578)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30578)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__30578)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30572] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30572)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30572)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__30572)) )
| ? [Vvar__0___24Anonymous__30573] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30573)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30573)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__30573)) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__30567] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30567)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__30567)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__30567 )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__22405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22405)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22405)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__22405)) )
| ? [Vvar__0___24Anonymous__22406] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22406)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22406)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22406) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
! [Vvar__27113] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__27113)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__27113) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30623)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30623)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__30636___24a1(Vvar__0___24Anonymous__30623) )
| ? [Vvar__0___24Anonymous__30627] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30627)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30627)
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__30643___24a1(Vvar__0___24Anonymous__30627) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__30647 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__14225] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__14225)
& ? [Vvar__1__Qden__14226] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__14226)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14225,Vvar__1__Qden__14226)
& cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__14226 ) ) ) ).
fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
! [V0__q] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
=> ? [Vvar__0__Qnum__14220] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__14220)
& ? [Vvar__1__Qden__14221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__14221)
& V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14220,Vvar__1__Qden__14221)
& cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__14220 ) ) ) ).
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__14509] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14509)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__14509)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__14509) )
| ? [Vvar__0___24Anonymous__14510] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14510)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__14510)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__14510)) ) ) ) ).
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.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('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__1915___24a1(V0__A) ).
fof('$_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('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__1915___24a1(V0__U) ).
fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__27424___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('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
! [V0__A,V1__cmp,V2__x,V3__y] :
( cType___24t(V0__A)
=> ( c_24__type__27424___24t(V0__A,V1__cmp)
=> ( t(V2__x,V0__A)
=> ( t(V3__y,V0__A)
=> ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
| ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).
fof('$_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__27111] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__27111)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__27111) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__25236] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__25236)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__25236) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
! [V1__p,V2__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__27079] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27079)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27079)
& ( ? [Vvar__0___24Anonymous__27083] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27083)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27083)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__27079,Vvar__0___24Anonymous__27083) ) )
| ? [Vvar__0___24Anonymous__27084] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27084)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27084)
& ( 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__27085] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27085)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27085)
& ( ? [Vvar__0___24Anonymous__27089] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27089)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27089)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__27090] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27090)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27090)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__27085,Vvar__0___24Anonymous__27090) ) )
| ( 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__27091] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27091)
& V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27091)
& ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__27092] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27092)
& V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27092)
& ( 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('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__25204] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__25204)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__25204) ) ).
fof('$_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__22741] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__22741)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__22741) ) ).
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__27213] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__27213)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__27213) ) ).
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('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__25237] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__25237)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__25237) ) ).
fof('$_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__22751] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22751)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22751)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22751) )
| ? [Vvar__0___24Anonymous__22752] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22752)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22752)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22752) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__22757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22757)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22757)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22757) )
| ? [Vvar__0___24Anonymous__22758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22758)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22758)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22758) ) ) ) ).
fof('$_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__22753] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22753)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22753)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__22753) )
| ? [Vvar__0___24Anonymous__22754] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22754)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22754)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__22754) ) ) ) ).
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__1002] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1002)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1002)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__1006] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1006)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1006)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__1002,Vvar__0___24Anonymous__1006)) )
| ? [Vvar__0___24Anonymous__1007] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1007)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1007)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__1002,Vvar__0___24Anonymous__1007) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1008] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1008)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1008)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__1012] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1012)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1012)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__1012,Vvar__0___24Anonymous__1008) )
| ? [Vvar__0___24Anonymous__1013] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1013)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1013)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__1008,Vvar__0___24Anonymous__1013)) ) ) ) ) ) ) ) ).
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__1015] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1015)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1015)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1016] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1016)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1016)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__1017] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1017)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1017)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__1021] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1021)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1021)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__1017,Vvar__0___24Anonymous__1021) )
| ? [Vvar__0___24Anonymous__1022] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1022)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1022)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__1023] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1023)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1023)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1027] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1027)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1027)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1028] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1028)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1028)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__1023,Vvar__0___24Anonymous__1028)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__877] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__877)
& ? [Vvar__3___24Anonymous__878] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__878)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__877,Vvar__3___24Anonymous__878)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__877 ) ) ) ) ).
fof('$_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__22770] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22770)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22770)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22770)
& ( ? [Vvar__0___24Anonymous__22774] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22774)
& Vvar__0___24Anonymous__22770 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22774)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__22775] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22775)
& Vvar__0___24Anonymous__22770 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22775)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__22770 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__22776] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22776)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22776)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22776)
& ( ? [Vvar__0___24Anonymous__22780] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22780)
& Vvar__0___24Anonymous__22776 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22780)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__22781] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22781)
& Vvar__0___24Anonymous__22776 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22781)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__22776 = 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__885] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__885)
& ? [Vvar__3___24Anonymous__886] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__886)
& 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__885,Vvar__3___24Anonymous__886)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__886 ) ) ) ) ).
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__860] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__860)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__860)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__864] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__864)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__864)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__860,Vvar__0___24Anonymous__864)) )
| ? [Vvar__0___24Anonymous__865] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__865)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__865)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__860,Vvar__0___24Anonymous__865)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__866] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__866)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__866)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__870] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__870)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__870)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__866,Vvar__0___24Anonymous__870)) )
| ? [Vvar__0___24Anonymous__871] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__871)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__871)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__866,Vvar__0___24Anonymous__871)) ) ) ) ) ) ) ) ).
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__22784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22784)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22784)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22784)
& ( ? [Vvar__0___24Anonymous__22788] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22788)
& Vvar__0___24Anonymous__22784 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22788)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__22789] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22789)
& Vvar__0___24Anonymous__22784 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22789)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__22784 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
| ? [Vvar__0___24Anonymous__22790] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22790)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22790)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22790)
& ( ? [Vvar__0___24Anonymous__22794] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22794)
& Vvar__0___24Anonymous__22790 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22794)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__22795] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22795)
& Vvar__0___24Anonymous__22790 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22795)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
| ( Vvar__0___24Anonymous__22790 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__22766] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22766)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__22766)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22766) ) ) ) ).
fof('$_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__22763] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22763)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__22763)
& 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__22763)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.one',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eone = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) ).
fof('$_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__9688] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9688)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9688)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__9688) )
| ? [Vvar__0___24Anonymous__9689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9689)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__9689)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__9689) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__30691] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30691)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30691)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__30691) )
| ? [Vvar__0___24Anonymous__30692] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30692)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30692)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_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('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
! [Vvar__27228] :
( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__27228)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__27228) ) ).
fof('$_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__30694] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30694)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30694)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30694) )
| ? [Vvar__0___24Anonymous__30695] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30695)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30695)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__22761] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22761)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22761)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__22761) )
| ? [Vvar__0___24Anonymous__22762] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22762)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22762)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('$_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__27229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27229)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__27229)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__27229 )
| ? [Vvar__0___24Anonymous__27230] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27230)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__27230)
& 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('$_def_Coq.ZArith.Zcomplements.floor_pos',axiom,
! [V1__a] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__a)
=> ( ? [Vvar__0___24Anonymous__30467] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30467)
& V1__a = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30467)
& cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V1__a) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(Vvar__0___24Anonymous__30467)) )
| ? [Vvar__0___24Anonymous__30468] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30468)
& V1__a = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30468)
& cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V1__a) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(Vvar__0___24Anonymous__30468)) )
| ( V1__a = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V1__a) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_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__27024] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27024)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27024)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__27024)
& ( ? [Vvar__0___24Anonymous__27028] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27028)
& Vvar__0___24Anonymous__27024 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27028)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__27029] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27029)
& Vvar__0___24Anonymous__27024 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27029)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__27024 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__27030] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27030)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27030)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__27030)
& ( ? [Vvar__0___24Anonymous__27034] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27034)
& Vvar__0___24Anonymous__27030 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27034)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__27035] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27035)
& Vvar__0___24Anonymous__27030 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27035)
& ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
<=> p(c_24True) ) )
| ( Vvar__0___24Anonymous__27030 = 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__22229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22229)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22229)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__22229)
& ( ? [Vvar__0___24Anonymous__22233] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22233)
& Vvar__0___24Anonymous__22229 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22233)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__22234] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22234)
& Vvar__0___24Anonymous__22229 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22234)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__22229 = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__22235] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22235)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22235)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__22235)
& ( ? [Vvar__0___24Anonymous__22239] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22239)
& Vvar__0___24Anonymous__22235 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__22239)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24True) ) )
| ? [Vvar__0___24Anonymous__22240] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22240)
& Vvar__0___24Anonymous__22235 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__22240)
& ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
<=> p(c_24False) ) )
| ( Vvar__0___24Anonymous__22235 = 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__27037] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27037)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27037)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__27038] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27038)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27038)
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__27038) ) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
<=> p(c_24True) ) ) ) ) ).
fof('$_def_Coq.ZArith.Zlogarithm.log_inf',axiom,
! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( ? [Vvar__0___24Anonymous__30476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30476)
& V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30476)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__30476)) )
| ? [Vvar__0___24Anonymous__30477] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30477)
& V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30477)
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__30477)) )
| ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.Znat.neq',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__22906___24a1(V0__D) ).
fof('$_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__14545] :
( t(Vvar__1___24Anonymous__14545,V1__A)
& ? [Vvar__2___24Anonymous__14546] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14546)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14546)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__14545,Vvar__2___24Anonymous__14546)
& ( ( Vvar__2___24Anonymous__14546 = 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__14545)) ) )
| ? [Vvar__1___24Anonymous__14557] :
( t(Vvar__1___24Anonymous__14557,V1__A)
& ? [Vvar__2___24Anonymous__14558] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14558)
& Vvar__2___24Anonymous__14546 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__14557,Vvar__2___24Anonymous__14558)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__14545))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__14546) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__14524] :
( t(Vvar__1___24Anonymous__14524,V1__A)
& ? [Vvar__2___24Anonymous__14525] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__14525)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__14524,Vvar__2___24Anonymous__14525)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__14524))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__14525,V4__goal) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__29393___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__29401___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__29409___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__29417___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__29490___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__29498___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__29506___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__29514___24a2(V0__R,V3__rlt) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__29477] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29477)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29477)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__29478] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29478)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29478)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__29481] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29481)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29481)
& cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__29478,Vvar__0___24Anonymous__29481) ) ) ) ) ) ) ) ).
fof('$_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__22217] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__22217)
<=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__22217) ) ).
fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
! [Vvar__30465] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__30465)
<=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__30465) ) ).
fof('$_def_Coq.micromega.ZMicromega.isZ0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30436] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30436)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30436)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30437] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30437)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30437)
& cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V0__x) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
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__12498] :
( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__12498)
<=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__12498) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__12458] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12458)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12458)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__12458) ) ) ) ) ).
fof('$_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__25496] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25496)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25496)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25496)
& ( ? [Vvar__0___24Anonymous__25500] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25500)
& Vvar__0___24Anonymous__25496 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25500)
& 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__25496))) )
| ? [Vvar__0___24Anonymous__25501] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25501)
& Vvar__0___24Anonymous__25496 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25501)
& 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__25496))) )
| ( Vvar__0___24Anonymous__25496 = 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__25502] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25502)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25502)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25502)
& ( ? [Vvar__0___24Anonymous__25506] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25506)
& Vvar__0___24Anonymous__25502 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25506)
& 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__25502)) )
| ? [Vvar__0___24Anonymous__25507] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25507)
& Vvar__0___24Anonymous__25502 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25507)
& 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__25502)) )
| ( Vvar__0___24Anonymous__25502 = 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('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__25463] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25463)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25463)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__25463))) )
| ? [Vvar__0___24Anonymous__25464] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25464)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25464)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__25464)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_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__12379] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12379)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__12379)
& 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__12379) )
| ? [Vvar__0___24Anonymous__12380] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12380)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__12380)
& 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__12380)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.hypo_type',axiom,
! [V0__h] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V0__h)
=> ? [Vvar__0__hypo__type__27455] :
( cType___24t(Vvar__0__hypo__type__27455)
& ? [Vvar__1__hypo__proof__27456] :
( t(Vvar__1__hypo__proof__27456,Vvar__0__hypo__type__27455)
& V0__h = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__27455,Vvar__1__hypo__proof__27456)
& cCoq_2esetoid__ring_2eInitialRing_2ehypo__type___24a1(V0__h) = Vvar__0__hypo__type__27455 ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring.bool_eq',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eRing_2ebool__eq___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b2) ) ) ) ).
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__3491] :
( t(Vvar__1___24Anonymous__3491,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__3491)
& ( ? [Vvar__1___24Anonymous__3501] :
( t(Vvar__1___24Anonymous__3501,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__3501)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__3491),Vvar__1___24Anonymous__3501) )
| ? [Vvar__1___24Anonymous__3503] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3503)
& ? [Vvar__2___24Anonymous__3504] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__3504)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__3503,Vvar__2___24Anonymous__3504)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__3507] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3507)
& ? [Vvar__2___24Anonymous__3508] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3508)
& ? [Vvar__3___24Anonymous__3509] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__3509)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__3507,Vvar__2___24Anonymous__3508,Vvar__3___24Anonymous__3509)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__3514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3514)
& ? [Vvar__2___24Anonymous__3515] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__3515)
& ( 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__3514,Vvar__2___24Anonymous__3515)
& ( ? [Vvar__1___24Anonymous__3535] :
( t(Vvar__1___24Anonymous__3535,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__3535)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__3537] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3537)
& ? [Vvar__2___24Anonymous__3538] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__3538)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3514)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3537)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__3537,Vvar__2___24Anonymous__3538)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__3514,Vvar__1___24Anonymous__3537) = 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__3515,Vvar__2___24Anonymous__3538) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__3514,Vvar__1___24Anonymous__3537) = 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__3514,Vvar__1___24Anonymous__3537) = 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__3543] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3543)
& ? [Vvar__2___24Anonymous__3544] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3544)
& ? [Vvar__3___24Anonymous__3545] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__3545)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__3543,Vvar__2___24Anonymous__3544,Vvar__3___24Anonymous__3545)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__3550] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3550)
& ? [Vvar__2___24Anonymous__3551] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3551)
& ? [Vvar__3___24Anonymous__3552] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__3552)
& ( 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__3550,Vvar__2___24Anonymous__3551,Vvar__3___24Anonymous__3552)
& ( ? [Vvar__1___24Anonymous__3585] :
( t(Vvar__1___24Anonymous__3585,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__3585)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__3587] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3587)
& ? [Vvar__2___24Anonymous__3588] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__3588)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__3587,Vvar__2___24Anonymous__3588)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__3591] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3591)
& ? [Vvar__2___24Anonymous__3592] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3592)
& ? [Vvar__3___24Anonymous__3593] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__3593)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3551)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3592)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__3591,Vvar__2___24Anonymous__3592,Vvar__3___24Anonymous__3593)
& ( ( cType___24t(V0__C)
=> ( c_24__type__2987___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3550)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__3591)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__3551,Vvar__2___24Anonymous__3592) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__3550,Vvar__1___24Anonymous__3591) = 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__3552,Vvar__3___24Anonymous__3593) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__3550,Vvar__1___24Anonymous__3591) = 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__3551,Vvar__2___24Anonymous__3592) = 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__3551,Vvar__2___24Anonymous__3592) = 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__25576] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25576)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__25576)
& 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__25576),V4__x,Vvar__0___24Anonymous__25576) )
| ? [Vvar__0___24Anonymous__25577] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__25577)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__25577)
& 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__25577),V4__x,Vvar__0___24Anonymous__25577) )
| ( 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__5225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5225)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__5225)
& 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__5225) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__20710] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20710)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__20710)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__20711__20714___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20710)),c_24__let__var__6__p__20711__20714___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20710))) )
| ? [Vvar__0___24Anonymous__20712] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__20712)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__20712)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__20713__20715___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20712)),c_24__let__var__6__p__20713__20715___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__20712)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_Hammer.Tactics.Reconstr.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eReconstr_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Hammer.Tactics.Tactics.default',axiom,
cHammer_2eTactics_2eTactics_2edefault = cCoq_2eInit_2eDatatypes_2ett ).
fof('$_def_Hammer.Tactics.Tactics.hints',axiom,
cHammer_2eTactics_2eTactics_2ehints = cCoq_2eInit_2eDatatypes_2ett ).
fof('$_def_Hammer.Tactics.Tactics.logic',axiom,
cHammer_2eTactics_2eTactics_2elogic = cCoq_2eInit_2eDatatypes_2ett ).
fof('$_def_Hammer.Tactics.Tactics.nohints',axiom,
cHammer_2eTactics_2eTactics_2enohints = cCoq_2eInit_2eDatatypes_2ett ).
fof('$_def_Hammer.Tactics.Tactics.none',axiom,
cHammer_2eTactics_2eTactics_2enone = cCoq_2eInit_2eDatatypes_2ett ).
fof('$_def_Hammer.Tactics.Tactics.rdone',axiom,
! [V0__T,V1__x] :
( cHammer_2eTactics_2eTactics_2erdone___24a2(V0__T,V1__x)
<=> p(c_24True) ) ).
fof('$_def_Lambda.Terms.lambda_rec',axiom,
! [V0__P] : cLambda_2eTerms_2elambda__rec___24a1(V0__P) = cLambda_2eTerms_2elambda__rect___24a1(V0__P) ).
fof('$_def_Lambda.Terms.lambda_rect',axiom,
! [V0__P,V1__f,V2__f,V3__f,V5__l] :
( c_24__type__108___24t(V0__P,V0__P)
=> ( cLambda_2eTerms_2elambda___24t(V5__l)
=> ( ? [Vvar__0___24Anonymous__102] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__102)
& V5__l = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__102)
& cLambda_2eTerms_2elambda__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__l) = happ(V1__f,Vvar__0___24Anonymous__102) )
| ? [Vvar__0___24Anonymous__103] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__103)
& V5__l = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__103)
& cLambda_2eTerms_2elambda__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__l) = happ(happ(V2__f,Vvar__0___24Anonymous__103),cLambda_2eTerms_2elambda__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__0___24Anonymous__103)) )
| ? [Vvar__0___24Anonymous__104] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__104)
& ? [Vvar__1___24Anonymous__105] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__105)
& V5__l = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__104,Vvar__1___24Anonymous__105)
& cLambda_2eTerms_2elambda__rect___24a5(V0__P,V1__f,V2__f,V3__f,V5__l) = happ(happ(happ(happ(V3__f,Vvar__0___24Anonymous__104),cLambda_2eTerms_2elambda__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__0___24Anonymous__104)),Vvar__1___24Anonymous__105),cLambda_2eTerms_2elambda__rect___24a5(V0__P,V1__f,V2__f,V3__f,Vvar__1___24Anonymous__105)) ) ) ) ) ) ).
fof('$_def_Lambda.Terms.lift',axiom,
! [V0__n,V1__N] : cLambda_2eTerms_2elift___24a2(V0__n,V1__N) = cLambda_2eTerms_2elift__rec___24a3(V1__N,cCoq_2eInit_2eDatatypes_2eO,V0__n) ).
fof('$_def_Lambda.Terms.lift_rec',axiom,
! [V1__L,V2__k,V3__n] :
( cLambda_2eTerms_2elambda___24t(V1__L)
=> ( ? [Vvar__0___24Anonymous__225] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__225)
& V1__L = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__225)
& cLambda_2eTerms_2elift__rec___24a3(V1__L,V2__k,V3__n) = cLambda_2eTerms_2eRef___24a1(cLambda_2eTerms_2erelocate___24a3(Vvar__0___24Anonymous__225,V2__k,V3__n)) )
| ? [Vvar__0___24Anonymous__226] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__226)
& V1__L = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__226)
& cLambda_2eTerms_2elift__rec___24a3(V1__L,V2__k,V3__n) = cLambda_2eTerms_2eAbs___24a1(cLambda_2eTerms_2elift__rec___24a3(Vvar__0___24Anonymous__226,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__k),V3__n)) )
| ? [Vvar__0___24Anonymous__227] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__227)
& ? [Vvar__1___24Anonymous__228] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__228)
& V1__L = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__227,Vvar__1___24Anonymous__228)
& cLambda_2eTerms_2elift__rec___24a3(V1__L,V2__k,V3__n) = cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2elift__rec___24a3(Vvar__0___24Anonymous__227,V2__k,V3__n),cLambda_2eTerms_2elift__rec___24a3(Vvar__1___24Anonymous__228,V2__k,V3__n)) ) ) ) ) ).
fof('$_def_Lambda.Terms.relocate',axiom,
! [V0__i,V1__k,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__i)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V0__i))
& cLambda_2eTest_2etest___24a2(V1__k,V0__i) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V0__i),cCoq_2eInit_2ePeano_2egt___24a2(V1__k,V0__i))
& cLambda_2eTerms_2erelocate___24a3(V0__i,V1__k,V2__n) = cCoq_2eInit_2eNat_2eadd___24a2(V2__n,V0__i) )
| ( p(cCoq_2eInit_2ePeano_2egt___24a2(V1__k,V0__i))
& cLambda_2eTest_2etest___24a2(V1__k,V0__i) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(V1__k,V0__i),cCoq_2eInit_2ePeano_2egt___24a2(V1__k,V0__i))
& cLambda_2eTerms_2erelocate___24a3(V0__i,V1__k,V2__n) = V0__i ) ) ) ) ).
fof('$_def_Lambda.Terms.subst',axiom,
! [V0__N,V1__M] : cLambda_2eTerms_2esubst___24a2(V0__N,V1__M) = cLambda_2eTerms_2esubst__rec___24a3(V1__M,V0__N,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_def_Lambda.Terms.subst_rec',axiom,
! [V1__L,V2__N,V3__k] :
( cLambda_2eTerms_2elambda___24t(V1__L)
=> ( ? [Vvar__0___24Anonymous__267] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__267)
& V1__L = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__267)
& cLambda_2eTerms_2esubst__rec___24a3(V1__L,V2__N,V3__k) = cLambda_2eTerms_2einsert__Ref___24a3(V2__N,Vvar__0___24Anonymous__267,V3__k) )
| ? [Vvar__0___24Anonymous__268] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__268)
& V1__L = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__268)
& cLambda_2eTerms_2esubst__rec___24a3(V1__L,V2__N,V3__k) = cLambda_2eTerms_2eAbs___24a1(cLambda_2eTerms_2esubst__rec___24a3(Vvar__0___24Anonymous__268,V2__N,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k))) )
| ? [Vvar__0___24Anonymous__269] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__269)
& ? [Vvar__1___24Anonymous__270] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__270)
& V1__L = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__269,Vvar__1___24Anonymous__270)
& cLambda_2eTerms_2esubst__rec___24a3(V1__L,V2__N,V3__k) = cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2esubst__rec___24a3(Vvar__0___24Anonymous__269,V2__N,V3__k),cLambda_2eTerms_2esubst__rec___24a3(Vvar__1___24Anonymous__270,V2__N,V3__k)) ) ) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__22878,Vvar__1___24Anonymous__22879,Vvar__0__P__22880,Vvar__1___24Anonymous__22881] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__22878) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__22880) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__22431,Vvar__1___24Anonymous__22432,Vvar__2___24Anonymous__22433] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22431,Vvar__1___24Anonymous__22432,Vvar__2___24Anonymous__22433) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.CompEqT$Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__25368,Vvar__1__Plt__25369,Vvar__2__Pgt__25370,Vvar__3___24Anonymous__25371,Vvar__0__Peq__25372,Vvar__1__Plt__25373,Vvar__2__Pgt__25374,Vvar__3___24Anonymous__25375] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__25368,Vvar__1__Plt__25369,Vvar__2__Pgt__25370) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__25372,Vvar__1__Plt__25373,Vvar__2__Pgt__25374) ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__3] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1085,Vvar__1___24Anonymous__1086,Vvar__0__A__1087] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1085,Vvar__1___24Anonymous__1086) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1087) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__10466,Vvar__1__B__10467,Vvar__2___24Anonymous__10468,Vvar__0__A__10469,Vvar__1__B__10470,Vvar__2___24Anonymous__10471] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10466,Vvar__1__B__10467,Vvar__2___24Anonymous__10468) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10469,Vvar__1__B__10470,Vvar__2___24Anonymous__10471) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__1126,Vvar__0__A__1127,Vvar__1___24Anonymous__1128,Vvar__2___24Anonymous__1129] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1126) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1127,Vvar__1___24Anonymous__1128,Vvar__2___24Anonymous__1129) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Decimal$Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__25407,Vvar__1__f__25408,Vvar__0__i__25409,Vvar__1__f__25410,Vvar__2__e__25411] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__25407,Vvar__1__f__25408) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__25409,Vvar__1__f__25410,Vvar__2__e__25411) ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__10682] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__10682) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__22899,Vvar__0__d__22900] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__22899) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__22900) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__55,Vvar__1__B__56,Vvar__2___24Anonymous__57,Vvar__0__A__58,Vvar__1__B__59,Vvar__2___24Anonymous__60] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__55,Vvar__1__B__56,Vvar__2___24Anonymous__57) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__58,Vvar__1__B__59) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__25,Vvar__1__B__26,Vvar__2___24Anonymous__27,Vvar__0__A__28,Vvar__1__B__29,Vvar__2___24Anonymous__30] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__25,Vvar__1__B__26) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__28,Vvar__1__B__29) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__837] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__837) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__846] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__846) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__903,Vvar__0___24Anonymous__904] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__903) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__904) ).
fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__27207,Vvar__1___24Anonymous__27208] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__27207,Vvar__1___24Anonymous__27208) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__9597] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__9597) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__14861,Vvar__1___24Anonymous__14862,Vvar__0__x__14863,Vvar__1__n__14864,Vvar__2___24Anonymous__14865] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__14861) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__14863,Vvar__1__n__14864) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__24570,Vvar__1___24Anonymous__24571] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__24570,Vvar__1___24Anonymous__24571) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__14125,Vvar__1__lt__14126,Vvar__2__eq__14127,Vvar__3__x__14128,Vvar__4__y__14129,Vvar__5___24Anonymous__14130,Vvar__0__X__14131,Vvar__1__lt__14132,Vvar__2__eq__14133,Vvar__3__x__14134,Vvar__4__y__14135,Vvar__5___24Anonymous__14136] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__14125,Vvar__1__lt__14126,Vvar__2__eq__14127,Vvar__3__x__14128,Vvar__4__y__14129) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__14131,Vvar__1__lt__14132,Vvar__2__eq__14133,Vvar__3__x__14134,Vvar__4__y__14135) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.Fin.F1$Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__12367,Vvar__0__n__12368,Vvar__1___24Anonymous__12369] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__12367) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__12368,Vvar__1___24Anonymous__12369) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__21562,Vvar__0__A__21563,Vvar__1__h__21564,Vvar__2__n__21565,Vvar__3___24Anonymous__21566] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21562) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21563,Vvar__1__h__21564,Vvar__2__n__21565,Vvar__3___24Anonymous__21566) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__10834,Vvar__1___24Anonymous__10835,Vvar__0__C__10836,Vvar__1___24Anonymous__10837] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__10834,Vvar__1___24Anonymous__10835) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__10836,Vvar__1___24Anonymous__10837) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__10906,Vvar__1___24Anonymous__10907,Vvar__0__C__10908,Vvar__1___24Anonymous__10909,Vvar__2___24Anonymous__10910] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__10906,Vvar__1___24Anonymous__10907) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__10908,Vvar__1___24Anonymous__10909,Vvar__2___24Anonymous__10910) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__22919,Vvar__1___24Anonymous__22920] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__22919,Vvar__1___24Anonymous__22920) ).
fof('$_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$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__20434,Vvar__1___24Anonymous__20435,Vvar__0__C__20436,Vvar__1___24Anonymous__20437] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20434,Vvar__1___24Anonymous__20435) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20436,Vvar__1___24Anonymous__20437) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__24925,Vvar__1__TX__24926,Vvar__2__AA__24927,Vvar__3__AF__24928,Vvar__0__TA__24929,Vvar__1__TX__24930,Vvar__2__AA__24931,Vvar__3__AF__24932] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__24925,Vvar__1__TX__24926,Vvar__2__AA__24927,Vvar__3__AF__24928) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__24929,Vvar__1__TX__24930,Vvar__2__AA__24931,Vvar__3__AF__24932) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__25039,Vvar__0__A__25040,Vvar__1___24Anonymous__25041] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25039) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25040,Vvar__1___24Anonymous__25041) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__25122,Vvar__1___24Anonymous__25123] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25122,Vvar__1___24Anonymous__25123) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__2267,Vvar__0__C__2268] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__2267) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__2268) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__3821,Vvar__0__C__3822] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3821) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3822) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__3465,Vvar__1___24Anonymous__3466,Vvar__0__C__3467,Vvar__1___24Anonymous__3468,Vvar__2___24Anonymous__3469] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__3465,Vvar__1___24Anonymous__3466) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__3467,Vvar__1___24Anonymous__3468,Vvar__2___24Anonymous__3469) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__3631,Vvar__1___24Anonymous__3632] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3631,Vvar__1___24Anonymous__3632) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__26756,Vvar__1__req__26757,Vvar__2__reqb__26758,Vvar__3___24Anonymous__26759] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__26756,Vvar__1__req__26757,Vvar__2__reqb__26758) ).
fof('$_discrim_Hammer.Tactics.Reconstr.Empty$Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eEmpty != cHammer_2eTactics_2eReconstr_2eAllHyps ).
fof('$_discrim_Lambda.Terms.Ref$Lambda.Terms.Abs',axiom,
! [Vvar__0___24Anonymous__84,Vvar__0___24Anonymous__85] : cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__84) != cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__85) ).
fof('$_fix_27202_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__27203] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27203)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27203)
& c_24__fix__27202__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__27202__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__27203)) )
| ? [Vvar__0___24Anonymous__27204] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27204)
& Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__27204)
& c_24__fix__27202__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__27204) )
| ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__27202__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_fix_29246_v_CANONICAL_1',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)
& c_24__fix__29246__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
| ? [Vvar__1___24Anonymous__29250] :
( t(Vvar__1___24Anonymous__29250,Vv__CANONICAL__0)
& ? [Vvar__2___24Anonymous__29251] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__29251)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29250,Vvar__2___24Anonymous__29251)
& c_24__fix__29246__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__29250,c_24__fix__29246__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__29251,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_fix_769_v_CANONICAL_0',axiom,
! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> ( ? [Vvar__0___24Anonymous__770] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__770)
& Vv__CANONICAL__1 = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__770)
& c_24__fix__769__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2einsert__Ref___24a3(Vv__CANONICAL__2,Vvar__0___24Anonymous__770,Vv__CANONICAL__3) )
| ? [Vvar__0___24Anonymous__771] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__771)
& Vv__CANONICAL__1 = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__771)
& c_24__fix__769__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eAbs___24a1(c_24__fix__769__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__771,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3))) )
| ? [Vvar__0___24Anonymous__772] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__772)
& ? [Vvar__1___24Anonymous__773] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__773)
& Vv__CANONICAL__1 = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__772,Vvar__1___24Anonymous__773)
& c_24__fix__769__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cLambda_2eTerms_2eApp___24a2(c_24__fix__769__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__772,Vv__CANONICAL__2,Vv__CANONICAL__3),c_24__fix__769__v__CANONICAL__0___24a3(Vvar__1___24Anonymous__773,Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__22886,Vvar__0__P__22887,Vvar__1___24Anonymous__22888,Vvar__1___24Anonymous__22889] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__22886) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__22887)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__22886 = Vvar__0__P__22887 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__22882,Vvar__0__P__22883,Vvar__1___24Anonymous__22884,Vvar__1___24Anonymous__22885] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__22882) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__22883)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__22882 = Vvar__0__P__22883 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__22434,Vvar__0___24Anonymous__22435,Vvar__1___24Anonymous__22436,Vvar__1___24Anonymous__22437,Vvar__2___24Anonymous__22438,Vvar__2___24Anonymous__22439] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22434,Vvar__1___24Anonymous__22436,Vvar__2___24Anonymous__22438) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22435,Vvar__1___24Anonymous__22437,Vvar__2___24Anonymous__22439)
=> ( Vvar__2___24Anonymous__22438 = Vvar__2___24Anonymous__22439
& Vvar__1___24Anonymous__22436 = Vvar__1___24Anonymous__22437
& Vvar__0___24Anonymous__22434 = Vvar__0___24Anonymous__22435 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__25376,Vvar__0__Peq__25377,Vvar__1__Plt__25378,Vvar__1__Plt__25379,Vvar__2__Pgt__25380,Vvar__2__Pgt__25381,Vvar__3___24Anonymous__25382,Vvar__3___24Anonymous__25383] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__25376,Vvar__1__Plt__25378,Vvar__2__Pgt__25380) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__25377,Vvar__1__Plt__25379,Vvar__2__Pgt__25381)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__25380 = Vvar__2__Pgt__25381
& Vvar__1__Plt__25378 = Vvar__1__Plt__25379
& Vvar__0__Peq__25376 = Vvar__0__Peq__25377 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__25392,Vvar__0__Peq__25393,Vvar__1__Plt__25394,Vvar__1__Plt__25395,Vvar__2__Pgt__25396,Vvar__2__Pgt__25397,Vvar__3___24Anonymous__25398,Vvar__3___24Anonymous__25399] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__25392,Vvar__1__Plt__25394,Vvar__2__Pgt__25396) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__25393,Vvar__1__Plt__25395,Vvar__2__Pgt__25397)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__25396 = Vvar__2__Pgt__25397
& Vvar__1__Plt__25394 = Vvar__1__Plt__25395
& Vvar__0__Peq__25392 = Vvar__0__Peq__25393 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__25384,Vvar__0__Peq__25385,Vvar__1__Plt__25386,Vvar__1__Plt__25387,Vvar__2__Pgt__25388,Vvar__2__Pgt__25389,Vvar__3___24Anonymous__25390,Vvar__3___24Anonymous__25391] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__25384,Vvar__1__Plt__25386,Vvar__2__Pgt__25388) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__25385,Vvar__1__Plt__25387,Vvar__2__Pgt__25389)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__25388 = Vvar__2__Pgt__25389
& Vvar__1__Plt__25386 = Vvar__1__Plt__25387
& Vvar__0__Peq__25384 = Vvar__0__Peq__25385 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1092,Vvar__0__A__1093] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1092) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1093)
=> Vvar__0__A__1092 = Vvar__0__A__1093 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__4,Vvar__0___24Anonymous__5] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5)
=> Vvar__0___24Anonymous__4 = Vvar__0___24Anonymous__5 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__1088,Vvar__0__A__1089,Vvar__1___24Anonymous__1090,Vvar__1___24Anonymous__1091] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1088,Vvar__1___24Anonymous__1090) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1089,Vvar__1___24Anonymous__1091)
=> ( Vvar__1___24Anonymous__1090 = Vvar__1___24Anonymous__1091
& Vvar__0__A__1088 = Vvar__0__A__1089 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__1132,Vvar__0__A__1133,Vvar__1___24Anonymous__1134,Vvar__1___24Anonymous__1135,Vvar__2___24Anonymous__1136,Vvar__2___24Anonymous__1137] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1132,Vvar__1___24Anonymous__1134,Vvar__2___24Anonymous__1136) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1133,Vvar__1___24Anonymous__1135,Vvar__2___24Anonymous__1137)
=> ( Vvar__2___24Anonymous__1136 = Vvar__2___24Anonymous__1137
& Vvar__1___24Anonymous__1134 = Vvar__1___24Anonymous__1135
& Vvar__0__A__1132 = Vvar__0__A__1133 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__10472,Vvar__0__A__10473,Vvar__1__B__10474,Vvar__1__B__10475,Vvar__2___24Anonymous__10476,Vvar__2___24Anonymous__10477] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10472,Vvar__1__B__10474,Vvar__2___24Anonymous__10476) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10473,Vvar__1__B__10475,Vvar__2___24Anonymous__10477)
=> ( Vvar__2___24Anonymous__10476 = Vvar__2___24Anonymous__10477
& Vvar__1__B__10474 = Vvar__1__B__10475
& Vvar__0__A__10472 = Vvar__0__A__10473 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__10478,Vvar__0__A__10479,Vvar__1__B__10480,Vvar__1__B__10481,Vvar__2___24Anonymous__10482,Vvar__2___24Anonymous__10483] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10478,Vvar__1__B__10480,Vvar__2___24Anonymous__10482) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10479,Vvar__1__B__10481,Vvar__2___24Anonymous__10483)
=> ( Vvar__2___24Anonymous__10482 = Vvar__2___24Anonymous__10483
& Vvar__1__B__10480 = Vvar__1__B__10481
& Vvar__0__A__10478 = Vvar__0__A__10479 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__1130,Vvar__0__A__1131] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1130) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1131)
=> Vvar__0__A__1130 = Vvar__0__A__1131 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__1104,Vvar__0__A__1105,Vvar__1__B__1106,Vvar__1__B__1107,Vvar__2___24Anonymous__1108,Vvar__2___24Anonymous__1109,Vvar__3___24Anonymous__1110,Vvar__3___24Anonymous__1111] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1104,Vvar__1__B__1106,Vvar__2___24Anonymous__1108,Vvar__3___24Anonymous__1110) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1105,Vvar__1__B__1107,Vvar__2___24Anonymous__1109,Vvar__3___24Anonymous__1111)
=> ( Vvar__3___24Anonymous__1110 = Vvar__3___24Anonymous__1111
& Vvar__2___24Anonymous__1108 = Vvar__2___24Anonymous__1109
& Vvar__1__B__1106 = Vvar__1__B__1107
& Vvar__0__A__1104 = Vvar__0__A__1105 ) ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__10683,Vvar__0___24Anonymous__10684] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__10683) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__10684)
=> Vvar__0___24Anonymous__10683 = Vvar__0___24Anonymous__10684 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__10685,Vvar__0___24Anonymous__10686] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__10685) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__10686)
=> Vvar__0___24Anonymous__10685 = Vvar__0___24Anonymous__10686 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__10687,Vvar__0___24Anonymous__10688] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__10687) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__10688)
=> Vvar__0___24Anonymous__10687 = Vvar__0___24Anonymous__10688 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__10689,Vvar__0___24Anonymous__10690] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__10689) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__10690)
=> Vvar__0___24Anonymous__10689 = Vvar__0___24Anonymous__10690 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__10691,Vvar__0___24Anonymous__10692] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__10691) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__10692)
=> Vvar__0___24Anonymous__10691 = Vvar__0___24Anonymous__10692 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__10693,Vvar__0___24Anonymous__10694] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__10693) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__10694)
=> Vvar__0___24Anonymous__10693 = Vvar__0___24Anonymous__10694 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__10695,Vvar__0___24Anonymous__10696] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__10695) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__10696)
=> Vvar__0___24Anonymous__10695 = Vvar__0___24Anonymous__10696 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__10697,Vvar__0___24Anonymous__10698] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__10697) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__10698)
=> Vvar__0___24Anonymous__10697 = Vvar__0___24Anonymous__10698 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__10699,Vvar__0___24Anonymous__10700] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__10699) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__10700)
=> Vvar__0___24Anonymous__10699 = Vvar__0___24Anonymous__10700 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__10701,Vvar__0___24Anonymous__10702] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__10701) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__10702)
=> Vvar__0___24Anonymous__10701 = Vvar__0___24Anonymous__10702 ) ).
fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
! [Vvar__0__i__25412,Vvar__0__i__25413,Vvar__1__f__25414,Vvar__1__f__25415] :
( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__25412,Vvar__1__f__25414) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__25413,Vvar__1__f__25415)
=> ( Vvar__1__f__25414 = Vvar__1__f__25415
& Vvar__0__i__25412 = Vvar__0__i__25413 ) ) ).
fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
! [Vvar__0__i__25416,Vvar__0__i__25417,Vvar__1__f__25418,Vvar__1__f__25419,Vvar__2__e__25420,Vvar__2__e__25421] :
( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__25416,Vvar__1__f__25418,Vvar__2__e__25420) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__25417,Vvar__1__f__25419,Vvar__2__e__25421)
=> ( Vvar__2__e__25420 = Vvar__2__e__25421
& Vvar__1__f__25418 = Vvar__1__f__25419
& Vvar__0__i__25416 = Vvar__0__i__25417 ) ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__22903,Vvar__0__d__22904] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__22903) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__22904)
=> Vvar__0__d__22903 = Vvar__0__d__22904 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__22901,Vvar__0__d__22902] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__22901) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__22902)
=> Vvar__0__d__22901 = Vvar__0__d__22902 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__21121,Vvar__0__A__21122,Vvar__1__P__21123,Vvar__1__P__21124,Vvar__2__x__21125,Vvar__2__x__21126,Vvar__3___24Anonymous__21127,Vvar__3___24Anonymous__21128] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__21121,Vvar__1__P__21123,Vvar__2__x__21125) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__21122,Vvar__1__P__21124,Vvar__2__x__21126)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__21125 = Vvar__2__x__21126
& Vvar__1__P__21123 = Vvar__1__P__21124
& Vvar__0__A__21121 = Vvar__0__A__21122 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__24499,Vvar__0__A__24500,Vvar__1__P__24501,Vvar__1__P__24502,Vvar__2__Q__24503,Vvar__2__Q__24504,Vvar__3__x__24505,Vvar__3__x__24506,Vvar__4___24Anonymous__24507,Vvar__4___24Anonymous__24508,Vvar__5___24Anonymous__24509,Vvar__5___24Anonymous__24510] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__24499,Vvar__1__P__24501,Vvar__2__Q__24503,Vvar__3__x__24505) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__24500,Vvar__1__P__24502,Vvar__2__Q__24504,Vvar__3__x__24506)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__24505 = Vvar__3__x__24506
& Vvar__2__Q__24503 = Vvar__2__Q__24504
& Vvar__1__P__24501 = Vvar__1__P__24502
& Vvar__0__A__24499 = Vvar__0__A__24500 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__21160,Vvar__0__A__21161,Vvar__1__P__21162,Vvar__1__P__21163,Vvar__2__x__21164,Vvar__2__x__21165,Vvar__3___24Anonymous__21166,Vvar__3___24Anonymous__21167] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__21160,Vvar__1__P__21162,Vvar__2__x__21164,Vvar__3___24Anonymous__21166) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__21161,Vvar__1__P__21163,Vvar__2__x__21165,Vvar__3___24Anonymous__21167)
=> ( Vvar__3___24Anonymous__21166 = Vvar__3___24Anonymous__21167
& Vvar__2__x__21164 = Vvar__2__x__21165
& Vvar__1__P__21162 = Vvar__1__P__21163
& Vvar__0__A__21160 = Vvar__0__A__21161 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__24555,Vvar__0__A__24556,Vvar__1__P__24557,Vvar__1__P__24558,Vvar__2__Q__24559,Vvar__2__Q__24560,Vvar__3__x__24561,Vvar__3__x__24562,Vvar__4___24Anonymous__24563,Vvar__4___24Anonymous__24564,Vvar__5___24Anonymous__24565,Vvar__5___24Anonymous__24566] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__24555,Vvar__1__P__24557,Vvar__2__Q__24559,Vvar__3__x__24561,Vvar__4___24Anonymous__24563,Vvar__5___24Anonymous__24565) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__24556,Vvar__1__P__24558,Vvar__2__Q__24560,Vvar__3__x__24562,Vvar__4___24Anonymous__24564,Vvar__5___24Anonymous__24566)
=> ( Vvar__5___24Anonymous__24565 = Vvar__5___24Anonymous__24566
& Vvar__4___24Anonymous__24563 = Vvar__4___24Anonymous__24564
& Vvar__3__x__24561 = Vvar__3__x__24562
& Vvar__2__Q__24559 = Vvar__2__Q__24560
& Vvar__1__P__24557 = Vvar__1__P__24558
& Vvar__0__A__24555 = Vvar__0__A__24556 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__61,Vvar__0__A__62,Vvar__1__B__63,Vvar__1__B__64,Vvar__2___24Anonymous__65,Vvar__2___24Anonymous__66] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__61,Vvar__1__B__63,Vvar__2___24Anonymous__65) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__62,Vvar__1__B__64,Vvar__2___24Anonymous__66)
=> ( Vvar__2___24Anonymous__65 = Vvar__2___24Anonymous__66
& Vvar__1__B__63 = Vvar__1__B__64
& Vvar__0__A__61 = Vvar__0__A__62 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__67,Vvar__0__A__68,Vvar__1__B__69,Vvar__1__B__70,Vvar__2___24Anonymous__71,Vvar__2___24Anonymous__72] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__67,Vvar__1__B__69) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__68,Vvar__1__B__70)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__69 = Vvar__1__B__70
& Vvar__0__A__67 = Vvar__0__A__68 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__31,Vvar__0__A__32,Vvar__1__B__33,Vvar__1__B__34,Vvar__2___24Anonymous__35,Vvar__2___24Anonymous__36] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__31,Vvar__1__B__33) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__32,Vvar__1__B__34)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__33 = Vvar__1__B__34
& Vvar__0__A__31 = Vvar__0__A__32 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__37,Vvar__0__A__38,Vvar__1__B__39,Vvar__1__B__40,Vvar__2___24Anonymous__41,Vvar__2___24Anonymous__42] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__37,Vvar__1__B__39) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__38,Vvar__1__B__40)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__39 = Vvar__1__B__40
& Vvar__0__A__37 = Vvar__0__A__38 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__838,Vvar__0___24Anonymous__839] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__838) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__839)
=> Vvar__0___24Anonymous__838 = Vvar__0___24Anonymous__839 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__849,Vvar__0___24Anonymous__850] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__849) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__850)
=> Vvar__0___24Anonymous__849 = Vvar__0___24Anonymous__850 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__847,Vvar__0___24Anonymous__848] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__847) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__848)
=> Vvar__0___24Anonymous__847 = Vvar__0___24Anonymous__848 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__905,Vvar__0___24Anonymous__906] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__905) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__906)
=> Vvar__0___24Anonymous__905 = Vvar__0___24Anonymous__906 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__907,Vvar__0___24Anonymous__908] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__907) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__908)
=> Vvar__0___24Anonymous__907 = Vvar__0___24Anonymous__908 ) ).
fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
! [Vvar__0__p__27209,Vvar__0__p__27210,Vvar__1___24Anonymous__27211,Vvar__1___24Anonymous__27212] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__27209,Vvar__1___24Anonymous__27211) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__27210,Vvar__1___24Anonymous__27212)
=> ( Vvar__1___24Anonymous__27211 = Vvar__1___24Anonymous__27212
& Vvar__0__p__27209 = Vvar__0__p__27210 ) ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__9598,Vvar__0___24Anonymous__9599] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__9598) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__9599)
=> Vvar__0___24Anonymous__9598 = Vvar__0___24Anonymous__9599 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__14213,Vvar__0__Qnum__14214,Vvar__1__Qden__14215,Vvar__1__Qden__14216] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14213,Vvar__1__Qden__14215) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14214,Vvar__1__Qden__14216)
=> ( Vvar__1__Qden__14215 = Vvar__1__Qden__14216
& Vvar__0__Qnum__14213 = Vvar__0__Qnum__14214 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
! [Vvar__0__neg__25558,Vvar__0__neg__25559,Vvar__1__cond__neg__25560,Vvar__1__cond__neg__25561] :
( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__25558) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__25559)
=> ( c_24Proof = c_24Proof
& Vvar__0__neg__25558 = Vvar__0__neg__25559 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
! [Vvar__0__nonneg__25544,Vvar__0__nonneg__25545,Vvar__1__cond__nonneg__25546,Vvar__1__cond__nonneg__25547] :
( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__25544) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__25545)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonneg__25544 = Vvar__0__nonneg__25545 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
! [Vvar__0__nonpos__14280,Vvar__0__nonpos__14281,Vvar__1__cond__nonpos__14282,Vvar__1__cond__nonpos__14283] :
( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__14280) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__14281)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonpos__14280 = Vvar__0__nonpos__14281 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__25565,Vvar__0__nonzero__25566,Vvar__1__cond__nonzero__25567,Vvar__1__cond__nonzero__25568] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__25565) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__25566)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__25565 = Vvar__0__nonzero__25566 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
! [Vvar__0__pos__25551,Vvar__0__pos__25552,Vvar__1__cond__pos__25553,Vvar__1__cond__pos__25554] :
( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__25551) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__25552)
=> ( c_24Proof = c_24Proof
& Vvar__0__pos__25551 = Vvar__0__pos__25552 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__14876,Vvar__0__x__14877,Vvar__1__n__14878,Vvar__1__n__14879,Vvar__2___24Anonymous__14880,Vvar__2___24Anonymous__14881] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__14876,Vvar__1__n__14878) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__14877,Vvar__1__n__14879)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__14878 = Vvar__1__n__14879
& Vvar__0__x__14876 = Vvar__0__x__14877 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__14866,Vvar__0__x__14867,Vvar__1___24Anonymous__14868,Vvar__1___24Anonymous__14869] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__14866) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__14867)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__14866 = Vvar__0__x__14867 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__14870,Vvar__0__x__14871,Vvar__1__n__14872,Vvar__1__n__14873,Vvar__2___24Anonymous__14874,Vvar__2___24Anonymous__14875] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__14870,Vvar__1__n__14872) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__14871,Vvar__1__n__14873)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__14872 = Vvar__1__n__14873
& Vvar__0__x__14870 = Vvar__0__x__14871 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__22852,Vvar__0___24Anonymous__22853,Vvar__1___24Anonymous__22854,Vvar__1___24Anonymous__22855,Vvar__2___24Anonymous__22856,Vvar__2___24Anonymous__22857,Vvar__3___24Anonymous__22858,Vvar__3___24Anonymous__22859,Vvar__4___24Anonymous__22860,Vvar__4___24Anonymous__22861,Vvar__5___24Anonymous__22862,Vvar__5___24Anonymous__22863,Vvar__6___24Anonymous__22864,Vvar__6___24Anonymous__22865,Vvar__7___24Anonymous__22866,Vvar__7___24Anonymous__22867] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__22852,Vvar__1___24Anonymous__22854,Vvar__2___24Anonymous__22856,Vvar__3___24Anonymous__22858,Vvar__4___24Anonymous__22860,Vvar__5___24Anonymous__22862,Vvar__6___24Anonymous__22864,Vvar__7___24Anonymous__22866) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__22853,Vvar__1___24Anonymous__22855,Vvar__2___24Anonymous__22857,Vvar__3___24Anonymous__22859,Vvar__4___24Anonymous__22861,Vvar__5___24Anonymous__22863,Vvar__6___24Anonymous__22865,Vvar__7___24Anonymous__22867)
=> ( Vvar__7___24Anonymous__22866 = Vvar__7___24Anonymous__22867
& Vvar__6___24Anonymous__22864 = Vvar__6___24Anonymous__22865
& Vvar__5___24Anonymous__22862 = Vvar__5___24Anonymous__22863
& Vvar__4___24Anonymous__22860 = Vvar__4___24Anonymous__22861
& Vvar__3___24Anonymous__22858 = Vvar__3___24Anonymous__22859
& Vvar__2___24Anonymous__22856 = Vvar__2___24Anonymous__22857
& Vvar__1___24Anonymous__22854 = Vvar__1___24Anonymous__22855
& Vvar__0___24Anonymous__22852 = Vvar__0___24Anonymous__22853 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__24572,Vvar__0___24Anonymous__24573,Vvar__1___24Anonymous__24574,Vvar__1___24Anonymous__24575] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__24572,Vvar__1___24Anonymous__24574) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__24573,Vvar__1___24Anonymous__24575)
=> ( Vvar__1___24Anonymous__24574 = Vvar__1___24Anonymous__24575
& Vvar__0___24Anonymous__24572 = Vvar__0___24Anonymous__24573 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__14149,Vvar__0__X__14150,Vvar__1__lt__14151,Vvar__1__lt__14152,Vvar__2__eq__14153,Vvar__2__eq__14154,Vvar__3__x__14155,Vvar__3__x__14156,Vvar__4__y__14157,Vvar__4__y__14158,Vvar__5___24Anonymous__14159,Vvar__5___24Anonymous__14160] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__14149,Vvar__1__lt__14151,Vvar__2__eq__14153,Vvar__3__x__14155,Vvar__4__y__14157) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__14150,Vvar__1__lt__14152,Vvar__2__eq__14154,Vvar__3__x__14156,Vvar__4__y__14158)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__14157 = Vvar__4__y__14158
& Vvar__3__x__14155 = Vvar__3__x__14156
& Vvar__2__eq__14153 = Vvar__2__eq__14154
& Vvar__1__lt__14151 = Vvar__1__lt__14152
& Vvar__0__X__14149 = Vvar__0__X__14150 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__14161,Vvar__0__X__14162,Vvar__1__lt__14163,Vvar__1__lt__14164,Vvar__2__eq__14165,Vvar__2__eq__14166,Vvar__3__x__14167,Vvar__3__x__14168,Vvar__4__y__14169,Vvar__4__y__14170,Vvar__5___24Anonymous__14171,Vvar__5___24Anonymous__14172] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__14161,Vvar__1__lt__14163,Vvar__2__eq__14165,Vvar__3__x__14167,Vvar__4__y__14169) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__14162,Vvar__1__lt__14164,Vvar__2__eq__14166,Vvar__3__x__14168,Vvar__4__y__14170)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__14169 = Vvar__4__y__14170
& Vvar__3__x__14167 = Vvar__3__x__14168
& Vvar__2__eq__14165 = Vvar__2__eq__14166
& Vvar__1__lt__14163 = Vvar__1__lt__14164
& Vvar__0__X__14161 = Vvar__0__X__14162 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__14137,Vvar__0__X__14138,Vvar__1__lt__14139,Vvar__1__lt__14140,Vvar__2__eq__14141,Vvar__2__eq__14142,Vvar__3__x__14143,Vvar__3__x__14144,Vvar__4__y__14145,Vvar__4__y__14146,Vvar__5___24Anonymous__14147,Vvar__5___24Anonymous__14148] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__14137,Vvar__1__lt__14139,Vvar__2__eq__14141,Vvar__3__x__14143,Vvar__4__y__14145) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__14138,Vvar__1__lt__14140,Vvar__2__eq__14142,Vvar__3__x__14144,Vvar__4__y__14146)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__14145 = Vvar__4__y__14146
& Vvar__3__x__14143 = Vvar__3__x__14144
& Vvar__2__eq__14141 = Vvar__2__eq__14142
& Vvar__1__lt__14139 = Vvar__1__lt__14140
& Vvar__0__X__14137 = Vvar__0__X__14138 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__12370,Vvar__0__n__12371] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__12370) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__12371)
=> Vvar__0__n__12370 = Vvar__0__n__12371 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__12372,Vvar__0__n__12373,Vvar__1___24Anonymous__12374,Vvar__1___24Anonymous__12375] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__12372,Vvar__1___24Anonymous__12374) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__12373,Vvar__1___24Anonymous__12375)
=> ( Vvar__1___24Anonymous__12374 = Vvar__1___24Anonymous__12375
& Vvar__0__n__12372 = Vvar__0__n__12373 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__21569,Vvar__0__A__21570,Vvar__1__h__21571,Vvar__1__h__21572,Vvar__2__n__21573,Vvar__2__n__21574,Vvar__3___24Anonymous__21575,Vvar__3___24Anonymous__21576] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21569,Vvar__1__h__21571,Vvar__2__n__21573,Vvar__3___24Anonymous__21575) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21570,Vvar__1__h__21572,Vvar__2__n__21574,Vvar__3___24Anonymous__21576)
=> ( Vvar__3___24Anonymous__21575 = Vvar__3___24Anonymous__21576
& Vvar__2__n__21573 = Vvar__2__n__21574
& Vvar__1__h__21571 = Vvar__1__h__21572
& Vvar__0__A__21569 = Vvar__0__A__21570 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__21567,Vvar__0__A__21568] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21567) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21568)
=> Vvar__0__A__21567 = Vvar__0__A__21568 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__25177,Vvar__0__a__25178,Vvar__1__b__25179,Vvar__1__b__25180,Vvar__2__u__25181,Vvar__2__u__25182,Vvar__3__v__25183,Vvar__3__v__25184,Vvar__4__d__25185,Vvar__4__d__25186,Vvar__5___24Anonymous__25187,Vvar__5___24Anonymous__25188,Vvar__6___24Anonymous__25189,Vvar__6___24Anonymous__25190] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__25177,Vvar__1__b__25179,Vvar__2__u__25181,Vvar__3__v__25183,Vvar__4__d__25185) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__25178,Vvar__1__b__25180,Vvar__2__u__25182,Vvar__3__v__25184,Vvar__4__d__25186)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__25185 = Vvar__4__d__25186
& Vvar__3__v__25183 = Vvar__3__v__25184
& Vvar__2__u__25181 = Vvar__2__u__25182
& Vvar__1__b__25179 = Vvar__1__b__25180
& Vvar__0__a__25177 = Vvar__0__a__25178 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__27063,Vvar__0__x__27064,Vvar__1__p__27065,Vvar__1__p__27066,Vvar__2__q__27067,Vvar__2__q__27068,Vvar__3__r__27069,Vvar__3__r__27070,Vvar__4___24Anonymous__27071,Vvar__4___24Anonymous__27072,Vvar__5___24Anonymous__27073,Vvar__5___24Anonymous__27074,Vvar__6___24Anonymous__27075,Vvar__6___24Anonymous__27076] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__27063,Vvar__1__p__27065,Vvar__2__q__27067,Vvar__3__r__27069) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__27064,Vvar__1__p__27066,Vvar__2__q__27068,Vvar__3__r__27070)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__27069 = Vvar__3__r__27070
& Vvar__2__q__27067 = Vvar__2__q__27068
& Vvar__1__p__27065 = Vvar__1__p__27066
& Vvar__0__x__27063 = Vvar__0__x__27064 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__10842,Vvar__0__C__10843,Vvar__1___24Anonymous__10844,Vvar__1___24Anonymous__10845] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__10842,Vvar__1___24Anonymous__10844) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__10843,Vvar__1___24Anonymous__10845)
=> ( Vvar__1___24Anonymous__10844 = Vvar__1___24Anonymous__10845
& Vvar__0__C__10842 = Vvar__0__C__10843 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__10846,Vvar__0__C__10847,Vvar__1___24Anonymous__10848,Vvar__1___24Anonymous__10849,Vvar__2___24Anonymous__10850,Vvar__2___24Anonymous__10851] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__10846,Vvar__1___24Anonymous__10848,Vvar__2___24Anonymous__10850) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__10847,Vvar__1___24Anonymous__10849,Vvar__2___24Anonymous__10851)
=> ( Vvar__2___24Anonymous__10850 = Vvar__2___24Anonymous__10851
& Vvar__1___24Anonymous__10848 = Vvar__1___24Anonymous__10849
& Vvar__0__C__10846 = Vvar__0__C__10847 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__10838,Vvar__0__C__10839,Vvar__1___24Anonymous__10840,Vvar__1___24Anonymous__10841] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__10838,Vvar__1___24Anonymous__10840) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__10839,Vvar__1___24Anonymous__10841)
=> ( Vvar__1___24Anonymous__10840 = Vvar__1___24Anonymous__10841
& Vvar__0__C__10838 = Vvar__0__C__10839 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__10858,Vvar__0__C__10859,Vvar__1___24Anonymous__10860,Vvar__1___24Anonymous__10861,Vvar__2___24Anonymous__10862,Vvar__2___24Anonymous__10863] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__10858,Vvar__1___24Anonymous__10860,Vvar__2___24Anonymous__10862) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__10859,Vvar__1___24Anonymous__10861,Vvar__2___24Anonymous__10863)
=> ( Vvar__2___24Anonymous__10862 = Vvar__2___24Anonymous__10863
& Vvar__1___24Anonymous__10860 = Vvar__1___24Anonymous__10861
& Vvar__0__C__10858 = Vvar__0__C__10859 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__10864,Vvar__0__C__10865,Vvar__1___24Anonymous__10866,Vvar__1___24Anonymous__10867] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__10864,Vvar__1___24Anonymous__10866) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__10865,Vvar__1___24Anonymous__10867)
=> ( Vvar__1___24Anonymous__10866 = Vvar__1___24Anonymous__10867
& Vvar__0__C__10864 = Vvar__0__C__10865 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__10868,Vvar__0__C__10869,Vvar__1___24Anonymous__10870,Vvar__1___24Anonymous__10871,Vvar__2___24Anonymous__10872,Vvar__2___24Anonymous__10873] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__10868,Vvar__1___24Anonymous__10870,Vvar__2___24Anonymous__10872) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__10869,Vvar__1___24Anonymous__10871,Vvar__2___24Anonymous__10873)
=> ( Vvar__2___24Anonymous__10872 = Vvar__2___24Anonymous__10873
& Vvar__1___24Anonymous__10870 = Vvar__1___24Anonymous__10871
& Vvar__0__C__10868 = Vvar__0__C__10869 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__10852,Vvar__0__C__10853,Vvar__1___24Anonymous__10854,Vvar__1___24Anonymous__10855,Vvar__2___24Anonymous__10856,Vvar__2___24Anonymous__10857] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__10852,Vvar__1___24Anonymous__10854,Vvar__2___24Anonymous__10856) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__10853,Vvar__1___24Anonymous__10855,Vvar__2___24Anonymous__10857)
=> ( Vvar__2___24Anonymous__10856 = Vvar__2___24Anonymous__10857
& Vvar__1___24Anonymous__10854 = Vvar__1___24Anonymous__10855
& Vvar__0__C__10852 = Vvar__0__C__10853 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__10921,Vvar__0__C__10922,Vvar__1___24Anonymous__10923,Vvar__1___24Anonymous__10924,Vvar__2___24Anonymous__10925,Vvar__2___24Anonymous__10926,Vvar__3___24Anonymous__10927,Vvar__3___24Anonymous__10928] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__10921,Vvar__1___24Anonymous__10923,Vvar__2___24Anonymous__10925,Vvar__3___24Anonymous__10927) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__10922,Vvar__1___24Anonymous__10924,Vvar__2___24Anonymous__10926,Vvar__3___24Anonymous__10928)
=> ( Vvar__3___24Anonymous__10927 = Vvar__3___24Anonymous__10928
& Vvar__2___24Anonymous__10925 = Vvar__2___24Anonymous__10926
& Vvar__1___24Anonymous__10923 = Vvar__1___24Anonymous__10924
& Vvar__0__C__10921 = Vvar__0__C__10922 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__10911,Vvar__0__C__10912,Vvar__1___24Anonymous__10913,Vvar__1___24Anonymous__10914] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__10911,Vvar__1___24Anonymous__10913) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__10912,Vvar__1___24Anonymous__10914)
=> ( Vvar__1___24Anonymous__10913 = Vvar__1___24Anonymous__10914
& Vvar__0__C__10911 = Vvar__0__C__10912 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__10915,Vvar__0__C__10916,Vvar__1___24Anonymous__10917,Vvar__1___24Anonymous__10918,Vvar__2___24Anonymous__10919,Vvar__2___24Anonymous__10920] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__10915,Vvar__1___24Anonymous__10917,Vvar__2___24Anonymous__10919) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__10916,Vvar__1___24Anonymous__10918,Vvar__2___24Anonymous__10920)
=> ( Vvar__2___24Anonymous__10919 = Vvar__2___24Anonymous__10920
& Vvar__1___24Anonymous__10917 = Vvar__1___24Anonymous__10918
& Vvar__0__C__10915 = Vvar__0__C__10916 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__22925,Vvar__0___24Anonymous__22926,Vvar__1___24Anonymous__22927,Vvar__1___24Anonymous__22928] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__22925,Vvar__1___24Anonymous__22927) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__22926,Vvar__1___24Anonymous__22928)
=> ( Vvar__1___24Anonymous__22927 = Vvar__1___24Anonymous__22928
& Vvar__0___24Anonymous__22925 = Vvar__0___24Anonymous__22926 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__22921,Vvar__0___24Anonymous__22922,Vvar__1___24Anonymous__22923,Vvar__1___24Anonymous__22924] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__22921,Vvar__1___24Anonymous__22923) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__22922,Vvar__1___24Anonymous__22924)
=> ( Vvar__1___24Anonymous__22923 = Vvar__1___24Anonymous__22924
& Vvar__0___24Anonymous__22921 = Vvar__0___24Anonymous__22922 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__14430,Vvar__0__r__14431] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__14430) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__14431)
=> Vvar__0__r__14430 = Vvar__0__r__14431 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__14418,Vvar__0__r1__14419,Vvar__1__r2__14420,Vvar__1__r2__14421] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__14418,Vvar__1__r2__14420) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__14419,Vvar__1__r2__14421)
=> ( Vvar__1__r2__14420 = Vvar__1__r2__14421
& Vvar__0__r1__14418 = Vvar__0__r1__14419 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__14422,Vvar__0__r1__14423,Vvar__1__r2__14424,Vvar__1__r2__14425] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__14422,Vvar__1__r2__14424) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__14423,Vvar__1__r2__14425)
=> ( Vvar__1__r2__14424 = Vvar__1__r2__14425
& Vvar__0__r1__14422 = Vvar__0__r1__14423 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__14432,Vvar__0__r__14433] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__14432) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__14433)
=> Vvar__0__r__14432 = Vvar__0__r__14433 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__14414,Vvar__0__r1__14415,Vvar__1__r2__14416,Vvar__1__r2__14417] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__14414,Vvar__1__r2__14416) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__14415,Vvar__1__r2__14417)
=> ( Vvar__1__r2__14416 = Vvar__1__r2__14417
& Vvar__0__r1__14414 = Vvar__0__r1__14415 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__14426,Vvar__0__r1__14427,Vvar__1__z__14428,Vvar__1__z__14429] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__14426,Vvar__1__z__14428) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__14427,Vvar__1__z__14429)
=> ( Vvar__1__z__14428 = Vvar__1__z__14429
& Vvar__0__r1__14426 = Vvar__0__r1__14427 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__14410,Vvar__0__r__14411] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__14410) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__14411)
=> Vvar__0__r__14410 = Vvar__0__r__14411 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__14412,Vvar__0__r__14413] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__14412) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__14413)
=> Vvar__0__r__14412 = Vvar__0__r__14413 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__20557,Vvar__0__T__20558,Vvar__1__Flhs__20559,Vvar__1__Flhs__20560,Vvar__2__Fop__20561,Vvar__2__Fop__20562,Vvar__3__Frhs__20563,Vvar__3__Frhs__20564] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20557,Vvar__1__Flhs__20559,Vvar__2__Fop__20561,Vvar__3__Frhs__20563) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20558,Vvar__1__Flhs__20560,Vvar__2__Fop__20562,Vvar__3__Frhs__20564)
=> ( Vvar__3__Frhs__20563 = Vvar__3__Frhs__20564
& Vvar__2__Fop__20561 = Vvar__2__Fop__20562
& Vvar__1__Flhs__20559 = Vvar__1__Flhs__20560
& Vvar__0__T__20557 = Vvar__0__T__20558 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__20458,Vvar__0__C__20459,Vvar__1___24Anonymous__20460,Vvar__1___24Anonymous__20461,Vvar__2___24Anonymous__20462,Vvar__2___24Anonymous__20463] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20458,Vvar__1___24Anonymous__20460,Vvar__2___24Anonymous__20462) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20459,Vvar__1___24Anonymous__20461,Vvar__2___24Anonymous__20463)
=> ( Vvar__2___24Anonymous__20462 = Vvar__2___24Anonymous__20463
& Vvar__1___24Anonymous__20460 = Vvar__1___24Anonymous__20461
& Vvar__0__C__20458 = Vvar__0__C__20459 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__20464,Vvar__0__C__20465,Vvar__1___24Anonymous__20466,Vvar__1___24Anonymous__20467] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20464,Vvar__1___24Anonymous__20466) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20465,Vvar__1___24Anonymous__20467)
=> ( Vvar__1___24Anonymous__20466 = Vvar__1___24Anonymous__20467
& Vvar__0__C__20464 = Vvar__0__C__20465 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__20438,Vvar__0__C__20439,Vvar__1___24Anonymous__20440,Vvar__1___24Anonymous__20441] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20438,Vvar__1___24Anonymous__20440) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20439,Vvar__1___24Anonymous__20441)
=> ( Vvar__1___24Anonymous__20440 = Vvar__1___24Anonymous__20441
& Vvar__0__C__20438 = Vvar__0__C__20439 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__20446,Vvar__0__C__20447,Vvar__1___24Anonymous__20448,Vvar__1___24Anonymous__20449,Vvar__2___24Anonymous__20450,Vvar__2___24Anonymous__20451] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20446,Vvar__1___24Anonymous__20448,Vvar__2___24Anonymous__20450) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20447,Vvar__1___24Anonymous__20449,Vvar__2___24Anonymous__20451)
=> ( Vvar__2___24Anonymous__20450 = Vvar__2___24Anonymous__20451
& Vvar__1___24Anonymous__20448 = Vvar__1___24Anonymous__20449
& Vvar__0__C__20446 = Vvar__0__C__20447 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__20452,Vvar__0__C__20453,Vvar__1___24Anonymous__20454,Vvar__1___24Anonymous__20455,Vvar__2___24Anonymous__20456,Vvar__2___24Anonymous__20457] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20452,Vvar__1___24Anonymous__20454,Vvar__2___24Anonymous__20456) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20453,Vvar__1___24Anonymous__20455,Vvar__2___24Anonymous__20457)
=> ( Vvar__2___24Anonymous__20456 = Vvar__2___24Anonymous__20457
& Vvar__1___24Anonymous__20454 = Vvar__1___24Anonymous__20455
& Vvar__0__C__20452 = Vvar__0__C__20453 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__20442,Vvar__0__C__20443,Vvar__1___24Anonymous__20444,Vvar__1___24Anonymous__20445] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20442,Vvar__1___24Anonymous__20444) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20443,Vvar__1___24Anonymous__20445)
=> ( Vvar__1___24Anonymous__20444 = Vvar__1___24Anonymous__20445
& Vvar__0__C__20442 = Vvar__0__C__20443 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__20468,Vvar__0__C__20469] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20468) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20469)
=> Vvar__0__C__20468 = Vvar__0__C__20469 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__24959,Vvar__0__TA__24960,Vvar__1__TX__24961,Vvar__1__TX__24962,Vvar__2__AA__24963,Vvar__2__AA__24964,Vvar__3__AF__24965,Vvar__3__AF__24966,Vvar__4___24Anonymous__24967,Vvar__4___24Anonymous__24968,Vvar__5___24Anonymous__24969,Vvar__5___24Anonymous__24970] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__24959,Vvar__1__TX__24961,Vvar__2__AA__24963,Vvar__3__AF__24965,Vvar__4___24Anonymous__24967,Vvar__5___24Anonymous__24969) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__24960,Vvar__1__TX__24962,Vvar__2__AA__24964,Vvar__3__AF__24966,Vvar__4___24Anonymous__24968,Vvar__5___24Anonymous__24970)
=> ( Vvar__5___24Anonymous__24969 = Vvar__5___24Anonymous__24970
& Vvar__4___24Anonymous__24967 = Vvar__4___24Anonymous__24968
& Vvar__3__AF__24965 = Vvar__3__AF__24966
& Vvar__2__AA__24963 = Vvar__2__AA__24964
& Vvar__1__TX__24961 = Vvar__1__TX__24962
& Vvar__0__TA__24959 = Vvar__0__TA__24960 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__24971,Vvar__0__TA__24972,Vvar__1__TX__24973,Vvar__1__TX__24974,Vvar__2__AA__24975,Vvar__2__AA__24976,Vvar__3__AF__24977,Vvar__3__AF__24978,Vvar__4___24Anonymous__24979,Vvar__4___24Anonymous__24980,Vvar__5___24Anonymous__24981,Vvar__5___24Anonymous__24982] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__24971,Vvar__1__TX__24973,Vvar__2__AA__24975,Vvar__3__AF__24977,Vvar__4___24Anonymous__24979,Vvar__5___24Anonymous__24981) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__24972,Vvar__1__TX__24974,Vvar__2__AA__24976,Vvar__3__AF__24978,Vvar__4___24Anonymous__24980,Vvar__5___24Anonymous__24982)
=> ( Vvar__5___24Anonymous__24981 = Vvar__5___24Anonymous__24982
& Vvar__4___24Anonymous__24979 = Vvar__4___24Anonymous__24980
& Vvar__3__AF__24977 = Vvar__3__AF__24978
& Vvar__2__AA__24975 = Vvar__2__AA__24976
& Vvar__1__TX__24973 = Vvar__1__TX__24974
& Vvar__0__TA__24971 = Vvar__0__TA__24972 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__24983,Vvar__0__TA__24984,Vvar__1__TX__24985,Vvar__1__TX__24986,Vvar__2__AA__24987,Vvar__2__AA__24988,Vvar__3__AF__24989,Vvar__3__AF__24990,Vvar__4___24Anonymous__24991,Vvar__4___24Anonymous__24992,Vvar__5___24Anonymous__24993,Vvar__5___24Anonymous__24994] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__24983,Vvar__1__TX__24985,Vvar__2__AA__24987,Vvar__3__AF__24989,Vvar__4___24Anonymous__24991,Vvar__5___24Anonymous__24993) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__24984,Vvar__1__TX__24986,Vvar__2__AA__24988,Vvar__3__AF__24990,Vvar__4___24Anonymous__24992,Vvar__5___24Anonymous__24994)
=> ( Vvar__5___24Anonymous__24993 = Vvar__5___24Anonymous__24994
& Vvar__4___24Anonymous__24991 = Vvar__4___24Anonymous__24992
& Vvar__3__AF__24989 = Vvar__3__AF__24990
& Vvar__2__AA__24987 = Vvar__2__AA__24988
& Vvar__1__TX__24985 = Vvar__1__TX__24986
& Vvar__0__TA__24983 = Vvar__0__TA__24984 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__24941,Vvar__0__TA__24942,Vvar__1__TX__24943,Vvar__1__TX__24944,Vvar__2__AA__24945,Vvar__2__AA__24946,Vvar__3__AF__24947,Vvar__3__AF__24948] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__24941,Vvar__1__TX__24943,Vvar__2__AA__24945,Vvar__3__AF__24947) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__24942,Vvar__1__TX__24944,Vvar__2__AA__24946,Vvar__3__AF__24948)
=> ( Vvar__3__AF__24947 = Vvar__3__AF__24948
& Vvar__2__AA__24945 = Vvar__2__AA__24946
& Vvar__1__TX__24943 = Vvar__1__TX__24944
& Vvar__0__TA__24941 = Vvar__0__TA__24942 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__25005,Vvar__0__TA__25006,Vvar__1__TX__25007,Vvar__1__TX__25008,Vvar__2__AA__25009,Vvar__2__AA__25010,Vvar__3__AF__25011,Vvar__3__AF__25012,Vvar__4___24Anonymous__25013,Vvar__4___24Anonymous__25014,Vvar__5___24Anonymous__25015,Vvar__5___24Anonymous__25016,Vvar__6___24Anonymous__25017,Vvar__6___24Anonymous__25018] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__25005,Vvar__1__TX__25007,Vvar__2__AA__25009,Vvar__3__AF__25011,Vvar__4___24Anonymous__25013,Vvar__5___24Anonymous__25015,Vvar__6___24Anonymous__25017) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__25006,Vvar__1__TX__25008,Vvar__2__AA__25010,Vvar__3__AF__25012,Vvar__4___24Anonymous__25014,Vvar__5___24Anonymous__25016,Vvar__6___24Anonymous__25018)
=> ( Vvar__6___24Anonymous__25017 = Vvar__6___24Anonymous__25018
& Vvar__5___24Anonymous__25015 = Vvar__5___24Anonymous__25016
& Vvar__4___24Anonymous__25013 = Vvar__4___24Anonymous__25014
& Vvar__3__AF__25011 = Vvar__3__AF__25012
& Vvar__2__AA__25009 = Vvar__2__AA__25010
& Vvar__1__TX__25007 = Vvar__1__TX__25008
& Vvar__0__TA__25005 = Vvar__0__TA__25006 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__24995,Vvar__0__TA__24996,Vvar__1__TX__24997,Vvar__1__TX__24998,Vvar__2__AA__24999,Vvar__2__AA__25000,Vvar__3__AF__25001,Vvar__3__AF__25002,Vvar__4___24Anonymous__25003,Vvar__4___24Anonymous__25004] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__24995,Vvar__1__TX__24997,Vvar__2__AA__24999,Vvar__3__AF__25001,Vvar__4___24Anonymous__25003) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__24996,Vvar__1__TX__24998,Vvar__2__AA__25000,Vvar__3__AF__25002,Vvar__4___24Anonymous__25004)
=> ( Vvar__4___24Anonymous__25003 = Vvar__4___24Anonymous__25004
& Vvar__3__AF__25001 = Vvar__3__AF__25002
& Vvar__2__AA__24999 = Vvar__2__AA__25000
& Vvar__1__TX__24997 = Vvar__1__TX__24998
& Vvar__0__TA__24995 = Vvar__0__TA__24996 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__24933,Vvar__0__TA__24934,Vvar__1__TX__24935,Vvar__1__TX__24936,Vvar__2__AA__24937,Vvar__2__AA__24938,Vvar__3__AF__24939,Vvar__3__AF__24940] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__24933,Vvar__1__TX__24935,Vvar__2__AA__24937,Vvar__3__AF__24939) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__24934,Vvar__1__TX__24936,Vvar__2__AA__24938,Vvar__3__AF__24940)
=> ( Vvar__3__AF__24939 = Vvar__3__AF__24940
& Vvar__2__AA__24937 = Vvar__2__AA__24938
& Vvar__1__TX__24935 = Vvar__1__TX__24936
& Vvar__0__TA__24933 = Vvar__0__TA__24934 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__24949,Vvar__0__TA__24950,Vvar__1__TX__24951,Vvar__1__TX__24952,Vvar__2__AA__24953,Vvar__2__AA__24954,Vvar__3__AF__24955,Vvar__3__AF__24956,Vvar__4___24Anonymous__24957,Vvar__4___24Anonymous__24958] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__24949,Vvar__1__TX__24951,Vvar__2__AA__24953,Vvar__3__AF__24955,Vvar__4___24Anonymous__24957) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__24950,Vvar__1__TX__24952,Vvar__2__AA__24954,Vvar__3__AF__24956,Vvar__4___24Anonymous__24958)
=> ( Vvar__4___24Anonymous__24957 = Vvar__4___24Anonymous__24958
& Vvar__3__AF__24955 = Vvar__3__AF__24956
& Vvar__2__AA__24953 = Vvar__2__AA__24954
& Vvar__1__TX__24951 = Vvar__1__TX__24952
& Vvar__0__TA__24949 = Vvar__0__TA__24950 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__25048,Vvar__0__A__25049,Vvar__1___24Anonymous__25050,Vvar__1___24Anonymous__25051,Vvar__2___24Anonymous__25052,Vvar__2___24Anonymous__25053,Vvar__3___24Anonymous__25054,Vvar__3___24Anonymous__25055] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__25048,Vvar__1___24Anonymous__25050,Vvar__2___24Anonymous__25052,Vvar__3___24Anonymous__25054) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__25049,Vvar__1___24Anonymous__25051,Vvar__2___24Anonymous__25053,Vvar__3___24Anonymous__25055)
=> ( Vvar__3___24Anonymous__25054 = Vvar__3___24Anonymous__25055
& Vvar__2___24Anonymous__25052 = Vvar__2___24Anonymous__25053
& Vvar__1___24Anonymous__25050 = Vvar__1___24Anonymous__25051
& Vvar__0__A__25048 = Vvar__0__A__25049 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__25044,Vvar__0__A__25045,Vvar__1___24Anonymous__25046,Vvar__1___24Anonymous__25047] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25044,Vvar__1___24Anonymous__25046) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25045,Vvar__1___24Anonymous__25047)
=> ( Vvar__1___24Anonymous__25046 = Vvar__1___24Anonymous__25047
& Vvar__0__A__25044 = Vvar__0__A__25045 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__25042,Vvar__0__A__25043] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25042) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25043)
=> Vvar__0__A__25042 = Vvar__0__A__25043 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__25128,Vvar__0___24Anonymous__25129,Vvar__1___24Anonymous__25130,Vvar__1___24Anonymous__25131] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__25128,Vvar__1___24Anonymous__25130) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__25129,Vvar__1___24Anonymous__25131)
=> ( Vvar__1___24Anonymous__25130 = Vvar__1___24Anonymous__25131
& Vvar__0___24Anonymous__25128 = Vvar__0___24Anonymous__25129 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__25132,Vvar__0___24Anonymous__25133,Vvar__1___24Anonymous__25134,Vvar__1___24Anonymous__25135,Vvar__2___24Anonymous__25136,Vvar__2___24Anonymous__25137] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__25132,Vvar__1___24Anonymous__25134,Vvar__2___24Anonymous__25136) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__25133,Vvar__1___24Anonymous__25135,Vvar__2___24Anonymous__25137)
=> ( Vvar__2___24Anonymous__25136 = Vvar__2___24Anonymous__25137
& Vvar__1___24Anonymous__25134 = Vvar__1___24Anonymous__25135
& Vvar__0___24Anonymous__25132 = Vvar__0___24Anonymous__25133 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__25124,Vvar__0___24Anonymous__25125,Vvar__1___24Anonymous__25126,Vvar__1___24Anonymous__25127] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25124,Vvar__1___24Anonymous__25126) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25125,Vvar__1___24Anonymous__25127)
=> ( Vvar__1___24Anonymous__25126 = Vvar__1___24Anonymous__25127
& Vvar__0___24Anonymous__25124 = Vvar__0___24Anonymous__25125 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__2271,Vvar__0__C__2272] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__2271) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__2272)
=> Vvar__0__C__2271 = Vvar__0__C__2272 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__2269,Vvar__0__C__2270] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__2269) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__2270)
=> Vvar__0__C__2269 = Vvar__0__C__2270 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__2277,Vvar__0__C__2278,Vvar__1___24Anonymous__2279,Vvar__1___24Anonymous__2280] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__2277,Vvar__1___24Anonymous__2279) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__2278,Vvar__1___24Anonymous__2280)
=> ( Vvar__1___24Anonymous__2279 = Vvar__1___24Anonymous__2280
& Vvar__0__C__2277 = Vvar__0__C__2278 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__2281,Vvar__0__C__2282,Vvar__1___24Anonymous__2283,Vvar__1___24Anonymous__2284,Vvar__2___24Anonymous__2285,Vvar__2___24Anonymous__2286] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__2281,Vvar__1___24Anonymous__2283,Vvar__2___24Anonymous__2285) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__2282,Vvar__1___24Anonymous__2284,Vvar__2___24Anonymous__2286)
=> ( Vvar__2___24Anonymous__2285 = Vvar__2___24Anonymous__2286
& Vvar__1___24Anonymous__2283 = Vvar__1___24Anonymous__2284
& Vvar__0__C__2281 = Vvar__0__C__2282 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__2273,Vvar__0__C__2274,Vvar__1___24Anonymous__2275,Vvar__1___24Anonymous__2276] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__2273,Vvar__1___24Anonymous__2275) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__2274,Vvar__1___24Anonymous__2276)
=> ( Vvar__1___24Anonymous__2275 = Vvar__1___24Anonymous__2276
& Vvar__0__C__2273 = Vvar__0__C__2274 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__2307,Vvar__0__C__2308,Vvar__1___24Anonymous__2309,Vvar__1___24Anonymous__2310,Vvar__2___24Anonymous__2311,Vvar__2___24Anonymous__2312] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__2307,Vvar__1___24Anonymous__2309,Vvar__2___24Anonymous__2311) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__2308,Vvar__1___24Anonymous__2310,Vvar__2___24Anonymous__2312)
=> ( Vvar__2___24Anonymous__2311 = Vvar__2___24Anonymous__2312
& Vvar__1___24Anonymous__2309 = Vvar__1___24Anonymous__2310
& Vvar__0__C__2307 = Vvar__0__C__2308 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__2303,Vvar__0__C__2304,Vvar__1___24Anonymous__2305,Vvar__1___24Anonymous__2306] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__2303,Vvar__1___24Anonymous__2305) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__2304,Vvar__1___24Anonymous__2306)
=> ( Vvar__1___24Anonymous__2305 = Vvar__1___24Anonymous__2306
& Vvar__0__C__2303 = Vvar__0__C__2304 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__2293,Vvar__0__C__2294,Vvar__1___24Anonymous__2295,Vvar__1___24Anonymous__2296,Vvar__2___24Anonymous__2297,Vvar__2___24Anonymous__2298] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__2293,Vvar__1___24Anonymous__2295,Vvar__2___24Anonymous__2297) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__2294,Vvar__1___24Anonymous__2296,Vvar__2___24Anonymous__2298)
=> ( Vvar__2___24Anonymous__2297 = Vvar__2___24Anonymous__2298
& Vvar__1___24Anonymous__2295 = Vvar__1___24Anonymous__2296
& Vvar__0__C__2293 = Vvar__0__C__2294 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__2299,Vvar__0__C__2300,Vvar__1___24Anonymous__2301,Vvar__1___24Anonymous__2302] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__2299,Vvar__1___24Anonymous__2301) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__2300,Vvar__1___24Anonymous__2302)
=> ( Vvar__1___24Anonymous__2301 = Vvar__1___24Anonymous__2302
& Vvar__0__C__2299 = Vvar__0__C__2300 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__2313,Vvar__0__C__2314,Vvar__1___24Anonymous__2315,Vvar__1___24Anonymous__2316,Vvar__2___24Anonymous__2317,Vvar__2___24Anonymous__2318] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__2313,Vvar__1___24Anonymous__2315,Vvar__2___24Anonymous__2317) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__2314,Vvar__1___24Anonymous__2316,Vvar__2___24Anonymous__2318)
=> ( Vvar__2___24Anonymous__2317 = Vvar__2___24Anonymous__2318
& Vvar__1___24Anonymous__2315 = Vvar__1___24Anonymous__2316
& Vvar__0__C__2313 = Vvar__0__C__2314 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__2287,Vvar__0__C__2288,Vvar__1___24Anonymous__2289,Vvar__1___24Anonymous__2290,Vvar__2___24Anonymous__2291,Vvar__2___24Anonymous__2292] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__2287,Vvar__1___24Anonymous__2289,Vvar__2___24Anonymous__2291) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__2288,Vvar__1___24Anonymous__2290,Vvar__2___24Anonymous__2292)
=> ( Vvar__2___24Anonymous__2291 = Vvar__2___24Anonymous__2292
& Vvar__1___24Anonymous__2289 = Vvar__1___24Anonymous__2290
& Vvar__0__C__2287 = Vvar__0__C__2288 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__2616,Vvar__0__C__2617,Vvar__1__num__2618,Vvar__1__num__2619,Vvar__2__denum__2620,Vvar__2__denum__2621,Vvar__3__condition__2622,Vvar__3__condition__2623] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__2616,Vvar__1__num__2618,Vvar__2__denum__2620,Vvar__3__condition__2622) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__2617,Vvar__1__num__2619,Vvar__2__denum__2621,Vvar__3__condition__2623)
=> ( Vvar__3__condition__2622 = Vvar__3__condition__2623
& Vvar__2__denum__2620 = Vvar__2__denum__2621
& Vvar__1__num__2618 = Vvar__1__num__2619
& Vvar__0__C__2616 = Vvar__0__C__2617 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__2905,Vvar__0__C__2906,Vvar__1__rsplit__left__2907,Vvar__1__rsplit__left__2908,Vvar__2__rsplit__common__2909,Vvar__2__rsplit__common__2910,Vvar__3__rsplit__right__2911,Vvar__3__rsplit__right__2912] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__2905,Vvar__1__rsplit__left__2907,Vvar__2__rsplit__common__2909,Vvar__3__rsplit__right__2911) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__2906,Vvar__1__rsplit__left__2908,Vvar__2__rsplit__common__2910,Vvar__3__rsplit__right__2912)
=> ( Vvar__3__rsplit__right__2911 = Vvar__3__rsplit__right__2912
& Vvar__2__rsplit__common__2909 = Vvar__2__rsplit__common__2910
& Vvar__1__rsplit__left__2907 = Vvar__1__rsplit__left__2908
& Vvar__0__C__2905 = Vvar__0__C__2906 ) ) ).
fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
! [Vvar__0__hypo__type__25533,Vvar__0__hypo__type__25534,Vvar__1__hypo__proof__25535,Vvar__1__hypo__proof__25536] :
( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__25533,Vvar__1__hypo__proof__25535) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__25534,Vvar__1__hypo__proof__25536)
=> ( Vvar__1__hypo__proof__25535 = Vvar__1__hypo__proof__25536
& Vvar__0__hypo__type__25533 = Vvar__0__hypo__type__25534 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__3825,Vvar__0__C__3826] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3825) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3826)
=> Vvar__0__C__3825 = Vvar__0__C__3826 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__3823,Vvar__0__C__3824] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3823) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3824)
=> Vvar__0__C__3823 = Vvar__0__C__3824 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__3831,Vvar__0__C__3832,Vvar__1___24Anonymous__3833,Vvar__1___24Anonymous__3834] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3831,Vvar__1___24Anonymous__3833) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3832,Vvar__1___24Anonymous__3834)
=> ( Vvar__1___24Anonymous__3833 = Vvar__1___24Anonymous__3834
& Vvar__0__C__3831 = Vvar__0__C__3832 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__3835,Vvar__0__C__3836,Vvar__1___24Anonymous__3837,Vvar__1___24Anonymous__3838,Vvar__2___24Anonymous__3839,Vvar__2___24Anonymous__3840] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3835,Vvar__1___24Anonymous__3837,Vvar__2___24Anonymous__3839) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3836,Vvar__1___24Anonymous__3838,Vvar__2___24Anonymous__3840)
=> ( Vvar__2___24Anonymous__3839 = Vvar__2___24Anonymous__3840
& Vvar__1___24Anonymous__3837 = Vvar__1___24Anonymous__3838
& Vvar__0__C__3835 = Vvar__0__C__3836 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__3827,Vvar__0__C__3828,Vvar__1___24Anonymous__3829,Vvar__1___24Anonymous__3830] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3827,Vvar__1___24Anonymous__3829) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3828,Vvar__1___24Anonymous__3830)
=> ( Vvar__1___24Anonymous__3829 = Vvar__1___24Anonymous__3830
& Vvar__0__C__3827 = Vvar__0__C__3828 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__3847,Vvar__0__C__3848,Vvar__1___24Anonymous__3849,Vvar__1___24Anonymous__3850,Vvar__2___24Anonymous__3851,Vvar__2___24Anonymous__3852] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3847,Vvar__1___24Anonymous__3849,Vvar__2___24Anonymous__3851) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3848,Vvar__1___24Anonymous__3850,Vvar__2___24Anonymous__3852)
=> ( Vvar__2___24Anonymous__3851 = Vvar__2___24Anonymous__3852
& Vvar__1___24Anonymous__3849 = Vvar__1___24Anonymous__3850
& Vvar__0__C__3847 = Vvar__0__C__3848 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__3853,Vvar__0__C__3854,Vvar__1___24Anonymous__3855,Vvar__1___24Anonymous__3856] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3853,Vvar__1___24Anonymous__3855) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3854,Vvar__1___24Anonymous__3856)
=> ( Vvar__1___24Anonymous__3855 = Vvar__1___24Anonymous__3856
& Vvar__0__C__3853 = Vvar__0__C__3854 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__3857,Vvar__0__C__3858,Vvar__1___24Anonymous__3859,Vvar__1___24Anonymous__3860,Vvar__2___24Anonymous__3861,Vvar__2___24Anonymous__3862] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3857,Vvar__1___24Anonymous__3859,Vvar__2___24Anonymous__3861) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3858,Vvar__1___24Anonymous__3860,Vvar__2___24Anonymous__3862)
=> ( Vvar__2___24Anonymous__3861 = Vvar__2___24Anonymous__3862
& Vvar__1___24Anonymous__3859 = Vvar__1___24Anonymous__3860
& Vvar__0__C__3857 = Vvar__0__C__3858 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__3841,Vvar__0__C__3842,Vvar__1___24Anonymous__3843,Vvar__1___24Anonymous__3844,Vvar__2___24Anonymous__3845,Vvar__2___24Anonymous__3846] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3841,Vvar__1___24Anonymous__3843,Vvar__2___24Anonymous__3845) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3842,Vvar__1___24Anonymous__3844,Vvar__2___24Anonymous__3846)
=> ( Vvar__2___24Anonymous__3845 = Vvar__2___24Anonymous__3846
& Vvar__1___24Anonymous__3843 = Vvar__1___24Anonymous__3844
& Vvar__0__C__3841 = Vvar__0__C__3842 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__3480,Vvar__0__C__3481,Vvar__1___24Anonymous__3482,Vvar__1___24Anonymous__3483,Vvar__2___24Anonymous__3484,Vvar__2___24Anonymous__3485,Vvar__3___24Anonymous__3486,Vvar__3___24Anonymous__3487] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__3480,Vvar__1___24Anonymous__3482,Vvar__2___24Anonymous__3484,Vvar__3___24Anonymous__3486) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__3481,Vvar__1___24Anonymous__3483,Vvar__2___24Anonymous__3485,Vvar__3___24Anonymous__3487)
=> ( Vvar__3___24Anonymous__3486 = Vvar__3___24Anonymous__3487
& Vvar__2___24Anonymous__3484 = Vvar__2___24Anonymous__3485
& Vvar__1___24Anonymous__3482 = Vvar__1___24Anonymous__3483
& Vvar__0__C__3480 = Vvar__0__C__3481 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__3470,Vvar__0__C__3471,Vvar__1___24Anonymous__3472,Vvar__1___24Anonymous__3473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__3470,Vvar__1___24Anonymous__3472) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__3471,Vvar__1___24Anonymous__3473)
=> ( Vvar__1___24Anonymous__3472 = Vvar__1___24Anonymous__3473
& Vvar__0__C__3470 = Vvar__0__C__3471 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__3474,Vvar__0__C__3475,Vvar__1___24Anonymous__3476,Vvar__1___24Anonymous__3477,Vvar__2___24Anonymous__3478,Vvar__2___24Anonymous__3479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__3474,Vvar__1___24Anonymous__3476,Vvar__2___24Anonymous__3478) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__3475,Vvar__1___24Anonymous__3477,Vvar__2___24Anonymous__3479)
=> ( Vvar__2___24Anonymous__3478 = Vvar__2___24Anonymous__3479
& Vvar__1___24Anonymous__3476 = Vvar__1___24Anonymous__3477
& Vvar__0__C__3474 = Vvar__0__C__3475 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__3637,Vvar__0___24Anonymous__3638,Vvar__1___24Anonymous__3639,Vvar__1___24Anonymous__3640] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__3637,Vvar__1___24Anonymous__3639) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__3638,Vvar__1___24Anonymous__3640)
=> ( Vvar__1___24Anonymous__3639 = Vvar__1___24Anonymous__3640
& Vvar__0___24Anonymous__3637 = Vvar__0___24Anonymous__3638 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__3633,Vvar__0___24Anonymous__3634,Vvar__1___24Anonymous__3635,Vvar__1___24Anonymous__3636] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3633,Vvar__1___24Anonymous__3635) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3634,Vvar__1___24Anonymous__3636)
=> ( Vvar__1___24Anonymous__3635 = Vvar__1___24Anonymous__3636
& Vvar__0___24Anonymous__3633 = Vvar__0___24Anonymous__3634 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__26760,Vvar__0__R__26761,Vvar__1__req__26762,Vvar__1__req__26763,Vvar__2__reqb__26764,Vvar__2__reqb__26765,Vvar__3___24Anonymous__26766,Vvar__3___24Anonymous__26767] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__26760,Vvar__1__req__26762,Vvar__2__reqb__26764) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__26761,Vvar__1__req__26763,Vvar__2__reqb__26765)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__26764 = Vvar__2__reqb__26765
& Vvar__1__req__26762 = Vvar__1__req__26763
& Vvar__0__R__26760 = Vvar__0__R__26761 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__26768,Vvar__0__R__26769,Vvar__1__rO__26770,Vvar__1__rO__26771,Vvar__2__rI__26772,Vvar__2__rI__26773,Vvar__3__radd__26774,Vvar__3__radd__26775,Vvar__4__rmul__26776,Vvar__4__rmul__26777,Vvar__5__rsub__26778,Vvar__5__rsub__26779,Vvar__6__ropp__26780,Vvar__6__ropp__26781,Vvar__7__req__26782,Vvar__7__req__26783,Vvar__8__C__26784,Vvar__8__C__26785,Vvar__9__cO__26786,Vvar__9__cO__26787,Vvar__10__cI__26788,Vvar__10__cI__26789,Vvar__11__cadd__26790,Vvar__11__cadd__26791,Vvar__12__cmul__26792,Vvar__12__cmul__26793,Vvar__13__csub__26794,Vvar__13__csub__26795,Vvar__14__copp__26796,Vvar__14__copp__26797,Vvar__15__ceqb__26798,Vvar__15__ceqb__26799,Vvar__16__phi__26800,Vvar__16__phi__26801,Vvar__17___24Anonymous__26802,Vvar__17___24Anonymous__26803] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__26768,Vvar__1__rO__26770,Vvar__2__rI__26772,Vvar__3__radd__26774,Vvar__4__rmul__26776,Vvar__5__rsub__26778,Vvar__6__ropp__26780,Vvar__7__req__26782,Vvar__8__C__26784,Vvar__9__cO__26786,Vvar__10__cI__26788,Vvar__11__cadd__26790,Vvar__12__cmul__26792,Vvar__13__csub__26794,Vvar__14__copp__26796,Vvar__15__ceqb__26798,Vvar__16__phi__26800) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__26769,Vvar__1__rO__26771,Vvar__2__rI__26773,Vvar__3__radd__26775,Vvar__4__rmul__26777,Vvar__5__rsub__26779,Vvar__6__ropp__26781,Vvar__7__req__26783,Vvar__8__C__26785,Vvar__9__cO__26787,Vvar__10__cI__26789,Vvar__11__cadd__26791,Vvar__12__cmul__26793,Vvar__13__csub__26795,Vvar__14__copp__26797,Vvar__15__ceqb__26799,Vvar__16__phi__26801)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__26800 = Vvar__16__phi__26801
& Vvar__15__ceqb__26798 = Vvar__15__ceqb__26799
& Vvar__14__copp__26796 = Vvar__14__copp__26797
& Vvar__13__csub__26794 = Vvar__13__csub__26795
& Vvar__12__cmul__26792 = Vvar__12__cmul__26793
& Vvar__11__cadd__26790 = Vvar__11__cadd__26791
& Vvar__10__cI__26788 = Vvar__10__cI__26789
& Vvar__9__cO__26786 = Vvar__9__cO__26787
& Vvar__8__C__26784 = Vvar__8__C__26785
& Vvar__7__req__26782 = Vvar__7__req__26783
& Vvar__6__ropp__26780 = Vvar__6__ropp__26781
& Vvar__5__rsub__26778 = Vvar__5__rsub__26779
& Vvar__4__rmul__26776 = Vvar__4__rmul__26777
& Vvar__3__radd__26774 = Vvar__3__radd__26775
& Vvar__2__rI__26772 = Vvar__2__rI__26773
& Vvar__1__rO__26770 = Vvar__1__rO__26771
& Vvar__0__R__26768 = Vvar__0__R__26769 ) ) ).
fof('$_inj_Lambda.Terms.Abs',axiom,
! [Vvar__0___24Anonymous__88,Vvar__0___24Anonymous__89] :
( cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__88) = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__89)
=> Vvar__0___24Anonymous__88 = Vvar__0___24Anonymous__89 ) ).
fof('$_inj_Lambda.Terms.App',axiom,
! [Vvar__0___24Anonymous__90,Vvar__0___24Anonymous__91,Vvar__1___24Anonymous__92,Vvar__1___24Anonymous__93] :
( cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__90,Vvar__1___24Anonymous__92) = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__91,Vvar__1___24Anonymous__93)
=> ( Vvar__1___24Anonymous__92 = Vvar__1___24Anonymous__93
& Vvar__0___24Anonymous__90 = Vvar__0___24Anonymous__91 ) ) ).
fof('$_inj_Lambda.Terms.Ref',axiom,
! [Vvar__0___24Anonymous__86,Vvar__0___24Anonymous__87] :
( cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__86) = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__87)
=> Vvar__0___24Anonymous__86 = Vvar__0___24Anonymous__87 ) ).
fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
! [Vvar__0__P__25278,Vvar__1__Q__25280,Vvar__2__init__25283,Vvar__3___24Anonymous__25284,Vvar__4___24Anonymous__25285] :
( c_24__type__25311___24t(Vvar__0__P__25278,Vvar__1__Q__25280,Vvar__2__init__25283,Vvar__3___24Anonymous__25284,Vvar__4___24Anonymous__25285,Vvar__0__P__25278)
=> ( c_24__type__25319___24t(Vvar__0__P__25278,Vvar__1__Q__25280,Vvar__2__init__25283,Vvar__3___24Anonymous__25284,Vvar__4___24Anonymous__25285,Vvar__1__Q__25280)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__25283)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__25284)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__25285)
=> ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__25278,Vvar__1__Q__25280,Vvar__2__init__25283,Vvar__3___24Anonymous__25284,Vvar__4___24Anonymous__25285)
=> ( ( Vvar__4___24Anonymous__25285 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__3___24Anonymous__25284 = Vvar__2__init__25283 )
| ? [Vvar__3__k__25299] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__25299)
& ? [Vvar__4__l__25300] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__25300)
& ? [Vvar__5__n__25301] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__25301)
& cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__25278,Vvar__1__Q__25280,Vvar__2__init__25283,Vvar__3__k__25299,Vvar__5__n__25301)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__25278,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__25299),Vvar__4__l__25300)
& p(happ(Vvar__1__Q__25280,Vvar__4__l__25300))
& Vvar__4___24Anonymous__25285 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__25301)
& Vvar__3___24Anonymous__25284 = Vvar__4__l__25300 ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__25238,Vvar__1__k__25240,Vvar__2___24Anonymous__25241] :
( c_24__type__25255___24t(Vvar__0__P__25238,Vvar__1__k__25240,Vvar__2___24Anonymous__25241,Vvar__0__P__25238)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__25240)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__25241)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__25238,Vvar__1__k__25240,Vvar__2___24Anonymous__25241)
=> ( Vvar__2___24Anonymous__25241 = Vvar__1__k__25240
| ? [Vvar__2__l__25249] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__25249)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__25238,Vvar__1__k__25240,Vvar__2__l__25249)
& p(happ(Vvar__0__P__25238,Vvar__2__l__25249))
& Vvar__2___24Anonymous__25241 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__25249) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__25257,Vvar__1__k__25259,Vvar__2___24Anonymous__25260] :
( c_24__type__25276___24t(Vvar__0__Q__25257,Vvar__1__k__25259,Vvar__2___24Anonymous__25260,Vvar__0__Q__25257)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__25259)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__25260)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__25257,Vvar__1__k__25259,Vvar__2___24Anonymous__25260)
=> ( ? [Vvar__2__l__25265] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__25265)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__25257,Vvar__1__k__25259,Vvar__2__l__25265)
& Vvar__2___24Anonymous__25260 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__25265) )
| ? [Vvar__2__l__25270] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__25270)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__25259,Vvar__2__l__25270))
& p(happ(Vvar__0__Q__25257,Vvar__2__l__25270))
& Vvar__2___24Anonymous__25260 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__25270) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__22953] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22953)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__22953)
=> ( Vvar__0___24Anonymous__22953 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__22955] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__22955)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__22955)
& Vvar__0___24Anonymous__22953 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__22955) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__22957] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__22957)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__22957)
=> ? [Vvar__0__n__22959] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__22959)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__22959)
& Vvar__0___24Anonymous__22957 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__22959) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__22868,Vvar__1___24Anonymous__22869,VX22870] :
( cProp___24t(Vvar__0__P__22868)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__22869)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__22868,Vvar__1___24Anonymous__22869,VX22870)
=> ( ( p(Vvar__0__P__22868)
& Vvar__1___24Anonymous__22869 = cCoq_2eInit_2eDatatypes_2etrue
& VX22870 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__22868) )
| ( ~ p(Vvar__0__P__22868)
& Vvar__1___24Anonymous__22869 = cCoq_2eInit_2eDatatypes_2efalse
& VX22870 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__22868) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
! [Vvar__0___24Anonymous__22720,Vvar__1___24Anonymous__22721,Vvar__2___24Anonymous__22722] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__22720)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__22721)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__22722)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__22720,Vvar__1___24Anonymous__22721,Vvar__2___24Anonymous__22722)
=> ( ? [Vvar__0__x__22724] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__22724)
& Vvar__2___24Anonymous__22722 = Vvar__0__x__22724
& Vvar__1___24Anonymous__22721 = Vvar__0__x__22724
& Vvar__0___24Anonymous__22720 = Vvar__0__x__22724 )
| ? [Vvar__0__x__22725] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__22725)
& Vvar__2___24Anonymous__22722 = Vvar__0__x__22725
& Vvar__1___24Anonymous__22721 = cCoq_2eInit_2eDatatypes_2eEq
& Vvar__0___24Anonymous__22720 = Vvar__0__x__22725 )
| ? [Vvar__0__x__22726] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__22726)
& Vvar__2___24Anonymous__22722 = Vvar__0__x__22726
& Vvar__1___24Anonymous__22721 = Vvar__0__x__22726
& Vvar__0___24Anonymous__22720 = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0__x__22727] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__22727)
& Vvar__2___24Anonymous__22722 = Vvar__0__x__22727
& Vvar__1___24Anonymous__22721 = cCoq_2eInit_2eDatatypes_2eLt
& Vvar__0___24Anonymous__22720 = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0__x__22728] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__22728)
& Vvar__2___24Anonymous__22722 = Vvar__0__x__22728
& Vvar__1___24Anonymous__22721 = cCoq_2eInit_2eDatatypes_2eGt
& Vvar__0___24Anonymous__22720 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX22427] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX22427)
=> ( VX22427 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__22428] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__22428)
& ? [Vvar__1___24Anonymous__22429] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__22429)
& ? [Vvar__2___24Anonymous__22430] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__22430)
& VX22427 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__22428,Vvar__1___24Anonymous__22429,Vvar__2___24Anonymous__22430) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX9778] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX9778)
=> ( VX9778 = cCoq_2eInit_2eByte_2ex00
| VX9778 = cCoq_2eInit_2eByte_2ex01
| VX9778 = cCoq_2eInit_2eByte_2ex02
| VX9778 = cCoq_2eInit_2eByte_2ex03
| VX9778 = cCoq_2eInit_2eByte_2ex04
| VX9778 = cCoq_2eInit_2eByte_2ex05
| VX9778 = cCoq_2eInit_2eByte_2ex06
| VX9778 = cCoq_2eInit_2eByte_2ex07
| VX9778 = cCoq_2eInit_2eByte_2ex08
| VX9778 = cCoq_2eInit_2eByte_2ex09
| VX9778 = cCoq_2eInit_2eByte_2ex0a
| VX9778 = cCoq_2eInit_2eByte_2ex0b
| VX9778 = cCoq_2eInit_2eByte_2ex0c
| VX9778 = cCoq_2eInit_2eByte_2ex0d
| VX9778 = cCoq_2eInit_2eByte_2ex0e
| VX9778 = cCoq_2eInit_2eByte_2ex0f
| VX9778 = cCoq_2eInit_2eByte_2ex10
| VX9778 = cCoq_2eInit_2eByte_2ex11
| VX9778 = cCoq_2eInit_2eByte_2ex12
| VX9778 = cCoq_2eInit_2eByte_2ex13
| VX9778 = cCoq_2eInit_2eByte_2ex14
| VX9778 = cCoq_2eInit_2eByte_2ex15
| VX9778 = cCoq_2eInit_2eByte_2ex16
| VX9778 = cCoq_2eInit_2eByte_2ex17
| VX9778 = cCoq_2eInit_2eByte_2ex18
| VX9778 = cCoq_2eInit_2eByte_2ex19
| VX9778 = cCoq_2eInit_2eByte_2ex1a
| VX9778 = cCoq_2eInit_2eByte_2ex1b
| VX9778 = cCoq_2eInit_2eByte_2ex1c
| VX9778 = cCoq_2eInit_2eByte_2ex1d
| VX9778 = cCoq_2eInit_2eByte_2ex1e
| VX9778 = cCoq_2eInit_2eByte_2ex1f
| VX9778 = cCoq_2eInit_2eByte_2ex20
| VX9778 = cCoq_2eInit_2eByte_2ex21
| VX9778 = cCoq_2eInit_2eByte_2ex22
| VX9778 = cCoq_2eInit_2eByte_2ex23
| VX9778 = cCoq_2eInit_2eByte_2ex24
| VX9778 = cCoq_2eInit_2eByte_2ex25
| VX9778 = cCoq_2eInit_2eByte_2ex26
| VX9778 = cCoq_2eInit_2eByte_2ex27
| VX9778 = cCoq_2eInit_2eByte_2ex28
| VX9778 = cCoq_2eInit_2eByte_2ex29
| VX9778 = cCoq_2eInit_2eByte_2ex2a
| VX9778 = cCoq_2eInit_2eByte_2ex2b
| VX9778 = cCoq_2eInit_2eByte_2ex2c
| VX9778 = cCoq_2eInit_2eByte_2ex2d
| VX9778 = cCoq_2eInit_2eByte_2ex2e
| VX9778 = cCoq_2eInit_2eByte_2ex2f
| VX9778 = cCoq_2eInit_2eByte_2ex30
| VX9778 = cCoq_2eInit_2eByte_2ex31
| VX9778 = cCoq_2eInit_2eByte_2ex32
| VX9778 = cCoq_2eInit_2eByte_2ex33
| VX9778 = cCoq_2eInit_2eByte_2ex34
| VX9778 = cCoq_2eInit_2eByte_2ex35
| VX9778 = cCoq_2eInit_2eByte_2ex36
| VX9778 = cCoq_2eInit_2eByte_2ex37
| VX9778 = cCoq_2eInit_2eByte_2ex38
| VX9778 = cCoq_2eInit_2eByte_2ex39
| VX9778 = cCoq_2eInit_2eByte_2ex3a
| VX9778 = cCoq_2eInit_2eByte_2ex3b
| VX9778 = cCoq_2eInit_2eByte_2ex3c
| VX9778 = cCoq_2eInit_2eByte_2ex3d
| VX9778 = cCoq_2eInit_2eByte_2ex3e
| VX9778 = cCoq_2eInit_2eByte_2ex3f
| VX9778 = cCoq_2eInit_2eByte_2ex40
| VX9778 = cCoq_2eInit_2eByte_2ex41
| VX9778 = cCoq_2eInit_2eByte_2ex42
| VX9778 = cCoq_2eInit_2eByte_2ex43
| VX9778 = cCoq_2eInit_2eByte_2ex44
| VX9778 = cCoq_2eInit_2eByte_2ex45
| VX9778 = cCoq_2eInit_2eByte_2ex46
| VX9778 = cCoq_2eInit_2eByte_2ex47
| VX9778 = cCoq_2eInit_2eByte_2ex48
| VX9778 = cCoq_2eInit_2eByte_2ex49
| VX9778 = cCoq_2eInit_2eByte_2ex4a
| VX9778 = cCoq_2eInit_2eByte_2ex4b
| VX9778 = cCoq_2eInit_2eByte_2ex4c
| VX9778 = cCoq_2eInit_2eByte_2ex4d
| VX9778 = cCoq_2eInit_2eByte_2ex4e
| VX9778 = cCoq_2eInit_2eByte_2ex4f
| VX9778 = cCoq_2eInit_2eByte_2ex50
| VX9778 = cCoq_2eInit_2eByte_2ex51
| VX9778 = cCoq_2eInit_2eByte_2ex52
| VX9778 = cCoq_2eInit_2eByte_2ex53
| VX9778 = cCoq_2eInit_2eByte_2ex54
| VX9778 = cCoq_2eInit_2eByte_2ex55
| VX9778 = cCoq_2eInit_2eByte_2ex56
| VX9778 = cCoq_2eInit_2eByte_2ex57
| VX9778 = cCoq_2eInit_2eByte_2ex58
| VX9778 = cCoq_2eInit_2eByte_2ex59
| VX9778 = cCoq_2eInit_2eByte_2ex5a
| VX9778 = cCoq_2eInit_2eByte_2ex5b
| VX9778 = cCoq_2eInit_2eByte_2ex5c
| VX9778 = cCoq_2eInit_2eByte_2ex5d
| VX9778 = cCoq_2eInit_2eByte_2ex5e
| VX9778 = cCoq_2eInit_2eByte_2ex5f
| VX9778 = cCoq_2eInit_2eByte_2ex60
| VX9778 = cCoq_2eInit_2eByte_2ex61
| VX9778 = cCoq_2eInit_2eByte_2ex62
| VX9778 = cCoq_2eInit_2eByte_2ex63
| VX9778 = cCoq_2eInit_2eByte_2ex64
| VX9778 = cCoq_2eInit_2eByte_2ex65
| VX9778 = cCoq_2eInit_2eByte_2ex66
| VX9778 = cCoq_2eInit_2eByte_2ex67
| VX9778 = cCoq_2eInit_2eByte_2ex68
| VX9778 = cCoq_2eInit_2eByte_2ex69
| VX9778 = cCoq_2eInit_2eByte_2ex6a
| VX9778 = cCoq_2eInit_2eByte_2ex6b
| VX9778 = cCoq_2eInit_2eByte_2ex6c
| VX9778 = cCoq_2eInit_2eByte_2ex6d
| VX9778 = cCoq_2eInit_2eByte_2ex6e
| VX9778 = cCoq_2eInit_2eByte_2ex6f
| VX9778 = cCoq_2eInit_2eByte_2ex70
| VX9778 = cCoq_2eInit_2eByte_2ex71
| VX9778 = cCoq_2eInit_2eByte_2ex72
| VX9778 = cCoq_2eInit_2eByte_2ex73
| VX9778 = cCoq_2eInit_2eByte_2ex74
| VX9778 = cCoq_2eInit_2eByte_2ex75
| VX9778 = cCoq_2eInit_2eByte_2ex76
| VX9778 = cCoq_2eInit_2eByte_2ex77
| VX9778 = cCoq_2eInit_2eByte_2ex78
| VX9778 = cCoq_2eInit_2eByte_2ex79
| VX9778 = cCoq_2eInit_2eByte_2ex7a
| VX9778 = cCoq_2eInit_2eByte_2ex7b
| VX9778 = cCoq_2eInit_2eByte_2ex7c
| VX9778 = cCoq_2eInit_2eByte_2ex7d
| VX9778 = cCoq_2eInit_2eByte_2ex7e
| VX9778 = cCoq_2eInit_2eByte_2ex7f
| VX9778 = cCoq_2eInit_2eByte_2ex80
| VX9778 = cCoq_2eInit_2eByte_2ex81
| VX9778 = cCoq_2eInit_2eByte_2ex82
| VX9778 = cCoq_2eInit_2eByte_2ex83
| VX9778 = cCoq_2eInit_2eByte_2ex84
| VX9778 = cCoq_2eInit_2eByte_2ex85
| VX9778 = cCoq_2eInit_2eByte_2ex86
| VX9778 = cCoq_2eInit_2eByte_2ex87
| VX9778 = cCoq_2eInit_2eByte_2ex88
| VX9778 = cCoq_2eInit_2eByte_2ex89
| VX9778 = cCoq_2eInit_2eByte_2ex8a
| VX9778 = cCoq_2eInit_2eByte_2ex8b
| VX9778 = cCoq_2eInit_2eByte_2ex8c
| VX9778 = cCoq_2eInit_2eByte_2ex8d
| VX9778 = cCoq_2eInit_2eByte_2ex8e
| VX9778 = cCoq_2eInit_2eByte_2ex8f
| VX9778 = cCoq_2eInit_2eByte_2ex90
| VX9778 = cCoq_2eInit_2eByte_2ex91
| VX9778 = cCoq_2eInit_2eByte_2ex92
| VX9778 = cCoq_2eInit_2eByte_2ex93
| VX9778 = cCoq_2eInit_2eByte_2ex94
| VX9778 = cCoq_2eInit_2eByte_2ex95
| VX9778 = cCoq_2eInit_2eByte_2ex96
| VX9778 = cCoq_2eInit_2eByte_2ex97
| VX9778 = cCoq_2eInit_2eByte_2ex98
| VX9778 = cCoq_2eInit_2eByte_2ex99
| VX9778 = cCoq_2eInit_2eByte_2ex9a
| VX9778 = cCoq_2eInit_2eByte_2ex9b
| VX9778 = cCoq_2eInit_2eByte_2ex9c
| VX9778 = cCoq_2eInit_2eByte_2ex9d
| VX9778 = cCoq_2eInit_2eByte_2ex9e
| VX9778 = cCoq_2eInit_2eByte_2ex9f
| VX9778 = cCoq_2eInit_2eByte_2exa0
| VX9778 = cCoq_2eInit_2eByte_2exa1
| VX9778 = cCoq_2eInit_2eByte_2exa2
| VX9778 = cCoq_2eInit_2eByte_2exa3
| VX9778 = cCoq_2eInit_2eByte_2exa4
| VX9778 = cCoq_2eInit_2eByte_2exa5
| VX9778 = cCoq_2eInit_2eByte_2exa6
| VX9778 = cCoq_2eInit_2eByte_2exa7
| VX9778 = cCoq_2eInit_2eByte_2exa8
| VX9778 = cCoq_2eInit_2eByte_2exa9
| VX9778 = cCoq_2eInit_2eByte_2exaa
| VX9778 = cCoq_2eInit_2eByte_2exab
| VX9778 = cCoq_2eInit_2eByte_2exac
| VX9778 = cCoq_2eInit_2eByte_2exad
| VX9778 = cCoq_2eInit_2eByte_2exae
| VX9778 = cCoq_2eInit_2eByte_2exaf
| VX9778 = cCoq_2eInit_2eByte_2exb0
| VX9778 = cCoq_2eInit_2eByte_2exb1
| VX9778 = cCoq_2eInit_2eByte_2exb2
| VX9778 = cCoq_2eInit_2eByte_2exb3
| VX9778 = cCoq_2eInit_2eByte_2exb4
| VX9778 = cCoq_2eInit_2eByte_2exb5
| VX9778 = cCoq_2eInit_2eByte_2exb6
| VX9778 = cCoq_2eInit_2eByte_2exb7
| VX9778 = cCoq_2eInit_2eByte_2exb8
| VX9778 = cCoq_2eInit_2eByte_2exb9
| VX9778 = cCoq_2eInit_2eByte_2exba
| VX9778 = cCoq_2eInit_2eByte_2exbb
| VX9778 = cCoq_2eInit_2eByte_2exbc
| VX9778 = cCoq_2eInit_2eByte_2exbd
| VX9778 = cCoq_2eInit_2eByte_2exbe
| VX9778 = cCoq_2eInit_2eByte_2exbf
| VX9778 = cCoq_2eInit_2eByte_2exc0
| VX9778 = cCoq_2eInit_2eByte_2exc1
| VX9778 = cCoq_2eInit_2eByte_2exc2
| VX9778 = cCoq_2eInit_2eByte_2exc3
| VX9778 = cCoq_2eInit_2eByte_2exc4
| VX9778 = cCoq_2eInit_2eByte_2exc5
| VX9778 = cCoq_2eInit_2eByte_2exc6
| VX9778 = cCoq_2eInit_2eByte_2exc7
| VX9778 = cCoq_2eInit_2eByte_2exc8
| VX9778 = cCoq_2eInit_2eByte_2exc9
| VX9778 = cCoq_2eInit_2eByte_2exca
| VX9778 = cCoq_2eInit_2eByte_2excb
| VX9778 = cCoq_2eInit_2eByte_2excc
| VX9778 = cCoq_2eInit_2eByte_2excd
| VX9778 = cCoq_2eInit_2eByte_2exce
| VX9778 = cCoq_2eInit_2eByte_2excf
| VX9778 = cCoq_2eInit_2eByte_2exd0
| VX9778 = cCoq_2eInit_2eByte_2exd1
| VX9778 = cCoq_2eInit_2eByte_2exd2
| VX9778 = cCoq_2eInit_2eByte_2exd3
| VX9778 = cCoq_2eInit_2eByte_2exd4
| VX9778 = cCoq_2eInit_2eByte_2exd5
| VX9778 = cCoq_2eInit_2eByte_2exd6
| VX9778 = cCoq_2eInit_2eByte_2exd7
| VX9778 = cCoq_2eInit_2eByte_2exd8
| VX9778 = cCoq_2eInit_2eByte_2exd9
| VX9778 = cCoq_2eInit_2eByte_2exda
| VX9778 = cCoq_2eInit_2eByte_2exdb
| VX9778 = cCoq_2eInit_2eByte_2exdc
| VX9778 = cCoq_2eInit_2eByte_2exdd
| VX9778 = cCoq_2eInit_2eByte_2exde
| VX9778 = cCoq_2eInit_2eByte_2exdf
| VX9778 = cCoq_2eInit_2eByte_2exe0
| VX9778 = cCoq_2eInit_2eByte_2exe1
| VX9778 = cCoq_2eInit_2eByte_2exe2
| VX9778 = cCoq_2eInit_2eByte_2exe3
| VX9778 = cCoq_2eInit_2eByte_2exe4
| VX9778 = cCoq_2eInit_2eByte_2exe5
| VX9778 = cCoq_2eInit_2eByte_2exe6
| VX9778 = cCoq_2eInit_2eByte_2exe7
| VX9778 = cCoq_2eInit_2eByte_2exe8
| VX9778 = cCoq_2eInit_2eByte_2exe9
| VX9778 = cCoq_2eInit_2eByte_2exea
| VX9778 = cCoq_2eInit_2eByte_2exeb
| VX9778 = cCoq_2eInit_2eByte_2exec
| VX9778 = cCoq_2eInit_2eByte_2exed
| VX9778 = cCoq_2eInit_2eByte_2exee
| VX9778 = cCoq_2eInit_2eByte_2exef
| VX9778 = cCoq_2eInit_2eByte_2exf0
| VX9778 = cCoq_2eInit_2eByte_2exf1
| VX9778 = cCoq_2eInit_2eByte_2exf2
| VX9778 = cCoq_2eInit_2eByte_2exf3
| VX9778 = cCoq_2eInit_2eByte_2exf4
| VX9778 = cCoq_2eInit_2eByte_2exf5
| VX9778 = cCoq_2eInit_2eByte_2exf6
| VX9778 = cCoq_2eInit_2eByte_2exf7
| VX9778 = cCoq_2eInit_2eByte_2exf8
| VX9778 = cCoq_2eInit_2eByte_2exf9
| VX9778 = cCoq_2eInit_2eByte_2exfa
| VX9778 = cCoq_2eInit_2eByte_2exfb
| VX9778 = cCoq_2eInit_2eByte_2exfc
| VX9778 = cCoq_2eInit_2eByte_2exfd
| VX9778 = cCoq_2eInit_2eByte_2exfe
| VX9778 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__10437,Vvar__1__Q__10438,Vvar__2___24Anonymous__10439] :
( cProp___24t(Vvar__0__P__10437)
=> ( cProp___24t(Vvar__1__Q__10438)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__10439)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__10437,Vvar__1__Q__10438,Vvar__2___24Anonymous__10439)
=> ( ( p(Vvar__0__P__10437)
& Vvar__2___24Anonymous__10439 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__10438)
& Vvar__2___24Anonymous__10439 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__913,Vvar__1__Plt__914,Vvar__2__Pgt__915,Vvar__3___24Anonymous__916] :
( cProp___24t(Vvar__0__Peq__913)
=> ( cProp___24t(Vvar__1__Plt__914)
=> ( cProp___24t(Vvar__2__Pgt__915)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__916)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__913,Vvar__1__Plt__914,Vvar__2__Pgt__915,Vvar__3___24Anonymous__916)
=> ( ( p(Vvar__0__Peq__913)
& Vvar__3___24Anonymous__916 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__914)
& Vvar__3___24Anonymous__916 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__915)
& Vvar__3___24Anonymous__916 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__25327,Vvar__1__Plt__25328,Vvar__2__Pgt__25329,Vvar__3___24Anonymous__25330,VX25331] :
( cProp___24t(Vvar__0__Peq__25327)
=> ( cProp___24t(Vvar__1__Plt__25328)
=> ( cProp___24t(Vvar__2__Pgt__25329)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__25330)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__25327,Vvar__1__Plt__25328,Vvar__2__Pgt__25329,Vvar__3___24Anonymous__25330,VX25331)
=> ( ( p(Vvar__0__Peq__25327)
& Vvar__3___24Anonymous__25330 = cCoq_2eInit_2eDatatypes_2eEq
& VX25331 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__25327,Vvar__1__Plt__25328,Vvar__2__Pgt__25329) )
| ( p(Vvar__1__Plt__25328)
& Vvar__3___24Anonymous__25330 = cCoq_2eInit_2eDatatypes_2eLt
& VX25331 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__25327,Vvar__1__Plt__25328,Vvar__2__Pgt__25329) )
| ( p(Vvar__2__Pgt__25329)
& Vvar__3___24Anonymous__25330 = cCoq_2eInit_2eDatatypes_2eGt
& VX25331 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__25327,Vvar__1__Plt__25328,Vvar__2__Pgt__25329) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX1077] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX1077)
=> ( VX1077 = cCoq_2eInit_2eDatatypes_2etrue
| VX1077 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX912] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX912)
=> ( VX912 = cCoq_2eInit_2eDatatypes_2eEq
| VX912 = cCoq_2eInit_2eDatatypes_2eLt
| VX912 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
! [Vvar__0___24Anonymous__10433] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__10433)
=> ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__10433)
=> Vvar__0___24Anonymous__10433 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__22890,Vvar__1__a__22891,Vvar__2___24Anonymous__22892] :
( cType___24t(Vvar__0__A__22890)
=> ( t(Vvar__1__a__22891,Vvar__0__A__22890)
=> ( t(Vvar__2___24Anonymous__22892,Vvar__0__A__22890)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__22890,Vvar__1__a__22891,Vvar__2___24Anonymous__22892)
=> Vvar__2___24Anonymous__22892 = Vvar__1__a__22891 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__1120,VX1121] :
( cType___24t(Vvar__0__A__1120)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1120,VX1121)
=> ( VX1121 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1120)
| ? [Vvar__1___24Anonymous__1124] :
( t(Vvar__1___24Anonymous__1124,Vvar__0__A__1120)
& ? [Vvar__2___24Anonymous__1125] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1120,Vvar__2___24Anonymous__1125)
& VX1121 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1120,Vvar__1___24Anonymous__1124,Vvar__2___24Anonymous__1125) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX1)
=> ( VX1 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2)
& VX1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__1078,VX1079] :
( cType___24t(Vvar__0__A__1078)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__1078,VX1079)
=> ( ? [Vvar__1___24Anonymous__1081] :
( t(Vvar__1___24Anonymous__1081,Vvar__0__A__1078)
& VX1079 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1078,Vvar__1___24Anonymous__1081) )
| VX1079 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1078) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__1094,Vvar__1__B__1095,VX1096] :
( cType___24t(Vvar__0__A__1094)
=> ( cType___24t(Vvar__1__B__1095)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1094,Vvar__1__B__1095,VX1096)
=> ? [Vvar__2___24Anonymous__1099] :
( t(Vvar__2___24Anonymous__1099,Vvar__0__A__1094)
& ? [Vvar__3___24Anonymous__1100] :
( t(Vvar__3___24Anonymous__1100,Vvar__1__B__1095)
& VX1096 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1094,Vvar__1__B__1095,Vvar__2___24Anonymous__1099,Vvar__3___24Anonymous__1100) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__10456,Vvar__1__B__10457,VX10458] :
( cType___24t(Vvar__0__A__10456)
=> ( cType___24t(Vvar__1__B__10457)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__10456,Vvar__1__B__10457,VX10458)
=> ( ? [Vvar__2___24Anonymous__10461] :
( t(Vvar__2___24Anonymous__10461,Vvar__0__A__10456)
& VX10458 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__10456,Vvar__1__B__10457,Vvar__2___24Anonymous__10461) )
| ? [Vvar__2___24Anonymous__10464] :
( t(Vvar__2___24Anonymous__10464,Vvar__1__B__10457)
& VX10458 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__10456,Vvar__1__B__10457,Vvar__2___24Anonymous__10464) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX911] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX911)
=> VX911 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
! [VX25401] :
( cCoq_2eInit_2eDecimal_2edecimal___24t(VX25401)
=> ( ? [Vvar__0__i__25402] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__25402)
& ? [Vvar__1__f__25403] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__25403)
& VX25401 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__25402,Vvar__1__f__25403) ) )
| ? [Vvar__0__i__25404] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__25404)
& ? [Vvar__1__f__25405] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__25405)
& ? [Vvar__2__e__25406] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__25406)
& VX25401 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__25404,Vvar__1__f__25405,Vvar__2__e__25406) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX22896] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX22896)
=> ( ? [Vvar__0__d__22897] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__22897)
& VX22896 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__22897) )
| ? [Vvar__0__d__22898] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__22898)
& VX22896 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__22898) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX10572] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX10572)
=> ( VX10572 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__10573] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10573)
& VX10572 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__10573) )
| ? [Vvar__0___24Anonymous__10574] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10574)
& VX10572 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__10574) )
| ? [Vvar__0___24Anonymous__10575] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10575)
& VX10572 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__10575) )
| ? [Vvar__0___24Anonymous__10576] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10576)
& VX10572 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__10576) )
| ? [Vvar__0___24Anonymous__10577] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10577)
& VX10572 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__10577) )
| ? [Vvar__0___24Anonymous__10578] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10578)
& VX10572 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__10578) )
| ? [Vvar__0___24Anonymous__10579] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10579)
& VX10572 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__10579) )
| ? [Vvar__0___24Anonymous__10580] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10580)
& VX10572 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__10580) )
| ? [Vvar__0___24Anonymous__10581] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10581)
& VX10572 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__10581) )
| ? [Vvar__0___24Anonymous__10582] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__10582)
& VX10572 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__10582) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__935,Vvar__1___24Anonymous__936] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__935)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__936)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__935,Vvar__1___24Anonymous__936))
=> ( Vvar__1___24Anonymous__936 = Vvar__0__n__935
| ? [Vvar__1__m__940] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__940)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__935,Vvar__1__m__940))
& Vvar__1___24Anonymous__936 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__940) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__21100,Vvar__1__P__21101,VX21104] :
( cType___24t(Vvar__0__A__21100)
=> ( c_24__type__21114___24t(Vvar__0__A__21100,Vvar__1__P__21101,Vvar__1__P__21101)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__21100,Vvar__1__P__21101,VX21104)
=> ? [Vvar__2__x__21109] :
( t(Vvar__2__x__21109,Vvar__0__A__21100)
& p(happ(Vvar__1__P__21101,Vvar__2__x__21109))
& VX21104 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__21100,Vvar__1__P__21101,Vvar__2__x__21109) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__24455,Vvar__1__P__24456,Vvar__2__Q__24459,VX24462] :
( cType___24t(Vvar__0__A__24455)
=> ( c_24__type__24479___24t(Vvar__0__A__24455,Vvar__1__P__24456,Vvar__2__Q__24459,Vvar__1__P__24456)
=> ( c_24__type__24487___24t(Vvar__0__A__24455,Vvar__1__P__24456,Vvar__2__Q__24459,Vvar__2__Q__24459)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__24455,Vvar__1__P__24456,Vvar__2__Q__24459,VX24462)
=> ? [Vvar__3__x__24470] :
( t(Vvar__3__x__24470,Vvar__0__A__24455)
& p(happ(Vvar__1__P__24456,Vvar__3__x__24470))
& p(happ(Vvar__2__Q__24459,Vvar__3__x__24470))
& VX24462 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__24455,Vvar__1__P__24456,Vvar__2__Q__24459,Vvar__3__x__24470) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__21139,Vvar__1__P__21140,VX21143] :
( cType___24t(Vvar__0__A__21139)
=> ( c_24__type__21153___24t(Vvar__0__A__21139,Vvar__1__P__21140,Vvar__1__P__21140)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__21139,Vvar__1__P__21140,VX21143)
=> ? [Vvar__2__x__21148] :
( t(Vvar__2__x__21148,Vvar__0__A__21139)
& ? [Vvar__3___24Anonymous__21149] :
( t(Vvar__3___24Anonymous__21149,happ(Vvar__1__P__21140,Vvar__2__x__21148))
& VX21143 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__21139,Vvar__1__P__21140,Vvar__2__x__21148,Vvar__3___24Anonymous__21149) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__24511,Vvar__1__P__24512,Vvar__2__Q__24515,VX24518] :
( cType___24t(Vvar__0__A__24511)
=> ( c_24__type__24535___24t(Vvar__0__A__24511,Vvar__1__P__24512,Vvar__2__Q__24515,Vvar__1__P__24512)
=> ( c_24__type__24543___24t(Vvar__0__A__24511,Vvar__1__P__24512,Vvar__2__Q__24515,Vvar__2__Q__24515)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__24511,Vvar__1__P__24512,Vvar__2__Q__24515,VX24518)
=> ? [Vvar__3__x__24526] :
( t(Vvar__3__x__24526,Vvar__0__A__24511)
& ? [Vvar__4___24Anonymous__24527] :
( t(Vvar__4___24Anonymous__24527,happ(Vvar__1__P__24512,Vvar__3__x__24526))
& ? [Vvar__5___24Anonymous__24528] :
( t(Vvar__5___24Anonymous__24528,happ(Vvar__2__Q__24515,Vvar__3__x__24526))
& VX24518 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__24511,Vvar__1__P__24512,Vvar__2__Q__24515,Vvar__3__x__24526,Vvar__4___24Anonymous__24527,Vvar__5___24Anonymous__24528) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__13,Vvar__1__B__14,VX15] :
( cProp___24t(Vvar__0__A__13)
=> ( cProp___24t(Vvar__1__B__14)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__13,Vvar__1__B__14,VX15)
=> ( ( p(Vvar__0__A__13)
& VX15 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__13,Vvar__1__B__14) )
| ( p(Vvar__1__B__14)
& VX15 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__13,Vvar__1__B__14) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__43,Vvar__1__B__44,VX45] :
( cType___24t(Vvar__0__A__43)
=> ( cProp___24t(Vvar__1__B__44)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__43,Vvar__1__B__44,VX45)
=> ( ? [Vvar__2___24Anonymous__48] :
( t(Vvar__2___24Anonymous__48,Vvar__0__A__43)
& VX45 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__43,Vvar__1__B__44,Vvar__2___24Anonymous__48) )
| ( p(Vvar__1__B__44)
& VX45 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__43,Vvar__1__B__44) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__25056,Vvar__1__R__25057,Vvar__2__x__25062] :
( cType___24t(Vvar__0__A__25056)
=> ( c_24__type__25091___24t(Vvar__0__A__25056,Vvar__1__R__25057,Vvar__2__x__25062,Vvar__1__R__25057)
=> ( t(Vvar__2__x__25062,Vvar__0__A__25056)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__25056,Vvar__1__R__25057,Vvar__2__x__25062)
=> ( ! [Vvar__var__var__var__var__3__y__25072__25074__25076__25078__25080] :
( t(Vvar__var__var__var__var__3__y__25072__25074__25076__25078__25080,Vvar__0__A__25056)
=> ( p(happ(happ(Vvar__1__R__25057,Vvar__var__var__var__var__3__y__25072__25074__25076__25078__25080),Vvar__2__x__25062))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__25056,Vvar__1__R__25057,Vvar__var__var__var__var__3__y__25072__25074__25076__25078__25080) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Add',axiom,
! [Vvar__0__A__27564,Vvar__1__a__27565,Vvar__2___24Anonymous__27566,Vvar__3___24Anonymous__27567] :
( cType___24t(Vvar__0__A__27564)
=> ( t(Vvar__1__a__27565,Vvar__0__A__27564)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27564,Vvar__2___24Anonymous__27566)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27564,Vvar__3___24Anonymous__27567)
=> ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__27564,Vvar__1__a__27565,Vvar__2___24Anonymous__27566,Vvar__3___24Anonymous__27567)
=> ( ? [Vvar__2__l__27571] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27564,Vvar__2__l__27571)
& Vvar__3___24Anonymous__27567 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27564,Vvar__1__a__27565,Vvar__2__l__27571)
& Vvar__2___24Anonymous__27566 = Vvar__2__l__27571 )
| ? [Vvar__2__x__27574] :
( t(Vvar__2__x__27574,Vvar__0__A__27564)
& ? [Vvar__3__l__27575] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27564,Vvar__3__l__27575)
& ? [Vvar__4__l_27__27576] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27564,Vvar__4__l_27__27576)
& cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__27564,Vvar__1__a__27565,Vvar__3__l__27575,Vvar__4__l_27__27576)
& Vvar__3___24Anonymous__27567 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27564,Vvar__2__x__27574,Vvar__4__l_27__27576)
& Vvar__2___24Anonymous__27566 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27564,Vvar__2__x__27574,Vvar__3__l__27575) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__27578,Vvar__1__P__27579,Vvar__2___24Anonymous__27582] :
( cType___24t(Vvar__0__A__27578)
=> ( c_24__type__27602___24t(Vvar__0__A__27578,Vvar__1__P__27579,Vvar__2___24Anonymous__27582,Vvar__1__P__27579)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27578,Vvar__2___24Anonymous__27582)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__27578,Vvar__1__P__27579,Vvar__2___24Anonymous__27582)
=> ( ? [Vvar__2__x__27588] :
( t(Vvar__2__x__27588,Vvar__0__A__27578)
& ? [Vvar__3__l__27589] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27578,Vvar__3__l__27589)
& p(happ(Vvar__1__P__27579,Vvar__2__x__27588))
& Vvar__2___24Anonymous__27582 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27578,Vvar__2__x__27588,Vvar__3__l__27589) ) )
| ? [Vvar__2__x__27595] :
( t(Vvar__2__x__27595,Vvar__0__A__27578)
& ? [Vvar__3__l__27596] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27578,Vvar__3__l__27596)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__27578,Vvar__1__P__27579,Vvar__3__l__27596)
& Vvar__2___24Anonymous__27582 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27578,Vvar__2__x__27595,Vvar__3__l__27596) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__27604,Vvar__1__P__27605,Vvar__2___24Anonymous__27608] :
( cType___24t(Vvar__0__A__27604)
=> ( c_24__type__27626___24t(Vvar__0__A__27604,Vvar__1__P__27605,Vvar__2___24Anonymous__27608,Vvar__1__P__27605)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27604,Vvar__2___24Anonymous__27608)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__27604,Vvar__1__P__27605,Vvar__2___24Anonymous__27608)
=> ( Vvar__2___24Anonymous__27608 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27604)
| ? [Vvar__2__x__27618] :
( t(Vvar__2__x__27618,Vvar__0__A__27604)
& ? [Vvar__3__l__27619] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27604,Vvar__3__l__27619)
& p(happ(Vvar__1__P__27605,Vvar__2__x__27618))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__27604,Vvar__1__P__27605,Vvar__3__l__27619)
& Vvar__2___24Anonymous__27608 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27604,Vvar__2__x__27618,Vvar__3__l__27619) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall2',axiom,
! [Vvar__0__A__27628,Vvar__1__B__27629,Vvar__2__R__27630,Vvar__3___24Anonymous__27635,Vvar__4___24Anonymous__27636] :
( cType___24t(Vvar__0__A__27628)
=> ( cType___24t(Vvar__1__B__27629)
=> ( c_24__type__27673___24t(Vvar__0__A__27628,Vvar__1__B__27629,Vvar__2__R__27630,Vvar__3___24Anonymous__27635,Vvar__4___24Anonymous__27636,Vvar__2__R__27630)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27628,Vvar__3___24Anonymous__27635)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__27629,Vvar__4___24Anonymous__27636)
=> ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__27628,Vvar__1__B__27629,Vvar__2__R__27630,Vvar__3___24Anonymous__27635,Vvar__4___24Anonymous__27636)
=> ( ( Vvar__4___24Anonymous__27636 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__27629)
& Vvar__3___24Anonymous__27635 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27628) )
| ? [Vvar__3__x__27652] :
( t(Vvar__3__x__27652,Vvar__0__A__27628)
& ? [Vvar__4__y__27653] :
( t(Vvar__4__y__27653,Vvar__1__B__27629)
& ? [Vvar__5__l__27654] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27628,Vvar__5__l__27654)
& ? [Vvar__6__l_27__27655] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__27629,Vvar__6__l_27__27655)
& p(happ(happ(Vvar__2__R__27630,Vvar__3__x__27652),Vvar__4__y__27653))
& cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__27628,Vvar__1__B__27629,Vvar__2__R__27630,Vvar__5__l__27654,Vvar__6__l_27__27655)
& Vvar__4___24Anonymous__27636 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__27629,Vvar__4__y__27653,Vvar__6__l_27__27655)
& Vvar__3___24Anonymous__27635 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27628,Vvar__3__x__27652,Vvar__5__l__27654) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
! [Vvar__0__A__27675,Vvar__1__R__27676,Vvar__2___24Anonymous__27681] :
( cType___24t(Vvar__0__A__27675)
=> ( c_24__type__27708___24t(Vvar__0__A__27675,Vvar__1__R__27676,Vvar__2___24Anonymous__27681,Vvar__1__R__27676)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27675,Vvar__2___24Anonymous__27681)
=> ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__27675,Vvar__1__R__27676,Vvar__2___24Anonymous__27681)
=> ( Vvar__2___24Anonymous__27681 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27675)
| ? [Vvar__2__a__27695] :
( t(Vvar__2__a__27695,Vvar__0__A__27675)
& ? [Vvar__3__l__27696] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27675,Vvar__3__l__27696)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__27675,happ(Vvar__1__R__27676,Vvar__2__a__27695),Vvar__3__l__27696)
& cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__27675,Vvar__1__R__27676,Vvar__3__l__27696)
& Vvar__2___24Anonymous__27681 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27675,Vvar__2__a__27695,Vvar__3__l__27696) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__12718,Vvar__1___24Anonymous__12719] :
( cType___24t(Vvar__0__A__12718)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12718,Vvar__1___24Anonymous__12719)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__12718,Vvar__1___24Anonymous__12719)
=> ( Vvar__1___24Anonymous__12719 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12718)
| ? [Vvar__1__x__12723] :
( t(Vvar__1__x__12723,Vvar__0__A__12718)
& ? [Vvar__2__l__12724] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12718,Vvar__2__l__12724)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__12718,Vvar__1__x__12723,Vvar__2__l__12724)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__12718,Vvar__2__l__12724)
& Vvar__1___24Anonymous__12719 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12718,Vvar__1__x__12723,Vvar__2__l__12724) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__26807,Vvar__1__eqA__26808,Vvar__2__x__26813,Vvar__3___24Anonymous__26814] :
( cType___24t(Vvar__0__A__26807)
=> ( c_24__type__26847___24t(Vvar__0__A__26807,Vvar__1__eqA__26808,Vvar__2__x__26813,Vvar__3___24Anonymous__26814,Vvar__1__eqA__26808)
=> ( t(Vvar__2__x__26813,Vvar__0__A__26807)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26807,Vvar__3___24Anonymous__26814)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__26807,Vvar__1__eqA__26808,Vvar__2__x__26813,Vvar__3___24Anonymous__26814)
=> ( ? [Vvar__3__y__26823] :
( t(Vvar__3__y__26823,Vvar__0__A__26807)
& ? [Vvar__4__l__26824] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26807,Vvar__4__l__26824)
& p(happ(happ(Vvar__1__eqA__26808,Vvar__2__x__26813),Vvar__3__y__26823))
& Vvar__3___24Anonymous__26814 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26807,Vvar__3__y__26823,Vvar__4__l__26824) ) )
| ? [Vvar__3__y__26833] :
( t(Vvar__3__y__26833,Vvar__0__A__26807)
& ? [Vvar__4__l__26834] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26807,Vvar__4__l__26834)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__26807,Vvar__1__eqA__26808,Vvar__2__x__26813,Vvar__4__l__26834)
& Vvar__3___24Anonymous__26814 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26807,Vvar__3__y__26833,Vvar__4__l__26834) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__26849,Vvar__1__eqA__26850,Vvar__2___24Anonymous__26855] :
( cType___24t(Vvar__0__A__26849)
=> ( c_24__type__26882___24t(Vvar__0__A__26849,Vvar__1__eqA__26850,Vvar__2___24Anonymous__26855,Vvar__1__eqA__26850)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26849,Vvar__2___24Anonymous__26855)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__26849,Vvar__1__eqA__26850,Vvar__2___24Anonymous__26855)
=> ( Vvar__2___24Anonymous__26855 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26849)
| ? [Vvar__2__x__26869] :
( t(Vvar__2__x__26869,Vvar__0__A__26849)
& ? [Vvar__3__l__26870] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26849,Vvar__3__l__26870)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__26849,Vvar__1__eqA__26850,Vvar__2__x__26869,Vvar__3__l__26870)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__26849,Vvar__1__eqA__26850,Vvar__3__l__26870)
& Vvar__2___24Anonymous__26855 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26849,Vvar__2__x__26869,Vvar__3__l__26870) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
! [Vvar__0__A__29765,Vvar__1__eqA__29766,Vvar__2___24Anonymous__29771,Vvar__3___24Anonymous__29772] :
( cType___24t(Vvar__0__A__29765)
=> ( c_24__type__29803___24t(Vvar__0__A__29765,Vvar__1__eqA__29766,Vvar__2___24Anonymous__29771,Vvar__3___24Anonymous__29772,Vvar__1__eqA__29766)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29765,Vvar__2___24Anonymous__29771)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29765,Vvar__3___24Anonymous__29772)
=> ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__29765,Vvar__1__eqA__29766,Vvar__2___24Anonymous__29771,Vvar__3___24Anonymous__29772)
=> ( ( Vvar__3___24Anonymous__29772 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29765)
& Vvar__2___24Anonymous__29771 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29765) )
| ? [Vvar__2__x__29786] :
( t(Vvar__2__x__29786,Vvar__0__A__29765)
& ? [Vvar__3__x_27__29787] :
( t(Vvar__3__x_27__29787,Vvar__0__A__29765)
& ? [Vvar__4__l__29788] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29765,Vvar__4__l__29788)
& ? [Vvar__5__l_27__29789] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29765,Vvar__5__l_27__29789)
& p(happ(happ(Vvar__1__eqA__29766,Vvar__2__x__29786),Vvar__3__x_27__29787))
& cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__29765,Vvar__1__eqA__29766,Vvar__4__l__29788,Vvar__5__l_27__29789)
& Vvar__3___24Anonymous__29772 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29765,Vvar__3__x_27__29787,Vvar__5__l_27__29789)
& Vvar__2___24Anonymous__29771 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29765,Vvar__2__x__29786,Vvar__4__l__29788) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__22929,Vvar__1__P__22930,Vvar__2__p__22933,Vvar__3__x__22934,Vvar__4__q__22935,Vvar__5___24Anonymous__22936] :
( cType___24t(Vvar__0__U__22929)
=> ( c_24__type__22951___24t(Vvar__0__U__22929,Vvar__1__P__22930,Vvar__2__p__22933,Vvar__3__x__22934,Vvar__4__q__22935,Vvar__5___24Anonymous__22936,Vvar__1__P__22930)
=> ( t(Vvar__2__p__22933,Vvar__0__U__22929)
=> ( t(Vvar__3__x__22934,happ(Vvar__1__P__22930,Vvar__2__p__22933))
=> ( t(Vvar__4__q__22935,Vvar__0__U__22929)
=> ( t(Vvar__5___24Anonymous__22936,happ(Vvar__1__P__22930,Vvar__4__q__22935))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__22929,Vvar__1__P__22930,Vvar__2__p__22933,Vvar__3__x__22934,Vvar__4__q__22935,Vvar__5___24Anonymous__22936)
=> ( Vvar__5___24Anonymous__22936 = Vvar__3__x__22934
& Vvar__4__q__22935 = Vvar__2__p__22933 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__25434,Vvar__1__P__25435,Vvar__2__p__25438,Vvar__3__x__25439,Vvar__4__q__25440,Vvar__5__y__25441] :
( cType___24t(Vvar__0__U__25434)
=> ( c_24__type__25460___24t(Vvar__0__U__25434,Vvar__1__P__25435,Vvar__2__p__25438,Vvar__3__x__25439,Vvar__4__q__25440,Vvar__5__y__25441,Vvar__1__P__25435)
=> ( t(Vvar__2__p__25438,Vvar__0__U__25434)
=> ( t(Vvar__3__x__25439,happ(Vvar__1__P__25435,Vvar__2__p__25438))
=> ( t(Vvar__4__q__25440,Vvar__0__U__25434)
=> ( t(Vvar__5__y__25441,happ(Vvar__1__P__25435,Vvar__4__q__25440))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__25434,Vvar__1__P__25435,Vvar__2__p__25438,Vvar__3__x__25439,Vvar__4__q__25440,Vvar__5__y__25441)
=> ( Vvar__4__q__25440 = Vvar__2__p__25438
& Vvar__3__x__25439 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__25434,Vvar__4__q__25440,Vvar__1__P__25435,Vvar__5__y__25441,Vvar__2__p__25438)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX835] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX835)
=> ( VX835 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__836] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__836)
& VX835 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__836) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX840] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX840)
=> ( VX840 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__841] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__841)
& VX840 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__841) )
| ? [Vvar__0___24Anonymous__842] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__842)
& VX840 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__842) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX898] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX898)
=> ( ? [Vvar__0___24Anonymous__899] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__899)
& VX898 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__899) )
| ? [Vvar__0___24Anonymous__900] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__900)
& VX898 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__900) )
| VX898 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
! [Vvar__0___24Anonymous__27148,VX27149] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__27148)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__27148,VX27149)
=> ( ( Vvar__0___24Anonymous__27148 = cCoq_2eNumbers_2eBinNums_2exH
& VX27149 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
| ? [Vvar__0__p__27150] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__27150)
& ? [Vvar__1___24Anonymous__27151] :
( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__27150,Vvar__1___24Anonymous__27151)
& Vvar__0___24Anonymous__27148 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2427186___24a2(Vvar__0___24Anonymous__27148,Vvar__0__p__27150)
& VX27149 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__27150,Vvar__1___24Anonymous__27151) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__30667,Vvar__1__q__30668,Vvar__2___24Anonymous__30669] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__30667)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__30668)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__30669)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__30667,Vvar__1__q__30668,Vvar__2___24Anonymous__30669)
=> ( ( Vvar__0__p__30667 = Vvar__1__q__30668
& Vvar__2___24Anonymous__30669 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__30676] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__30676)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__30668,Vvar__2__r__30676) = Vvar__0__p__30667
& Vvar__2___24Anonymous__30669 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__30676) )
| ? [Vvar__2__r__30680] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__30680)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__30667,Vvar__2__r__30680) = Vvar__1__q__30668
& Vvar__2___24Anonymous__30669 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX9594] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX9594)
=> ( VX9594 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__9595] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9595)
& VX9594 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__9595) )
| VX9594 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX14210] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX14210)
=> ? [Vvar__0__Qnum__14211] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__14211)
& ? [Vvar__1__Qden__14212] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__14212)
& VX14210 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__14211,Vvar__1__Qden__14212) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
! [VX25555] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(VX25555)
=> ? [Vvar__0__neg__25556] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__25556)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__25556,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX25555 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__25556) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
! [VX25541] :
( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX25541)
=> ? [Vvar__0__nonneg__25542] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__25542)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__25542)
& VX25541 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__25542) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
! [VX14277] :
( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX14277)
=> ? [Vvar__0__nonpos__14278] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__14278)
& cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__14278,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
& VX14277 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__14278) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX25562] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX25562)
=> ? [Vvar__0__nonzero__25563] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__25563)
& Vvar__0__nonzero__25563 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX25562 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__25563) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
! [VX25548] :
( cCoq_2eReals_2eRIneq_2eposreal___24t(VX25548)
=> ? [Vvar__0__pos__25549] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__25549)
& cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__25549)
& VX25548 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__25549) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__14793,Vvar__1___24Anonymous__14794,VX14795] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__14793)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__14794)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__14793,Vvar__1___24Anonymous__14794,VX14795)
=> ( ( Vvar__0__x__14793 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__14794 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX14795 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__14793) )
| ? [Vvar__1__n__14799] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__14799)
& Vvar__0__x__14793 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__14799)
& Vvar__1___24Anonymous__14794 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2414819___24a3(Vvar__0__x__14793,Vvar__1___24Anonymous__14794,Vvar__1__n__14799)
& VX14795 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__14793,Vvar__1__n__14799) )
| ? [Vvar__1__n__14804] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__14804)
& Vvar__0__x__14793 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__14804))
& Vvar__1___24Anonymous__14794 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2414836___24a3(Vvar__0__x__14793,Vvar__1___24Anonymous__14794,Vvar__1__n__14804)
& VX14795 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__14793,Vvar__1__n__14804) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__28377,Vvar__1__R__28378] :
( cType___24t(Vvar__0__A__28377)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28377,Vvar__1__R__28378)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__28377,Vvar__1__R__28378)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__28377,Vvar__1__R__28378)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__28377,Vvar__1__R__28378)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__28369,Vvar__1__R__28370] :
( cType___24t(Vvar__0__A__28369)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28369,Vvar__1__R__28370)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__28369,Vvar__1__R__28370)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__28369,Vvar__1__R__28370)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__28369,Vvar__1__R__28370)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__28369,Vvar__1__R__28370)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__28361,Vvar__1__R__28362] :
( cType___24t(Vvar__0__A__28361)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28361,Vvar__1__R__28362)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__28361,Vvar__1__R__28362)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__28361,Vvar__1__R__28362)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__28361,Vvar__1__R__28362)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__28361,Vvar__1__R__28362)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__28354,Vvar__1__R__28355] :
( cType___24t(Vvar__0__A__28354)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28354,Vvar__1__R__28355)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__28354,Vvar__1__R__28355)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__28354,Vvar__1__R__28355)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__28354,Vvar__1__R__28355)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
! [Vvar__0__A__28820,Vvar__1__leA__28821,Vvar__2___24Anonymous__28826] :
( cType___24t(Vvar__0__A__28820)
=> ( c_24__type__28916___24t(Vvar__0__A__28820,Vvar__1__leA__28821,Vvar__2___24Anonymous__28826,Vvar__1__leA__28821)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28820,Vvar__2___24Anonymous__28826)
=> ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__28820,Vvar__1__leA__28821,Vvar__2___24Anonymous__28826)
=> ( Vvar__2___24Anonymous__28826 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28820)
| ? [Vvar__2__x__28840] :
( t(Vvar__2__x__28840,Vvar__0__A__28820)
& Vvar__2___24Anonymous__28826 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28820,Vvar__2__x__28840,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28820)) )
| ? [Vvar__2__x__28847] :
( t(Vvar__2__x__28847,Vvar__0__A__28820)
& ? [Vvar__3__y__28848] :
( t(Vvar__3__y__28848,Vvar__0__A__28820)
& ? [Vvar__4__l__28849] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28820,Vvar__4__l__28849)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__28820,Vvar__1__leA__28821,Vvar__2__x__28847,Vvar__3__y__28848)
& cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__28820,Vvar__1__leA__28821,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__28820,Vvar__4__l__28849,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28820,Vvar__3__y__28848,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28820))))
& Vvar__2___24Anonymous__28826 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2429114___24a6(Vvar__0__A__28820,Vvar__1__leA__28821,Vvar__2___24Anonymous__28826,Vvar__2__x__28847,Vvar__3__y__28848,Vvar__4__l__28849) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
! [Vvar__0__A__28769,Vvar__1__leA__28770,Vvar__2___24Anonymous__28775,Vvar__3___24Anonymous__28776] :
( cType___24t(Vvar__0__A__28769)
=> ( c_24__type__28818___24t(Vvar__0__A__28769,Vvar__1__leA__28770,Vvar__2___24Anonymous__28775,Vvar__3___24Anonymous__28776,Vvar__1__leA__28770)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__2___24Anonymous__28775)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__3___24Anonymous__28776)
=> ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__28769,Vvar__1__leA__28770,Vvar__2___24Anonymous__28775,Vvar__3___24Anonymous__28776)
=> ( ? [Vvar__2__a__28784] :
( t(Vvar__2__a__28784,Vvar__0__A__28769)
& ? [Vvar__3__x__28785] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__3__x__28785)
& Vvar__3___24Anonymous__28776 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28769,Vvar__2__a__28784,Vvar__3__x__28785)
& Vvar__2___24Anonymous__28775 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28769) ) )
| ? [Vvar__2__a__28792] :
( t(Vvar__2__a__28792,Vvar__0__A__28769)
& ? [Vvar__3__b__28793] :
( t(Vvar__3__b__28793,Vvar__0__A__28769)
& p(happ(happ(Vvar__1__leA__28770,Vvar__2__a__28792),Vvar__3__b__28793))
& ? [Vvar__5__x__28795] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__5__x__28795)
& ? [Vvar__6__y__28796] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__6__y__28796)
& Vvar__3___24Anonymous__28776 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28769,Vvar__3__b__28793,Vvar__6__y__28796)
& Vvar__2___24Anonymous__28775 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28769,Vvar__2__a__28792,Vvar__5__x__28795) ) ) ) )
| ? [Vvar__2__a__28803] :
( t(Vvar__2__a__28803,Vvar__0__A__28769)
& ? [Vvar__3__x__28804] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__3__x__28804)
& ? [Vvar__4__y__28805] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28769,Vvar__4__y__28805)
& cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__28769,Vvar__1__leA__28770,Vvar__3__x__28804,Vvar__4__y__28805)
& Vvar__3___24Anonymous__28776 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28769,Vvar__2__a__28803,Vvar__4__y__28805)
& Vvar__2___24Anonymous__28775 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28769,Vvar__2__a__28803,Vvar__3__x__28804) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__28418,Vvar__1__R__28419,Vvar__2__x__28420,Vvar__3___24Anonymous__28421] :
( cType___24t(Vvar__0__A__28418)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28418,Vvar__1__R__28419)
=> ( t(Vvar__2__x__28420,Vvar__0__A__28418)
=> ( t(Vvar__3___24Anonymous__28421,Vvar__0__A__28418)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__28418,Vvar__1__R__28419,Vvar__2__x__28420,Vvar__3___24Anonymous__28421)
=> ( ? [Vvar__3__y__28426] :
( t(Vvar__3__y__28426,Vvar__0__A__28418)
& p(happ(happ(Vvar__1__R__28419,Vvar__2__x__28420),Vvar__3__y__28426))
& Vvar__3___24Anonymous__28421 = Vvar__3__y__28426 )
| Vvar__3___24Anonymous__28421 = Vvar__2__x__28420 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__28466,Vvar__1__R__28467,Vvar__1___24Anonymous__28468,Vvar__2___24Anonymous__28469] :
( cType___24t(Vvar__0__A__28466)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28466,Vvar__1__R__28467)
=> ( t(Vvar__1___24Anonymous__28468,Vvar__0__A__28466)
=> ( t(Vvar__2___24Anonymous__28469,Vvar__0__A__28466)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__28466,Vvar__1__R__28467,Vvar__1___24Anonymous__28468,Vvar__2___24Anonymous__28469)
=> ( ? [Vvar__2__x__28473] :
( t(Vvar__2__x__28473,Vvar__0__A__28466)
& ? [Vvar__3__y__28474] :
( t(Vvar__3__y__28474,Vvar__0__A__28466)
& p(happ(happ(Vvar__1__R__28467,Vvar__2__x__28473),Vvar__3__y__28474))
& Vvar__2___24Anonymous__28469 = Vvar__3__y__28474
& Vvar__1___24Anonymous__28468 = Vvar__2__x__28473 ) )
| ? [Vvar__2__x__28478] :
( t(Vvar__2__x__28478,Vvar__0__A__28466)
& Vvar__2___24Anonymous__28469 = Vvar__2__x__28478
& Vvar__1___24Anonymous__28468 = Vvar__2__x__28478 )
| ? [Vvar__2__x__28481] :
( t(Vvar__2__x__28481,Vvar__0__A__28466)
& ? [Vvar__3__y__28482] :
( t(Vvar__3__y__28482,Vvar__0__A__28466)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__28466,Vvar__1__R__28467,Vvar__2__x__28481,Vvar__3__y__28482)
& Vvar__2___24Anonymous__28469 = Vvar__2__x__28481
& Vvar__1___24Anonymous__28468 = Vvar__3__y__28482 ) )
| ? [Vvar__2__x__28486] :
( t(Vvar__2__x__28486,Vvar__0__A__28466)
& ? [Vvar__3__y__28487] :
( t(Vvar__3__y__28487,Vvar__0__A__28466)
& ? [Vvar__4__z__28488] :
( t(Vvar__4__z__28488,Vvar__0__A__28466)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__28466,Vvar__1__R__28467,Vvar__2__x__28486,Vvar__3__y__28487)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__28466,Vvar__1__R__28467,Vvar__3__y__28487,Vvar__4__z__28488)
& Vvar__2___24Anonymous__28469 = Vvar__4__z__28488
& Vvar__1___24Anonymous__28468 = Vvar__2__x__28486 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__28491,Vvar__1__R__28492,Vvar__2__x__28493,Vvar__3___24Anonymous__28494] :
( cType___24t(Vvar__0__A__28491)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28491,Vvar__1__R__28492)
=> ( t(Vvar__2__x__28493,Vvar__0__A__28491)
=> ( t(Vvar__3___24Anonymous__28494,Vvar__0__A__28491)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__28491,Vvar__1__R__28492,Vvar__2__x__28493,Vvar__3___24Anonymous__28494)
=> ( Vvar__3___24Anonymous__28494 = Vvar__2__x__28493
| ? [Vvar__3__y__28502] :
( t(Vvar__3__y__28502,Vvar__0__A__28491)
& ? [Vvar__4__z__28503] :
( t(Vvar__4__z__28503,Vvar__0__A__28491)
& ( p(happ(happ(Vvar__1__R__28492,Vvar__2__x__28493),Vvar__3__y__28502))
| p(happ(happ(Vvar__1__R__28492,Vvar__3__y__28502),Vvar__2__x__28493)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__28491,Vvar__1__R__28492,Vvar__3__y__28502,Vvar__4__z__28503)
& Vvar__3___24Anonymous__28494 = Vvar__4__z__28503 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__28506,Vvar__1__R__28507,Vvar__2__x__28508,Vvar__3___24Anonymous__28509] :
( cType___24t(Vvar__0__A__28506)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28506,Vvar__1__R__28507)
=> ( t(Vvar__2__x__28508,Vvar__0__A__28506)
=> ( t(Vvar__3___24Anonymous__28509,Vvar__0__A__28506)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__28506,Vvar__1__R__28507,Vvar__2__x__28508,Vvar__3___24Anonymous__28509)
=> ( Vvar__3___24Anonymous__28509 = Vvar__2__x__28508
| ? [Vvar__3__y__28517] :
( t(Vvar__3__y__28517,Vvar__0__A__28506)
& ? [Vvar__4__z__28518] :
( t(Vvar__4__z__28518,Vvar__0__A__28506)
& ( p(happ(happ(Vvar__1__R__28507,Vvar__3__y__28517),Vvar__4__z__28518))
| p(happ(happ(Vvar__1__R__28507,Vvar__4__z__28518),Vvar__3__y__28517)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__28506,Vvar__1__R__28507,Vvar__2__x__28508,Vvar__3__y__28517)
& Vvar__3___24Anonymous__28509 = Vvar__4__z__28518 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__28431,Vvar__1__R__28432,Vvar__2__x__28433,Vvar__3___24Anonymous__28434] :
( cType___24t(Vvar__0__A__28431)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28431,Vvar__1__R__28432)
=> ( t(Vvar__2__x__28433,Vvar__0__A__28431)
=> ( t(Vvar__3___24Anonymous__28434,Vvar__0__A__28431)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__28431,Vvar__1__R__28432,Vvar__2__x__28433,Vvar__3___24Anonymous__28434)
=> ( ? [Vvar__3__y__28439] :
( t(Vvar__3__y__28439,Vvar__0__A__28431)
& p(happ(happ(Vvar__1__R__28432,Vvar__2__x__28433),Vvar__3__y__28439))
& Vvar__3___24Anonymous__28434 = Vvar__3__y__28439 )
| Vvar__3___24Anonymous__28434 = Vvar__2__x__28433
| ? [Vvar__3__y__28447] :
( t(Vvar__3__y__28447,Vvar__0__A__28431)
& ? [Vvar__4__z__28448] :
( t(Vvar__4__z__28448,Vvar__0__A__28431)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__28431,Vvar__1__R__28432,Vvar__2__x__28433,Vvar__3__y__28447)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__28431,Vvar__1__R__28432,Vvar__3__y__28447,Vvar__4__z__28448)
& Vvar__3___24Anonymous__28434 = Vvar__4__z__28448 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__28451,Vvar__1__R__28452,Vvar__2__x__28453,Vvar__3___24Anonymous__28454] :
( cType___24t(Vvar__0__A__28451)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28451,Vvar__1__R__28452)
=> ( t(Vvar__2__x__28453,Vvar__0__A__28451)
=> ( t(Vvar__3___24Anonymous__28454,Vvar__0__A__28451)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__28451,Vvar__1__R__28452,Vvar__2__x__28453,Vvar__3___24Anonymous__28454)
=> ( Vvar__3___24Anonymous__28454 = Vvar__2__x__28453
| ? [Vvar__3__y__28462] :
( t(Vvar__3__y__28462,Vvar__0__A__28451)
& ? [Vvar__4__z__28463] :
( t(Vvar__4__z__28463,Vvar__0__A__28451)
& p(happ(happ(Vvar__1__R__28452,Vvar__2__x__28453),Vvar__3__y__28462))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__28451,Vvar__1__R__28452,Vvar__3__y__28462,Vvar__4__z__28463)
& Vvar__3___24Anonymous__28454 = Vvar__4__z__28463 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__14589,Vvar__1__R__14590,Vvar__2__x__14591,Vvar__3___24Anonymous__14592] :
( cType___24t(Vvar__0__A__14589)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__14589,Vvar__1__R__14590)
=> ( t(Vvar__2__x__14591,Vvar__0__A__14589)
=> ( t(Vvar__3___24Anonymous__14592,Vvar__0__A__14589)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__14589,Vvar__1__R__14590,Vvar__2__x__14591,Vvar__3___24Anonymous__14592)
=> ( Vvar__3___24Anonymous__14592 = Vvar__2__x__14591
| ? [Vvar__3__y__14600] :
( t(Vvar__3__y__14600,Vvar__0__A__14589)
& ? [Vvar__4__z__14601] :
( t(Vvar__4__z__14601,Vvar__0__A__14589)
& p(happ(happ(Vvar__1__R__14590,Vvar__3__y__14600),Vvar__4__z__14601))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__14589,Vvar__1__R__14590,Vvar__2__x__14591,Vvar__3__y__14600)
& Vvar__3___24Anonymous__14592 = Vvar__4__z__14601 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__14572,Vvar__1__R__14573,Vvar__2__x__14574,Vvar__3___24Anonymous__14575] :
( cType___24t(Vvar__0__A__14572)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__14572,Vvar__1__R__14573)
=> ( t(Vvar__2__x__14574,Vvar__0__A__14572)
=> ( t(Vvar__3___24Anonymous__14575,Vvar__0__A__14572)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__14572,Vvar__1__R__14573,Vvar__2__x__14574,Vvar__3___24Anonymous__14575)
=> ( ? [Vvar__3__y__14580] :
( t(Vvar__3__y__14580,Vvar__0__A__14572)
& p(happ(happ(Vvar__1__R__14573,Vvar__2__x__14574),Vvar__3__y__14580))
& Vvar__3___24Anonymous__14575 = Vvar__3__y__14580 )
| ? [Vvar__3__y__14585] :
( t(Vvar__3__y__14585,Vvar__0__A__14572)
& ? [Vvar__4__z__14586] :
( t(Vvar__4__z__14586,Vvar__0__A__14572)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__14572,Vvar__1__R__14573,Vvar__2__x__14574,Vvar__3__y__14585)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__14572,Vvar__1__R__14573,Vvar__3__y__14585,Vvar__4__z__14586)
& Vvar__3___24Anonymous__14575 = Vvar__4__z__14586 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__28384,Vvar__1__R__28385,Vvar__2__x__28386,Vvar__3___24Anonymous__28387] :
( cType___24t(Vvar__0__A__28384)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28384,Vvar__1__R__28385)
=> ( t(Vvar__2__x__28386,Vvar__0__A__28384)
=> ( t(Vvar__3___24Anonymous__28387,Vvar__0__A__28384)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__28384,Vvar__1__R__28385,Vvar__2__x__28386,Vvar__3___24Anonymous__28387)
=> ( ? [Vvar__3__y__28392] :
( t(Vvar__3__y__28392,Vvar__0__A__28384)
& p(happ(happ(Vvar__1__R__28385,Vvar__2__x__28386),Vvar__3__y__28392))
& Vvar__3___24Anonymous__28387 = Vvar__3__y__28392 )
| ? [Vvar__3__y__28397] :
( t(Vvar__3__y__28397,Vvar__0__A__28384)
& ? [Vvar__4__z__28398] :
( t(Vvar__4__z__28398,Vvar__0__A__28384)
& p(happ(happ(Vvar__1__R__28385,Vvar__2__x__28386),Vvar__3__y__28397))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__28384,Vvar__1__R__28385,Vvar__3__y__28397,Vvar__4__z__28398)
& Vvar__3___24Anonymous__28387 = Vvar__4__z__28398 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__28401,Vvar__1__R__28402,Vvar__2__x__28403,Vvar__3___24Anonymous__28404] :
( cType___24t(Vvar__0__A__28401)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__28401,Vvar__1__R__28402)
=> ( t(Vvar__2__x__28403,Vvar__0__A__28401)
=> ( t(Vvar__3___24Anonymous__28404,Vvar__0__A__28401)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__28401,Vvar__1__R__28402,Vvar__2__x__28403,Vvar__3___24Anonymous__28404)
=> ( ? [Vvar__3__y__28409] :
( t(Vvar__3__y__28409,Vvar__0__A__28401)
& p(happ(happ(Vvar__1__R__28402,Vvar__2__x__28403),Vvar__3__y__28409))
& Vvar__3___24Anonymous__28404 = Vvar__3__y__28409 )
| ? [Vvar__3__y__28414] :
( t(Vvar__3__y__28414,Vvar__0__A__28401)
& ? [Vvar__4__z__28415] :
( t(Vvar__4__z__28415,Vvar__0__A__28401)
& p(happ(happ(Vvar__1__R__28402,Vvar__3__y__28414),Vvar__4__z__28415))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__28401,Vvar__1__R__28402,Vvar__2__x__28403,Vvar__3__y__28414)
& Vvar__3___24Anonymous__28404 = Vvar__4__z__28415 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.le_AsB',axiom,
! [Vvar__0__A__28521,Vvar__1__B__28522,Vvar__2__leA__28523,Vvar__3__leB__28528,Vvar__4___24Anonymous__28533,Vvar__5___24Anonymous__28534] :
( cType___24t(Vvar__0__A__28521)
=> ( cType___24t(Vvar__1__B__28522)
=> ( c_24__type__28603___24t(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__2__leA__28523,Vvar__3__leB__28528,Vvar__4___24Anonymous__28533,Vvar__5___24Anonymous__28534,Vvar__2__leA__28523)
=> ( c_24__type__28628___24t(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__2__leA__28523,Vvar__3__leB__28528,Vvar__4___24Anonymous__28533,Vvar__5___24Anonymous__28534,Vvar__3__leB__28528)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__4___24Anonymous__28533)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__5___24Anonymous__28534)
=> ( cCoq_2eRelations_2eRelation__Operators_2ele__AsB___24a6(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__2__leA__28523,Vvar__3__leB__28528,Vvar__4___24Anonymous__28533,Vvar__5___24Anonymous__28534)
=> ( ? [Vvar__4__x__28548] :
( t(Vvar__4__x__28548,Vvar__0__A__28521)
& ? [Vvar__5__y__28549] :
( t(Vvar__5__y__28549,Vvar__0__A__28521)
& p(happ(happ(Vvar__2__leA__28523,Vvar__4__x__28548),Vvar__5__y__28549))
& Vvar__5___24Anonymous__28534 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__5__y__28549)
& Vvar__4___24Anonymous__28533 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__4__x__28548) ) )
| ? [Vvar__4__x__28563] :
( t(Vvar__4__x__28563,Vvar__0__A__28521)
& ? [Vvar__5__y__28564] :
( t(Vvar__5__y__28564,Vvar__1__B__28522)
& Vvar__5___24Anonymous__28534 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__5__y__28564)
& Vvar__4___24Anonymous__28533 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__4__x__28563) ) )
| ? [Vvar__4__x__28577] :
( t(Vvar__4__x__28577,Vvar__1__B__28522)
& ? [Vvar__5__y__28578] :
( t(Vvar__5__y__28578,Vvar__1__B__28522)
& p(happ(happ(Vvar__3__leB__28528,Vvar__4__x__28577),Vvar__5__y__28578))
& Vvar__5___24Anonymous__28534 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__5__y__28578)
& Vvar__4___24Anonymous__28533 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__28521,Vvar__1__B__28522,Vvar__4__x__28577) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
! [Vvar__0__A__14604,Vvar__1__B__14605,Vvar__2__leA__14608,Vvar__3__leB__14613,Vvar__4___24Anonymous__14620,Vvar__5___24Anonymous__14621] :
( cType___24t(Vvar__0__A__14604)
=> ( c_24__type__14684___24t(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__2__leA__14608,Vvar__3__leB__14613,Vvar__4___24Anonymous__14620,Vvar__5___24Anonymous__14621,Vvar__1__B__14605)
=> ( c_24__type__14713___24t(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__2__leA__14608,Vvar__3__leB__14613,Vvar__4___24Anonymous__14620,Vvar__5___24Anonymous__14621,Vvar__2__leA__14608)
=> ( c_24__type__14750___24t(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__2__leA__14608,Vvar__3__leB__14613,Vvar__4___24Anonymous__14620,Vvar__5___24Anonymous__14621,Vvar__3__leB__14613)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__4___24Anonymous__14620)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__5___24Anonymous__14621)
=> ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__2__leA__14608,Vvar__3__leB__14613,Vvar__4___24Anonymous__14620,Vvar__5___24Anonymous__14621)
=> ( ? [Vvar__4__x__14639] :
( t(Vvar__4__x__14639,Vvar__0__A__14604)
& ? [Vvar__5__x_27__14640] :
( t(Vvar__5__x_27__14640,Vvar__0__A__14604)
& ? [Vvar__6__y__14641] :
( t(Vvar__6__y__14641,happ(Vvar__1__B__14605,Vvar__4__x__14639))
& ? [Vvar__7__y_27__14642] :
( t(Vvar__7__y_27__14642,happ(Vvar__1__B__14605,Vvar__5__x_27__14640))
& p(happ(happ(Vvar__2__leA__14608,Vvar__4__x__14639),Vvar__5__x_27__14640))
& Vvar__5___24Anonymous__14621 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__5__x_27__14640,Vvar__7__y_27__14642)
& Vvar__4___24Anonymous__14620 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__4__x__14639,Vvar__6__y__14641) ) ) ) )
| ? [Vvar__4__x__14660] :
( t(Vvar__4__x__14660,Vvar__0__A__14604)
& ? [Vvar__5__y__14661] :
( t(Vvar__5__y__14661,happ(Vvar__1__B__14605,Vvar__4__x__14660))
& ? [Vvar__6__y_27__14662] :
( t(Vvar__6__y_27__14662,happ(Vvar__1__B__14605,Vvar__4__x__14660))
& p(happ(happ(happ(Vvar__3__leB__14613,Vvar__4__x__14660),Vvar__5__y__14661),Vvar__6__y_27__14662))
& Vvar__5___24Anonymous__14621 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__4__x__14660,Vvar__6__y_27__14662)
& Vvar__4___24Anonymous__14620 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__14604,Vvar__1__B__14605,Vvar__4__x__14660,Vvar__5__y__14661) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
! [Vvar__0__A__28727,Vvar__1__R__28728,Vvar__2___24Anonymous__28733,Vvar__3___24Anonymous__28734] :
( cType___24t(Vvar__0__A__28727)
=> ( c_24__type__28767___24t(Vvar__0__A__28727,Vvar__1__R__28728,Vvar__2___24Anonymous__28733,Vvar__3___24Anonymous__28734,Vvar__1__R__28728)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__2___24Anonymous__28733)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__3___24Anonymous__28734)
=> ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__28727,Vvar__1__R__28728,Vvar__2___24Anonymous__28733,Vvar__3___24Anonymous__28734)
=> ( ? [Vvar__2__x__28742] :
( t(Vvar__2__x__28742,Vvar__0__A__28727)
& ? [Vvar__3__y__28743] :
( t(Vvar__3__y__28743,Vvar__0__A__28727)
& ? [Vvar__4__p__28744] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__4__p__28744)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__1__R__28728,Vvar__1__R__28728,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__2__x__28742,Vvar__3__y__28743),Vvar__4__p__28744)
& Vvar__3___24Anonymous__28734 = Vvar__4__p__28744
& Vvar__2___24Anonymous__28733 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__2__x__28742,Vvar__3__y__28743) ) ) )
| ? [Vvar__2__x__28752] :
( t(Vvar__2__x__28752,Vvar__0__A__28727)
& ? [Vvar__3__y__28753] :
( t(Vvar__3__y__28753,Vvar__0__A__28727)
& ? [Vvar__4__p__28754] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__4__p__28754)
& cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__1__R__28728,Vvar__1__R__28728,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__2__x__28752,Vvar__3__y__28753),Vvar__4__p__28754)
& Vvar__3___24Anonymous__28734 = Vvar__4__p__28754
& Vvar__2___24Anonymous__28733 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28727,Vvar__0__A__28727,Vvar__3__y__28753,Vvar__2__x__28752) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
! [Vvar__0__A__28630,Vvar__1__B__28631,Vvar__2__leA__28632,Vvar__3__leB__28637,Vvar__4___24Anonymous__28642,Vvar__5___24Anonymous__28643] :
( cType___24t(Vvar__0__A__28630)
=> ( cType___24t(Vvar__1__B__28631)
=> ( c_24__type__28700___24t(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__2__leA__28632,Vvar__3__leB__28637,Vvar__4___24Anonymous__28642,Vvar__5___24Anonymous__28643,Vvar__2__leA__28632)
=> ( c_24__type__28725___24t(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__2__leA__28632,Vvar__3__leB__28637,Vvar__4___24Anonymous__28642,Vvar__5___24Anonymous__28643,Vvar__3__leB__28637)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__4___24Anonymous__28642)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__5___24Anonymous__28643)
=> ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__2__leA__28632,Vvar__3__leB__28637,Vvar__4___24Anonymous__28642,Vvar__5___24Anonymous__28643)
=> ( ? [Vvar__4__x__28657] :
( t(Vvar__4__x__28657,Vvar__0__A__28630)
& ? [Vvar__5__x_27__28658] :
( t(Vvar__5__x_27__28658,Vvar__0__A__28630)
& p(happ(happ(Vvar__2__leA__28632,Vvar__4__x__28657),Vvar__5__x_27__28658))
& ? [Vvar__7__y__28660] :
( t(Vvar__7__y__28660,Vvar__1__B__28631)
& Vvar__5___24Anonymous__28643 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__5__x_27__28658,Vvar__7__y__28660)
& Vvar__4___24Anonymous__28642 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__4__x__28657,Vvar__7__y__28660) ) ) )
| ? [Vvar__4__y__28673] :
( t(Vvar__4__y__28673,Vvar__1__B__28631)
& ? [Vvar__5__y_27__28674] :
( t(Vvar__5__y_27__28674,Vvar__1__B__28631)
& p(happ(happ(Vvar__3__leB__28637,Vvar__4__y__28673),Vvar__5__y_27__28674))
& ? [Vvar__7__x__28676] :
( t(Vvar__7__x__28676,Vvar__0__A__28630)
& Vvar__5___24Anonymous__28643 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__7__x__28676,Vvar__5__y_27__28674)
& Vvar__4___24Anonymous__28642 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__28630,Vvar__1__B__28631,Vvar__7__x__28676,Vvar__4__y__28673) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Equivalence',axiom,
! [Vvar__0__U__29354,Vvar__1__R__29355] :
( cType___24t(Vvar__0__U__29354)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__29354,Vvar__1__R__29355)
=> ( cCoq_2eSets_2eRelations__1_2eEquivalence___24a2(Vvar__0__U__29354,Vvar__1__R__29355)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__29354,Vvar__1__R__29355)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__29354,Vvar__1__R__29355)
& cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(Vvar__0__U__29354,Vvar__1__R__29355)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Order',axiom,
! [Vvar__0__U__29346,Vvar__1__R__29347] :
( cType___24t(Vvar__0__U__29346)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__29346,Vvar__1__R__29347)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__29346,Vvar__1__R__29347)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__29346,Vvar__1__R__29347)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__29346,Vvar__1__R__29347)
& cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(Vvar__0__U__29346,Vvar__1__R__29347)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.PER',axiom,
! [Vvar__0__U__29362,Vvar__1__R__29363] :
( cType___24t(Vvar__0__U__29362)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__29362,Vvar__1__R__29363)
=> ( cCoq_2eSets_2eRelations__1_2ePER___24a2(Vvar__0__U__29362,Vvar__1__R__29363)
=> ( cCoq_2eSets_2eRelations__1_2eSymmetric___24a2(Vvar__0__U__29362,Vvar__1__R__29363)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__29362,Vvar__1__R__29363)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Preorder',axiom,
! [Vvar__0__U__29339,Vvar__1__R__29340] :
( cType___24t(Vvar__0__U__29339)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__29339,Vvar__1__R__29340)
=> ( cCoq_2eSets_2eRelations__1_2ePreorder___24a2(Vvar__0__U__29339,Vvar__1__R__29340)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__29339,Vvar__1__R__29340)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__29339,Vvar__1__R__29340)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
! [Vvar__0__A__29848,Vvar__1__R__29849,Vvar__2__a__29854,Vvar__3___24Anonymous__29855] :
( cType___24t(Vvar__0__A__29848)
=> ( c_24__type__29885___24t(Vvar__0__A__29848,Vvar__1__R__29849,Vvar__2__a__29854,Vvar__3___24Anonymous__29855,Vvar__1__R__29849)
=> ( t(Vvar__2__a__29854,Vvar__0__A__29848)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29848,Vvar__3___24Anonymous__29855)
=> ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__29848,Vvar__1__R__29849,Vvar__2__a__29854,Vvar__3___24Anonymous__29855)
=> ( Vvar__3___24Anonymous__29855 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29848)
| ? [Vvar__3__b__29871] :
( t(Vvar__3__b__29871,Vvar__0__A__29848)
& ? [Vvar__4__l__29872] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29848,Vvar__4__l__29872)
& p(happ(happ(Vvar__1__R__29849,Vvar__2__a__29854),Vvar__3__b__29871))
& Vvar__3___24Anonymous__29855 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29848,Vvar__3__b__29871,Vvar__4__l__29872) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
! [Vvar__0__A__29805,Vvar__1__R__29806,Vvar__2___24Anonymous__29811] :
( cType___24t(Vvar__0__A__29805)
=> ( c_24__type__29846___24t(Vvar__0__A__29805,Vvar__1__R__29806,Vvar__2___24Anonymous__29811,Vvar__1__R__29806)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29805,Vvar__2___24Anonymous__29811)
=> ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__29805,Vvar__1__R__29806,Vvar__2___24Anonymous__29811)
=> ( Vvar__2___24Anonymous__29811 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29805)
| ? [Vvar__2__a__29825] :
( t(Vvar__2__a__29825,Vvar__0__A__29805)
& Vvar__2___24Anonymous__29811 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29805,Vvar__2__a__29825,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29805)) )
| ? [Vvar__2__a__29832] :
( t(Vvar__2__a__29832,Vvar__0__A__29805)
& ? [Vvar__3__b__29833] :
( t(Vvar__3__b__29833,Vvar__0__A__29805)
& ? [Vvar__4__l__29834] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29805,Vvar__4__l__29834)
& cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__29805,Vvar__1__R__29806,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29805,Vvar__3__b__29833,Vvar__4__l__29834))
& p(happ(happ(Vvar__1__R__29806,Vvar__2__a__29832),Vvar__3__b__29833))
& Vvar__2___24Anonymous__29811 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29805,Vvar__2__a__29832,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29805,Vvar__3__b__29833,Vvar__4__l__29834)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
! [Vvar__0__A__29887,Vvar__1__R__29888,Vvar__2___24Anonymous__29893] :
( cType___24t(Vvar__0__A__29887)
=> ( c_24__type__29920___24t(Vvar__0__A__29887,Vvar__1__R__29888,Vvar__2___24Anonymous__29893,Vvar__1__R__29888)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29887,Vvar__2___24Anonymous__29893)
=> ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__29887,Vvar__1__R__29888,Vvar__2___24Anonymous__29893)
=> ( Vvar__2___24Anonymous__29893 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29887)
| ? [Vvar__2__a__29907] :
( t(Vvar__2__a__29907,Vvar__0__A__29887)
& ? [Vvar__3__l__29908] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29887,Vvar__3__l__29908)
& cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__29887,Vvar__1__R__29888,Vvar__3__l__29908)
& cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__29887,Vvar__1__R__29888,Vvar__2__a__29907,Vvar__3__l__29908)
& Vvar__2___24Anonymous__29893 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29887,Vvar__2__a__29907,Vvar__3__l__29908) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__29922,Vvar__1__R__29923,Vvar__2___24Anonymous__29928] :
( cType___24t(Vvar__0__A__29922)
=> ( c_24__type__29955___24t(Vvar__0__A__29922,Vvar__1__R__29923,Vvar__2___24Anonymous__29928,Vvar__1__R__29923)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29922,Vvar__2___24Anonymous__29928)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__29922,Vvar__1__R__29923,Vvar__2___24Anonymous__29928)
=> ( Vvar__2___24Anonymous__29928 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__29922)
| ? [Vvar__2__a__29942] :
( t(Vvar__2__a__29942,Vvar__0__A__29922)
& ? [Vvar__3__l__29943] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__29922,Vvar__3__l__29943)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__29922,Vvar__1__R__29923,Vvar__3__l__29943)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__29922,happ(Vvar__1__R__29923,Vvar__2__a__29942),Vvar__3__l__29943)
& Vvar__2___24Anonymous__29928 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__29922,Vvar__2__a__29942,Vvar__3__l__29943) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX22843] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX22843)
=> ? [Vvar__0___24Anonymous__22844] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__22844)
& ? [Vvar__1___24Anonymous__22845] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__22845)
& ? [Vvar__2___24Anonymous__22846] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__22846)
& ? [Vvar__3___24Anonymous__22847] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__22847)
& ? [Vvar__4___24Anonymous__22848] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__22848)
& ? [Vvar__5___24Anonymous__22849] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__22849)
& ? [Vvar__6___24Anonymous__22850] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__22850)
& ? [Vvar__7___24Anonymous__22851] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__22851)
& VX22843 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__22844,Vvar__1___24Anonymous__22845,Vvar__2___24Anonymous__22846,Vvar__3___24Anonymous__22847,Vvar__4___24Anonymous__22848,Vvar__5___24Anonymous__22849,Vvar__6___24Anonymous__22850,Vvar__7___24Anonymous__22851) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX24567] :
( cCoq_2eStrings_2eString_2estring___24t(VX24567)
=> ( VX24567 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__24568] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__24568)
& ? [Vvar__1___24Anonymous__24569] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__24569)
& VX24567 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__24568,Vvar__1___24Anonymous__24569) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993,VX13994] :
( cType___24t(Vvar__0__X__13981)
=> ( c_24__type__14054___24t(Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993,Vvar__1__lt__13982)
=> ( c_24__type__14073___24t(Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993,Vvar__2__eq__13987)
=> ( t(Vvar__3__x__13992,Vvar__0__X__13981)
=> ( t(Vvar__4__y__13993,Vvar__0__X__13981)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993,VX13994)
=> ( ( p(happ(happ(Vvar__1__lt__13982,Vvar__3__x__13992),Vvar__4__y__13993))
& VX13994 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993) )
| ( p(happ(happ(Vvar__2__eq__13987,Vvar__3__x__13992),Vvar__4__y__13993))
& VX13994 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993) )
| ( p(happ(happ(Vvar__1__lt__13982,Vvar__4__y__13993),Vvar__3__x__13992))
& VX13994 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__13981,Vvar__1__lt__13982,Vvar__2__eq__13987,Vvar__3__x__13992,Vvar__4__y__13993) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__27214,Vvar__1___24Anonymous__27215] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__27214)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__27215)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__27214,Vvar__1___24Anonymous__27215)
=> ( ? [Vvar__0__a__27217] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__27217)
& ? [Vvar__1__s__27218] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__27218)
& Vvar__1___24Anonymous__27215 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__27217,Vvar__1__s__27218)
& Vvar__0___24Anonymous__27214 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__27219] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__27219)
& ? [Vvar__1__s1__27220] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__27220)
& ? [Vvar__2__s2__27221] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__27221)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__27220,Vvar__2__s2__27221)
& Vvar__1___24Anonymous__27215 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__27219,Vvar__2__s2__27221)
& Vvar__0___24Anonymous__27214 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__27219,Vvar__1__s1__27220) ) ) )
| ? [Vvar__0__a__27223] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__27223)
& ? [Vvar__1__b__27224] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__27224)
& ? [Vvar__2__s1__27225] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__27225)
& ? [Vvar__3__s2__27226] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__27226)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__27223),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__27224))
& Vvar__1___24Anonymous__27215 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__27224,Vvar__3__s2__27226)
& Vvar__0___24Anonymous__27214 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__27223,Vvar__2__s1__27225) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX14204] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX14204)
=> ( VX14204 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX14204 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX14204 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__12360,VX12361] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12360)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__12360,VX12361)
=> ( ? [Vvar__0__n__12362] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__12362)
& Vvar__0___24Anonymous__12360 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__12362)
& VX12361 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__12362) )
| ? [Vvar__0__n__12363] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__12363)
& ? [Vvar__1___24Anonymous__12364] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__12363,Vvar__1___24Anonymous__12364)
& Vvar__0___24Anonymous__12360 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__12363)
& VX12361 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__12363,Vvar__1___24Anonymous__12364) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists',axiom,
! [Vvar__0__A__30136,Vvar__1__P__30137,Vvar__2__n__30140,Vvar__3___24Anonymous__30141] :
( cType___24t(Vvar__0__A__30136)
=> ( c_24__type__30164___24t(Vvar__0__A__30136,Vvar__1__P__30137,Vvar__2__n__30140,Vvar__3___24Anonymous__30141,Vvar__1__P__30137)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__30140)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30136,Vvar__2__n__30140,Vvar__3___24Anonymous__30141)
=> ( cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__30136,Vvar__1__P__30137,Vvar__2__n__30140,Vvar__3___24Anonymous__30141)
=> ( ? [Vvar__2__m__30147] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__30147)
& ? [Vvar__3__x__30148] :
( t(Vvar__3__x__30148,Vvar__0__A__30136)
& ? [Vvar__4__v__30149] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30136,Vvar__2__m__30147,Vvar__4__v__30149)
& p(happ(Vvar__1__P__30137,Vvar__3__x__30148))
& Vvar__3___24Anonymous__30141 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30136,Vvar__3__x__30148,Vvar__2__m__30147,Vvar__4__v__30149)
& Vvar__2__n__30140 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__30147) ) ) )
| ? [Vvar__2__m__30155] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__30155)
& ? [Vvar__3__x__30156] :
( t(Vvar__3__x__30156,Vvar__0__A__30136)
& ? [Vvar__4__v__30157] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30136,Vvar__2__m__30155,Vvar__4__v__30157)
& cCoq_2eVectors_2eVectorDef_2eExists___24a4(Vvar__0__A__30136,Vvar__1__P__30137,Vvar__2__m__30155,Vvar__4__v__30157)
& Vvar__3___24Anonymous__30141 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30136,Vvar__3__x__30156,Vvar__2__m__30155,Vvar__4__v__30157)
& Vvar__2__n__30140 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__30155) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Exists2',axiom,
! [Vvar__0__A__30232,Vvar__1__B__30233,Vvar__2__P__30234,Vvar__3__n__30239,Vvar__4___24Anonymous__30240,Vvar__5___24Anonymous__30241] :
( cType___24t(Vvar__0__A__30232)
=> ( cType___24t(Vvar__1__B__30233)
=> ( c_24__type__30286___24t(Vvar__0__A__30232,Vvar__1__B__30233,Vvar__2__P__30234,Vvar__3__n__30239,Vvar__4___24Anonymous__30240,Vvar__5___24Anonymous__30241,Vvar__2__P__30234)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__30239)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30232,Vvar__3__n__30239,Vvar__4___24Anonymous__30240)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__30233,Vvar__3__n__30239,Vvar__5___24Anonymous__30241)
=> ( cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__30232,Vvar__1__B__30233,Vvar__2__P__30234,Vvar__3__n__30239,Vvar__4___24Anonymous__30240,Vvar__5___24Anonymous__30241)
=> ( ? [Vvar__3__m__30250] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__30250)
& ? [Vvar__4__x1__30251] :
( t(Vvar__4__x1__30251,Vvar__0__A__30232)
& ? [Vvar__5__x2__30252] :
( t(Vvar__5__x2__30252,Vvar__1__B__30233)
& ? [Vvar__6__v1__30253] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30232,Vvar__3__m__30250,Vvar__6__v1__30253)
& ? [Vvar__7__v2__30254] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__30233,Vvar__3__m__30250,Vvar__7__v2__30254)
& p(happ(happ(Vvar__2__P__30234,Vvar__4__x1__30251),Vvar__5__x2__30252))
& Vvar__5___24Anonymous__30241 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__30233,Vvar__5__x2__30252,Vvar__3__m__30250,Vvar__7__v2__30254)
& Vvar__4___24Anonymous__30240 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30232,Vvar__4__x1__30251,Vvar__3__m__30250,Vvar__6__v1__30253)
& Vvar__3__n__30239 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__30250) ) ) ) ) )
| ? [Vvar__3__m__30263] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__30263)
& ? [Vvar__4__x1__30264] :
( t(Vvar__4__x1__30264,Vvar__0__A__30232)
& ? [Vvar__5__x2__30265] :
( t(Vvar__5__x2__30265,Vvar__1__B__30233)
& ? [Vvar__6__v1__30266] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30232,Vvar__3__m__30263,Vvar__6__v1__30266)
& ? [Vvar__7__v2__30267] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__30233,Vvar__3__m__30263,Vvar__7__v2__30267)
& cCoq_2eVectors_2eVectorDef_2eExists2___24a6(Vvar__0__A__30232,Vvar__1__B__30233,Vvar__2__P__30234,Vvar__3__m__30263,Vvar__6__v1__30266,Vvar__7__v2__30267)
& Vvar__5___24Anonymous__30241 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__30233,Vvar__5__x2__30265,Vvar__3__m__30263,Vvar__7__v2__30267)
& Vvar__4___24Anonymous__30240 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30232,Vvar__4__x1__30264,Vvar__3__m__30263,Vvar__6__v1__30266)
& Vvar__3__n__30239 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__30263) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
! [Vvar__0__A__30109,Vvar__1__P__30110,Vvar__2__n__30113,Vvar__3__v__30114] :
( cType___24t(Vvar__0__A__30109)
=> ( c_24__type__30134___24t(Vvar__0__A__30109,Vvar__1__P__30110,Vvar__2__n__30113,Vvar__3__v__30114,Vvar__1__P__30110)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__30113)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30109,Vvar__2__n__30113,Vvar__3__v__30114)
=> ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__30109,Vvar__1__P__30110,Vvar__2__n__30113,Vvar__3__v__30114)
=> ( ( Vvar__3__v__30114 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__30109)
& Vvar__2__n__30113 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__2__n__30124] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__30124)
& ? [Vvar__3__x__30125] :
( t(Vvar__3__x__30125,Vvar__0__A__30109)
& ? [Vvar__4__v__30126] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30109,Vvar__2__n__30124,Vvar__4__v__30126)
& p(happ(Vvar__1__P__30110,Vvar__3__x__30125))
& cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__30109,Vvar__1__P__30110,Vvar__2__n__30124,Vvar__4__v__30126)
& Vvar__3__v__30114 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30109,Vvar__3__x__30125,Vvar__2__n__30124,Vvar__4__v__30126)
& Vvar__2__n__30113 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__30124) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
! [Vvar__0__A__30181,Vvar__1__B__30182,Vvar__2__P__30183,Vvar__3__n__30188,Vvar__4___24Anonymous__30189,Vvar__5___24Anonymous__30190] :
( cType___24t(Vvar__0__A__30181)
=> ( cType___24t(Vvar__1__B__30182)
=> ( c_24__type__30230___24t(Vvar__0__A__30181,Vvar__1__B__30182,Vvar__2__P__30183,Vvar__3__n__30188,Vvar__4___24Anonymous__30189,Vvar__5___24Anonymous__30190,Vvar__2__P__30183)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__30188)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30181,Vvar__3__n__30188,Vvar__4___24Anonymous__30189)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__30182,Vvar__3__n__30188,Vvar__5___24Anonymous__30190)
=> ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__30181,Vvar__1__B__30182,Vvar__2__P__30183,Vvar__3__n__30188,Vvar__4___24Anonymous__30189,Vvar__5___24Anonymous__30190)
=> ( ( Vvar__5___24Anonymous__30190 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__30182)
& Vvar__4___24Anonymous__30189 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__30181)
& Vvar__3__n__30188 = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__3__m__30206] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__30206)
& ? [Vvar__4__x1__30207] :
( t(Vvar__4__x1__30207,Vvar__0__A__30181)
& ? [Vvar__5__x2__30208] :
( t(Vvar__5__x2__30208,Vvar__1__B__30182)
& ? [Vvar__6__v1__30209] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30181,Vvar__3__m__30206,Vvar__6__v1__30209)
& ? [Vvar__7__v2__30210] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__30182,Vvar__3__m__30206,Vvar__7__v2__30210)
& p(happ(happ(Vvar__2__P__30183,Vvar__4__x1__30207),Vvar__5__x2__30208))
& cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__30181,Vvar__1__B__30182,Vvar__2__P__30183,Vvar__3__m__30206,Vvar__6__v1__30209,Vvar__7__v2__30210)
& Vvar__5___24Anonymous__30190 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__30182,Vvar__5__x2__30208,Vvar__3__m__30206,Vvar__7__v2__30210)
& Vvar__4___24Anonymous__30189 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30181,Vvar__4__x1__30207,Vvar__3__m__30206,Vvar__6__v1__30209)
& Vvar__3__n__30188 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__30206) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.In',axiom,
! [Vvar__0__A__30166,Vvar__1__a__30167,Vvar__2__n__30168,Vvar__3___24Anonymous__30169] :
( cType___24t(Vvar__0__A__30166)
=> ( t(Vvar__1__a__30167,Vvar__0__A__30166)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__30168)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30166,Vvar__2__n__30168,Vvar__3___24Anonymous__30169)
=> ( cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__30166,Vvar__1__a__30167,Vvar__2__n__30168,Vvar__3___24Anonymous__30169)
=> ( ? [Vvar__2__m__30173] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__30173)
& ? [Vvar__3__v__30174] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30166,Vvar__2__m__30173,Vvar__3__v__30174)
& Vvar__3___24Anonymous__30169 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30166,Vvar__1__a__30167,Vvar__2__m__30173,Vvar__3__v__30174)
& Vvar__2__n__30168 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__30173) ) )
| ? [Vvar__2__m__30177] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__m__30177)
& ? [Vvar__3__x__30178] :
( t(Vvar__3__x__30178,Vvar__0__A__30166)
& ? [Vvar__4__v__30179] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30166,Vvar__2__m__30177,Vvar__4__v__30179)
& cCoq_2eVectors_2eVectorDef_2eIn___24a4(Vvar__0__A__30166,Vvar__1__a__30167,Vvar__2__m__30177,Vvar__4__v__30179)
& Vvar__3___24Anonymous__30169 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30166,Vvar__3__x__30178,Vvar__2__m__30177,Vvar__4__v__30179)
& Vvar__2__n__30168 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__m__30177) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__21551,Vvar__1___24Anonymous__21552,VX21553] :
( cType___24t(Vvar__0__A__21551)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__21552)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__21551,Vvar__1___24Anonymous__21552,VX21553)
=> ( ( Vvar__1___24Anonymous__21552 = cCoq_2eInit_2eDatatypes_2eO
& VX21553 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__21551) )
| ? [Vvar__1__h__21556] :
( t(Vvar__1__h__21556,Vvar__0__A__21551)
& ? [Vvar__2__n__21557] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__21557)
& ? [Vvar__3___24Anonymous__21558] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__21551,Vvar__2__n__21557,Vvar__3___24Anonymous__21558)
& Vvar__1___24Anonymous__21552 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__21557)
& VX21553 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__21551,Vvar__1__h__21556,Vvar__2__n__21557,Vvar__3___24Anonymous__21558) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__9541,Vvar__1__b__9542,Vvar__2__d__9543] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__9541)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__9542)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__9543)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__9541,Vvar__1__b__9542,Vvar__2__d__9543)
=> ? [Vvar__3__u__9548] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__9548)
& ? [Vvar__4__v__9549] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__9549)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__9548,Vvar__0__a__9541),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__9549,Vvar__1__b__9542)) = Vvar__2__d__9543
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__25166,Vvar__1__b__25167,VX25168] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__25166)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__25167)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__25166,Vvar__1__b__25167,VX25168)
=> ? [Vvar__2__u__25171] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__25171)
& ? [Vvar__3__v__25172] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__25172)
& ? [Vvar__4__d__25173] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__25173)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__25171,Vvar__0__a__25166),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__25172,Vvar__1__b__25167)) = Vvar__4__d__25173
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__25166,Vvar__1__b__25167,Vvar__4__d__25173)
& VX25168 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__25166,Vvar__1__b__25167,Vvar__2__u__25171,Vvar__3__v__25172,Vvar__4__d__25173) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__25138,Vvar__1__b__25139,Vvar__2__g__25140] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__25138)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__25139)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__25140)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__25138,Vvar__1__b__25139,Vvar__2__g__25140)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__25140,Vvar__0__a__25138)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__25140,Vvar__1__b__25139)
& ! [Vvar__var__var__var__var__5__x__25148__25151__25154__25157__25160] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__25148__25151__25154__25157__25160)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__25148__25151__25154__25157__25160,Vvar__0__a__25138)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__25148__25151__25154__25157__25160,Vvar__1__b__25139)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__25148__25151__25154__25157__25160,Vvar__2__g__25140) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__25191] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__25191)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__25191)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__25191))
& ! [Vvar__var__var__2__n__25196__25198__25200] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__25196__25198__25200)
=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__25196__25198__25200))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__25196__25198__25200,Vvar__0__p__25191)) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__25196__25198__25200,Vvar__0__p__25191) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__27039,Vvar__1__p__27040,VX27041] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__27039)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__27040)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__27039,Vvar__1__p__27040,VX27041)
=> ? [Vvar__2__q__27044] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__27044)
& ? [Vvar__3__r__27045] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__27045)
& Vvar__0__x__27039 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__27044,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__27040)),Vvar__3__r__27045)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__27045))
& p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__27045,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__27040)))
& VX27041 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__27039,Vvar__1__p__27040,Vvar__2__q__27044,Vvar__3__r__27045) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__10705,Vvar__1__F__10706] :
( cType___24t(Vvar__0__T__10705)
=> ( t(Vvar__1__F__10706,Vvar__0__T__10705)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__10705,Vvar__1__F__10706)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
! [Vvar__0__T__25422,Vvar__1__F__25423] :
( cType___24t(Vvar__0__T__25422)
=> ( t(Vvar__1__F__25423,Vvar__0__T__25422)
=> ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__25422,Vvar__1__F__25423)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX22908] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX22908)
=> ( VX22908 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__22909] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22909)
& ? [Vvar__1___24Anonymous__22910] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__22910)
& VX22908 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__22909,Vvar__1___24Anonymous__22910) ) )
| ? [Vvar__0___24Anonymous__22911] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__22911)
& ? [Vvar__1___24Anonymous__22912] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__22912)
& VX22908 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__22911,Vvar__1___24Anonymous__22912) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__10710,VX10711] :
( cType___24t(Vvar__0__C__10710)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,VX10711)
=> ( ? [Vvar__1___24Anonymous__10713] :
( t(Vvar__1___24Anonymous__10713,Vvar__0__C__10710)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__10710,Vvar__1___24Anonymous__10713) )
| ? [Vvar__1___24Anonymous__10715] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10715)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__10710,Vvar__1___24Anonymous__10715) )
| ? [Vvar__1___24Anonymous__10717] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__1___24Anonymous__10717)
& ? [Vvar__2___24Anonymous__10718] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__2___24Anonymous__10718)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__10710,Vvar__1___24Anonymous__10717,Vvar__2___24Anonymous__10718) ) )
| ? [Vvar__1___24Anonymous__10720] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__1___24Anonymous__10720)
& ? [Vvar__2___24Anonymous__10721] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__2___24Anonymous__10721)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__10710,Vvar__1___24Anonymous__10720,Vvar__2___24Anonymous__10721) ) )
| ? [Vvar__1___24Anonymous__10723] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__1___24Anonymous__10723)
& ? [Vvar__2___24Anonymous__10724] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__2___24Anonymous__10724)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__10710,Vvar__1___24Anonymous__10723,Vvar__2___24Anonymous__10724) ) )
| ? [Vvar__1___24Anonymous__10726] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__1___24Anonymous__10726)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__10710,Vvar__1___24Anonymous__10726) )
| ? [Vvar__1___24Anonymous__10728] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__10710,Vvar__1___24Anonymous__10728)
& ? [Vvar__2___24Anonymous__10729] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__10729)
& VX10711 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__10710,Vvar__1___24Anonymous__10728,Vvar__2___24Anonymous__10729) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__10882,VX10883] :
( cType___24t(Vvar__0__C__10882)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10882,VX10883)
=> ( ? [Vvar__1___24Anonymous__10885] :
( t(Vvar__1___24Anonymous__10885,Vvar__0__C__10882)
& VX10883 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__10882,Vvar__1___24Anonymous__10885) )
| ? [Vvar__1___24Anonymous__10887] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__10887)
& ? [Vvar__2___24Anonymous__10888] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10882,Vvar__2___24Anonymous__10888)
& VX10883 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__10882,Vvar__1___24Anonymous__10887,Vvar__2___24Anonymous__10888) ) )
| ? [Vvar__1___24Anonymous__10890] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10882,Vvar__1___24Anonymous__10890)
& ? [Vvar__2___24Anonymous__10891] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__10891)
& ? [Vvar__3___24Anonymous__10892] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__10882,Vvar__3___24Anonymous__10892)
& VX10883 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__10882,Vvar__1___24Anonymous__10890,Vvar__2___24Anonymous__10891,Vvar__3___24Anonymous__10892) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854] :
( cType___24t(Vvar__0__R__12823)
=> ( t(Vvar__1__rO__12824,Vvar__0__R__12823)
=> ( t(Vvar__2__rI__12825,Vvar__0__R__12823)
=> ( c_24__type__13255___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__3__rplus__12826)
=> ( c_24__type__13356___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__4__rtimes__12831)
=> ( c_24__type__13457___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__5__rminus__12836)
=> ( c_24__type__13547___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__6__ropp__12841)
=> ( c_24__type__13648___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__7__req__12844)
=> ( c_24__type__13749___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__8__rle__12849)
=> ( c_24__type__13850___24t(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854,Vvar__9__rlt__12854)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844,Vvar__8__rle__12849,Vvar__9__rlt__12854)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__12823,Vvar__7__req__12844)
& ! [Vvar__var__var__var__var__11__x1__12898__12904__13009__13015__13021] :
( t(Vvar__var__var__var__var__11__x1__12898__12904__13009__13015__13021,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__12__x2__12899__12905__13010__13016__13022] :
( t(Vvar__var__var__var__var__12__x2__12899__12905__13010__13016__13022,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__11__x1__12898__12904__13009__13015__13021),Vvar__var__var__var__var__12__x2__12899__12905__13010__13016__13022))
=> ! [Vvar__var__var__var__var__14__y1__12900__12906__13011__13017__13023] :
( t(Vvar__var__var__var__var__14__y1__12900__12906__13011__13017__13023,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__15__y2__12901__12907__13012__13018__13024] :
( t(Vvar__var__var__var__var__15__y2__12901__12907__13012__13018__13024,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__14__y1__12900__12906__13011__13017__13023),Vvar__var__var__var__var__15__y2__12901__12907__13012__13018__13024))
=> p(happ(happ(Vvar__7__req__12844,happ(happ(Vvar__3__rplus__12826,Vvar__var__var__var__var__11__x1__12898__12904__13009__13015__13021),Vvar__var__var__var__var__14__y1__12900__12906__13011__13017__13023)),happ(happ(Vvar__3__rplus__12826,Vvar__var__var__var__var__12__x2__12899__12905__13010__13016__13022),Vvar__var__var__var__var__15__y2__12901__12907__13012__13018__13024))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__12911__12917__13027__13033__13039] :
( t(Vvar__var__var__var__var__12__x1__12911__12917__13027__13033__13039,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__13__x2__12912__12918__13028__13034__13040] :
( t(Vvar__var__var__var__var__13__x2__12912__12918__13028__13034__13040,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__12__x1__12911__12917__13027__13033__13039),Vvar__var__var__var__var__13__x2__12912__12918__13028__13034__13040))
=> ! [Vvar__var__var__var__var__15__y1__12913__12919__13029__13035__13041] :
( t(Vvar__var__var__var__var__15__y1__12913__12919__13029__13035__13041,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__16__y2__12914__12920__13030__13036__13042] :
( t(Vvar__var__var__var__var__16__y2__12914__12920__13030__13036__13042,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__15__y1__12913__12919__13029__13035__13041),Vvar__var__var__var__var__16__y2__12914__12920__13030__13036__13042))
=> p(happ(happ(Vvar__7__req__12844,happ(happ(Vvar__4__rtimes__12831,Vvar__var__var__var__var__12__x1__12911__12917__13027__13033__13039),Vvar__var__var__var__var__15__y1__12913__12919__13029__13035__13041)),happ(happ(Vvar__4__rtimes__12831,Vvar__var__var__var__var__13__x2__12912__12918__13028__13034__13040),Vvar__var__var__var__var__16__y2__12914__12920__13030__13036__13042))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__12924__12927__13045__13048__13051] :
( t(Vvar__var__var__var__var__13__x1__12924__12927__13045__13048__13051,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__14__x2__12925__12928__13046__13049__13052] :
( t(Vvar__var__var__var__var__14__x2__12925__12928__13046__13049__13052,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__13__x1__12924__12927__13045__13048__13051),Vvar__var__var__var__var__14__x2__12925__12928__13046__13049__13052))
=> p(happ(happ(Vvar__7__req__12844,happ(Vvar__6__ropp__12841,Vvar__var__var__var__var__13__x1__12924__12927__13045__13048__13051)),happ(Vvar__6__ropp__12841,Vvar__var__var__var__var__14__x2__12925__12928__13046__13049__13052))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__12931__12937__13054__13060__13066] :
( t(Vvar__var__var__var__var__14__x1__12931__12937__13054__13060__13066,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__15__x2__12932__12938__13055__13061__13067] :
( t(Vvar__var__var__var__var__15__x2__12932__12938__13055__13061__13067,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__14__x1__12931__12937__13054__13060__13066),Vvar__var__var__var__var__15__x2__12932__12938__13055__13061__13067))
=> ! [Vvar__var__var__var__var__17__y1__12933__12939__13056__13062__13068] :
( t(Vvar__var__var__var__var__17__y1__12933__12939__13056__13062__13068,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__18__y2__12934__12940__13057__13063__13069] :
( t(Vvar__var__var__var__var__18__y2__12934__12940__13057__13063__13069,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__17__y1__12933__12939__13056__13062__13068),Vvar__var__var__var__var__18__y2__12934__12940__13057__13063__13069))
=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__var__14__x1__12931__12937__13054__13060__13066),Vvar__var__var__var__var__17__y1__12933__12939__13056__13062__13068))
<=> p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__var__15__x2__12932__12938__13055__13061__13067),Vvar__var__var__var__var__18__y2__12934__12940__13057__13063__13069)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__12944__12950__13072__13078__13084] :
( t(Vvar__var__var__var__var__15__x1__12944__12950__13072__13078__13084,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__16__x2__12945__12951__13073__13079__13085] :
( t(Vvar__var__var__var__var__16__x2__12945__12951__13073__13079__13085,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__15__x1__12944__12950__13072__13078__13084),Vvar__var__var__var__var__16__x2__12945__12951__13073__13079__13085))
=> ! [Vvar__var__var__var__var__18__y1__12946__12952__13074__13080__13086] :
( t(Vvar__var__var__var__var__18__y1__12946__12952__13074__13080__13086,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__19__y2__12947__12953__13075__13081__13087] :
( t(Vvar__var__var__var__var__19__y2__12947__12953__13075__13081__13087,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__18__y1__12946__12952__13074__13080__13086),Vvar__var__var__var__var__19__y2__12947__12953__13075__13081__13087))
=> ( p(happ(happ(Vvar__9__rlt__12854,Vvar__var__var__var__var__15__x1__12944__12950__13072__13078__13084),Vvar__var__var__var__var__18__y1__12946__12952__13074__13080__13086))
<=> p(happ(happ(Vvar__9__rlt__12854,Vvar__var__var__var__var__16__x2__12945__12951__13073__13079__13085),Vvar__var__var__var__var__19__y2__12947__12953__13075__13081__13087)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__12823,Vvar__1__rO__12824,Vvar__2__rI__12825,Vvar__3__rplus__12826,Vvar__4__rtimes__12831,Vvar__5__rminus__12836,Vvar__6__ropp__12841,Vvar__7__req__12844)
& ! [Vvar__var__var__var__17__n__12958__12959__13090__13091] :
( t(Vvar__var__var__var__17__n__12958__12959__13090__13091,Vvar__0__R__12823)
=> p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__17__n__12958__12959__13090__13091),Vvar__var__var__var__17__n__12958__12959__13090__13091)) )
& ! [Vvar__var__var__var__var__18__n__12961__12965__13092__13096__13100] :
( t(Vvar__var__var__var__var__18__n__12961__12965__13092__13096__13100,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__19__m__12962__12966__13093__13097__13101] :
( t(Vvar__var__var__var__var__19__m__12962__12966__13093__13097__13101,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__var__18__n__12961__12965__13092__13096__13100),Vvar__var__var__var__var__19__m__12962__12966__13093__13097__13101))
=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__var__19__m__12962__12966__13093__13097__13101),Vvar__var__var__var__var__18__n__12961__12965__13092__13096__13100))
=> p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__18__n__12961__12965__13092__13096__13100),Vvar__var__var__var__var__19__m__12962__12966__13093__13097__13101)) ) ) ) )
& ! [Vvar__var__var__var__19__n__12970__12975__13104__13109] :
( t(Vvar__var__var__var__19__n__12970__12975__13104__13109,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__20__m__12971__12976__13105__13110] :
( t(Vvar__var__var__var__20__m__12971__12976__13105__13110,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__21__p__12972__12977__13106__13111] :
( t(Vvar__var__var__var__21__p__12972__12977__13106__13111,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__19__n__12970__12975__13104__13109),Vvar__var__var__var__20__m__12971__12976__13105__13110))
=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__20__m__12971__12976__13105__13110),Vvar__var__var__var__21__p__12972__12977__13106__13111))
=> p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__19__n__12970__12975__13104__13109),Vvar__var__var__var__21__p__12972__12977__13106__13111)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__12981__12983__13114__13116__13118__13120] :
( t(Vvar__var__var__var__var__var__20__n__12981__12983__13114__13116__13118__13120,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__var__21__m__12982__12984__13115__13117__13119__13121] :
( t(Vvar__var__var__var__var__var__21__m__12982__12984__13115__13117__13119__13121,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__9__rlt__12854,Vvar__var__var__var__var__var__20__n__12981__12983__13114__13116__13118__13120),Vvar__var__var__var__var__var__21__m__12982__12984__13115__13117__13119__13121))
<=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__var__var__20__n__12981__12983__13114__13116__13118__13120),Vvar__var__var__var__var__var__21__m__12982__12984__13115__13117__13119__13121))
& ~ p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__var__20__n__12981__12983__13114__13116__13118__13120),Vvar__var__var__var__var__var__21__m__12982__12984__13115__13117__13119__13121)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__12986__12988__13122__13124__13126] :
( t(Vvar__var__var__var__var__21__n__12986__12988__13122__13124__13126,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__22__m__12987__12989__13123__13125__13127] :
( t(Vvar__var__var__var__var__22__m__12987__12989__13123__13125__13127,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__9__rlt__12854,Vvar__var__var__var__var__21__n__12986__12988__13122__13124__13126),Vvar__var__var__var__var__22__m__12987__12989__13123__13125__13127))
| p(happ(happ(Vvar__7__req__12844,Vvar__var__var__var__var__21__n__12986__12988__13122__13124__13126),Vvar__var__var__var__var__22__m__12987__12989__13123__13125__13127))
| p(happ(happ(Vvar__9__rlt__12854,Vvar__var__var__var__var__22__m__12987__12989__13123__13125__13127),Vvar__var__var__var__var__21__n__12986__12988__13122__13124__13126)) ) ) )
& ! [Vvar__var__var__var__var__22__n__12991__12995__13128__13132__13136] :
( t(Vvar__var__var__var__var__22__n__12991__12995__13128__13132__13136,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__23__m__12992__12996__13129__13133__13137] :
( t(Vvar__var__var__var__var__23__m__12992__12996__13129__13133__13137,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__24__p__12993__12997__13130__13134__13138] :
( t(Vvar__var__var__var__var__24__p__12993__12997__13130__13134__13138,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__8__rle__12849,Vvar__var__var__var__var__22__n__12991__12995__13128__13132__13136),Vvar__var__var__var__var__23__m__12992__12996__13129__13133__13137))
=> p(happ(happ(Vvar__8__rle__12849,happ(happ(Vvar__3__rplus__12826,Vvar__var__var__var__var__24__p__12993__12997__13130__13134__13138),Vvar__var__var__var__var__22__n__12991__12995__13128__13132__13136)),happ(happ(Vvar__3__rplus__12826,Vvar__var__var__var__var__24__p__12993__12997__13130__13134__13138),Vvar__var__var__var__var__23__m__12992__12996__13129__13133__13137))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__13000__13004__13140__13144__13148__13152] :
( t(Vvar__var__var__var__var__var__23__n__13000__13004__13140__13144__13148__13152,Vvar__0__R__12823)
=> ! [Vvar__var__var__var__var__var__24__m__13001__13005__13141__13145__13149__13153] :
( t(Vvar__var__var__var__var__var__24__m__13001__13005__13141__13145__13149__13153,Vvar__0__R__12823)
=> ( p(happ(happ(Vvar__9__rlt__12854,Vvar__1__rO__12824),Vvar__var__var__var__var__var__23__n__13000__13004__13140__13144__13148__13152))
=> ( p(happ(happ(Vvar__9__rlt__12854,Vvar__1__rO__12824),Vvar__var__var__var__var__var__24__m__13001__13005__13141__13145__13149__13153))
=> p(happ(happ(Vvar__9__rlt__12854,Vvar__1__rO__12824),happ(happ(Vvar__4__rtimes__12831,Vvar__var__var__var__var__var__23__n__13000__13004__13140__13144__13148__13152),Vvar__var__var__var__var__var__24__m__13001__13005__13141__13145__13149__13153))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__12844,Vvar__1__rO__12824),Vvar__2__rI__12825))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX14289] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX14289)
=> ( VX14289 = cCoq_2emicromega_2eRMicromega_2eC0
| VX14289 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__14290] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__14290)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__14290) )
| ? [Vvar__0__r__14291] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__14291)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__14291) )
| ? [Vvar__0__r1__14292] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14292)
& ? [Vvar__1__r2__14293] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__14293)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__14292,Vvar__1__r2__14293) ) )
| ? [Vvar__0__r1__14294] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14294)
& ? [Vvar__1__r2__14295] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__14295)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__14294,Vvar__1__r2__14295) ) )
| ? [Vvar__0__r1__14296] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14296)
& ? [Vvar__1__r2__14297] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__14297)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__14296,Vvar__1__r2__14297) ) )
| ? [Vvar__0__r1__14298] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__14298)
& ? [Vvar__1__z__14299] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__14299)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__14298,Vvar__1__z__14299) ) )
| ? [Vvar__0__r__14300] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__14300)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__14300) )
| ? [Vvar__0__r__14301] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__14301)
& VX14289 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__14301) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__20551,VX20552] :
( cType___24t(Vvar__0__T__20551)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__20551,VX20552)
=> ? [Vvar__1__Flhs__20554] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__20551,Vvar__1__Flhs__20554)
& ? [Vvar__2__Fop__20555] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__20555)
& ? [Vvar__3__Frhs__20556] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__20551,Vvar__3__Frhs__20556)
& VX20552 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__20551,Vvar__1__Flhs__20554,Vvar__2__Fop__20555,Vvar__3__Frhs__20556) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX23703] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX23703)
=> ( VX23703 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX23703 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX23703 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX23703 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX20550] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX20550)
=> ( VX20550 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX20550 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX20550 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX20550 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX20550 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX20550 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__20324,VX20325] :
( cType___24t(Vvar__0__C__20324)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20324,VX20325)
=> ( ? [Vvar__1___24Anonymous__20327] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__20327)
& VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__20324,Vvar__1___24Anonymous__20327) )
| ? [Vvar__1___24Anonymous__20329] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__20324,Vvar__1___24Anonymous__20329)
& VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__20324,Vvar__1___24Anonymous__20329) )
| ? [Vvar__1___24Anonymous__20331] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__20324,Vvar__1___24Anonymous__20331)
& ? [Vvar__2___24Anonymous__20332] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20324,Vvar__2___24Anonymous__20332)
& VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__20324,Vvar__1___24Anonymous__20331,Vvar__2___24Anonymous__20332) ) )
| ? [Vvar__1___24Anonymous__20334] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20324,Vvar__1___24Anonymous__20334)
& ? [Vvar__2___24Anonymous__20335] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20324,Vvar__2___24Anonymous__20335)
& VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__20324,Vvar__1___24Anonymous__20334,Vvar__2___24Anonymous__20335) ) )
| ? [Vvar__1___24Anonymous__20337] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20324,Vvar__1___24Anonymous__20337)
& ? [Vvar__2___24Anonymous__20338] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__20324,Vvar__2___24Anonymous__20338)
& VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__20324,Vvar__1___24Anonymous__20337,Vvar__2___24Anonymous__20338) ) )
| ? [Vvar__1___24Anonymous__20340] :
( t(Vvar__1___24Anonymous__20340,Vvar__0__C__20324)
& VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__20324,Vvar__1___24Anonymous__20340) )
| VX20325 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__20324) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963] :
( cType___24t(Vvar__0__R__14894)
=> ( t(Vvar__1__rO__14895,Vvar__0__R__14894)
=> ( t(Vvar__2__rI__14896,Vvar__0__R__14894)
=> ( c_24__type__15427___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__3__rplus__14897)
=> ( c_24__type__15773___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__4__rtimes__14902)
=> ( c_24__type__16119___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__5__rminus__14907)
=> ( c_24__type__16442___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__6__ropp__14912)
=> ( c_24__type__16788___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__7__req__14915)
=> ( c_24__type__17134___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__8__rle__14920)
=> ( cType___24t(Vvar__9__C__14925)
=> ( t(Vvar__10__cO__14926,Vvar__9__C__14925)
=> ( t(Vvar__11__cI__14927,Vvar__9__C__14925)
=> ( c_24__type__17480___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__12__cplus__14928)
=> ( c_24__type__17826___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__13__ctimes__14933)
=> ( c_24__type__18172___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__14__cminus__14938)
=> ( c_24__type__18495___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__15__copp__14943)
=> ( c_24__type__18841___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__16__ceqb__14946)
=> ( c_24__type__19187___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__17__cleb__14951)
=> ( c_24__type__19510___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__18__phi__14956)
=> ( cType___24t(Vvar__19__E__14959)
=> ( c_24__type__19833___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__20__pow__phi__14960)
=> ( c_24__type__20179___24t(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963,Vvar__21__rpow__14963)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__8__rle__14920,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__17__cleb__14951,Vvar__18__phi__14956,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__14894,Vvar__1__rO__14895,Vvar__2__rI__14896,Vvar__3__rplus__14897,Vvar__4__rtimes__14902,Vvar__5__rminus__14907,Vvar__6__ropp__14912,Vvar__7__req__14915,Vvar__9__C__14925,Vvar__10__cO__14926,Vvar__11__cI__14927,Vvar__12__cplus__14928,Vvar__13__ctimes__14933,Vvar__14__cminus__14938,Vvar__15__copp__14943,Vvar__16__ceqb__14946,Vvar__18__phi__14956)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__14894,Vvar__2__rI__14896,Vvar__4__rtimes__14902,Vvar__7__req__14915,Vvar__19__E__14959,Vvar__20__pow__phi__14960,Vvar__21__rpow__14963)
& ! [Vvar__var__var__var__var__var__24__x__15046__15049__15059__15062__15065__15068] :
( t(Vvar__var__var__var__var__var__24__x__15046__15049__15059__15062__15065__15068,Vvar__9__C__14925)
=> ! [Vvar__var__var__var__var__var__25__y__15047__15050__15060__15063__15066__15069] :
( t(Vvar__var__var__var__var__var__25__y__15047__15050__15060__15063__15066__15069,Vvar__9__C__14925)
=> ( happ(happ(Vvar__16__ceqb__14946,Vvar__var__var__var__var__var__24__x__15046__15049__15059__15062__15065__15068),Vvar__var__var__var__var__var__25__y__15047__15050__15060__15063__15066__15069) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__14915,happ(Vvar__18__phi__14956,Vvar__var__var__var__var__var__24__x__15046__15049__15059__15062__15065__15068)),happ(Vvar__18__phi__14956,Vvar__var__var__var__var__var__25__y__15047__15050__15060__15063__15066__15069))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__15053__15056__15071__15074__15077__15080] :
( t(Vvar__var__var__var__var__var__25__x__15053__15056__15071__15074__15077__15080,Vvar__9__C__14925)
=> ! [Vvar__var__var__var__var__var__26__y__15054__15057__15072__15075__15078__15081] :
( t(Vvar__var__var__var__var__var__26__y__15054__15057__15072__15075__15078__15081,Vvar__9__C__14925)
=> ( happ(happ(Vvar__17__cleb__14951,Vvar__var__var__var__var__var__25__x__15053__15056__15071__15074__15077__15080),Vvar__var__var__var__var__var__26__y__15054__15057__15072__15075__15078__15081) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__14920,happ(Vvar__18__phi__14956,Vvar__var__var__var__var__var__25__x__15053__15056__15071__15074__15077__15080)),happ(Vvar__18__phi__14956,Vvar__var__var__var__var__var__26__y__15054__15057__15072__15075__15078__15081))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,VX24580] :
( cType___24t(Vvar__0__TA__24576)
=> ( cType___24t(Vvar__1__TX__24577)
=> ( cType___24t(Vvar__2__AA__24578)
=> ( cType___24t(Vvar__3__AF__24579)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,VX24580)
=> ( VX24580 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579)
| VX24580 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579)
| ? [Vvar__4___24Anonymous__24593] :
( t(Vvar__4___24Anonymous__24593,Vvar__1__TX__24577)
& VX24580 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24593) )
| ? [Vvar__4___24Anonymous__24598] :
( t(Vvar__4___24Anonymous__24598,Vvar__0__TA__24576)
& ? [Vvar__5___24Anonymous__24599] :
( t(Vvar__5___24Anonymous__24599,Vvar__2__AA__24578)
& VX24580 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24598,Vvar__5___24Anonymous__24599) ) )
| ? [Vvar__4___24Anonymous__24604] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24604)
& ? [Vvar__5___24Anonymous__24605] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__5___24Anonymous__24605)
& VX24580 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24604,Vvar__5___24Anonymous__24605) ) )
| ? [Vvar__4___24Anonymous__24610] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24610)
& ? [Vvar__5___24Anonymous__24611] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__5___24Anonymous__24611)
& VX24580 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24610,Vvar__5___24Anonymous__24611) ) )
| ? [Vvar__4___24Anonymous__24616] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24616)
& VX24580 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24616) )
| ? [Vvar__4___24Anonymous__24621] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24621)
& ? [Vvar__5___24Anonymous__24622] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__24579,Vvar__5___24Anonymous__24622)
& ? [Vvar__6___24Anonymous__24623] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__6___24Anonymous__24623)
& VX24580 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__24576,Vvar__1__TX__24577,Vvar__2__AA__24578,Vvar__3__AF__24579,Vvar__4___24Anonymous__24621,Vvar__5___24Anonymous__24622,Vvar__6___24Anonymous__24623) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__25019,VX25020] :
( cType___24t(Vvar__0__A__25019)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__25019,VX25020)
=> ( VX25020 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__25019)
| ? [Vvar__1___24Anonymous__25023] :
( t(Vvar__1___24Anonymous__25023,Vvar__0__A__25019)
& VX25020 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__25019,Vvar__1___24Anonymous__25023) )
| ? [Vvar__1___24Anonymous__25025] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__25019,Vvar__1___24Anonymous__25025)
& ? [Vvar__2___24Anonymous__25026] :
( t(Vvar__2___24Anonymous__25026,Vvar__0__A__25019)
& ? [Vvar__3___24Anonymous__25027] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__25019,Vvar__3___24Anonymous__25027)
& VX25020 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__25019,Vvar__1___24Anonymous__25025,Vvar__2___24Anonymous__25026,Vvar__3___24Anonymous__25027) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
! [Vvar__0___24Anonymous__27094] :
( cProp___24t(Vvar__0___24Anonymous__27094)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__27094)
=> ( ? [Vvar__0__P__27096] :
( cProp___24t(Vvar__0__P__27096)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__27096)
& Vvar__0___24Anonymous__27094 = Vvar__0__P__27096 )
| ? [Vvar__0__s__27098] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__27098)
& Vvar__0___24Anonymous__27094 = c_24__prop__27107___24a2(Vvar__0___24Anonymous__27094,Vvar__0__s__27098) )
| ? [Vvar__0__s1__27100] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__27100)
& ? [Vvar__1__s2__27101] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__27101)
& Vvar__0___24Anonymous__27094 = c_24__prop__27108___24a3(Vvar__0___24Anonymous__27094,Vvar__0__s1__27100,Vvar__1__s2__27101) ) )
| ? [Vvar__0__s1__27104] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__27104)
& ? [Vvar__1__s2__27105] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__27105)
& Vvar__0___24Anonymous__27094 = c_24__prop__27109___24a3(Vvar__0___24Anonymous__27094,Vvar__0__s1__27104,Vvar__1__s2__27105) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__25205] :
( cProp___24t(Vvar__0___24Anonymous__25205)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__25205)
=> ( ? [Vvar__0__S__25207] :
( cType___24t(Vvar__0__S__25207)
& ? [Vvar__1__x__25208] :
( t(Vvar__1__x__25208,Vvar__0__S__25207)
& ? [Vvar__2__y__25209] :
( t(Vvar__2__y__25209,Vvar__0__S__25207)
& Vvar__0___24Anonymous__25205 = c_24__prop__25229___24a4(Vvar__0___24Anonymous__25205,Vvar__0__S__25207,Vvar__1__x__25208,Vvar__2__y__25209) ) ) )
| ? [Vvar__0__x__25210] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__25210)
& ? [Vvar__1__y__25211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__25211)
& Vvar__0___24Anonymous__25205 = c_24__prop__25230___24a3(Vvar__0___24Anonymous__25205,Vvar__0__x__25210,Vvar__1__y__25211) ) )
| ? [Vvar__0__x__25212] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__25212)
& ? [Vvar__1__s__25213] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__25213)
& Vvar__0___24Anonymous__25205 = c_24__prop__25231___24a3(Vvar__0___24Anonymous__25205,Vvar__0__x__25212,Vvar__1__s__25213) ) )
| Vvar__0___24Anonymous__25205 = c_24True
| Vvar__0___24Anonymous__25205 = c_24False
| ? [Vvar__0__P__25214] :
( cProp___24t(Vvar__0__P__25214)
& ? [Vvar__1__Q__25215] :
( cProp___24t(Vvar__1__Q__25215)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__25214)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__25215)
& Vvar__0___24Anonymous__25205 = c_24__prop__25232___24a3(Vvar__0___24Anonymous__25205,Vvar__0__P__25214,Vvar__1__Q__25215) ) )
| ? [Vvar__0__P__25218] :
( cProp___24t(Vvar__0__P__25218)
& ? [Vvar__1__Q__25219] :
( cProp___24t(Vvar__1__Q__25219)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__25218)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__25219)
& Vvar__0___24Anonymous__25205 = c_24__prop__25233___24a3(Vvar__0___24Anonymous__25205,Vvar__0__P__25218,Vvar__1__Q__25219) ) )
| ? [Vvar__0__P__25222] :
( cProp___24t(Vvar__0__P__25222)
& ? [Vvar__1__Q__25223] :
( cProp___24t(Vvar__1__Q__25223)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__25222)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__25223)
& Vvar__0___24Anonymous__25205 = c_24__prop__25234___24a3(Vvar__0___24Anonymous__25205,Vvar__0__P__25222,Vvar__1__Q__25223) ) )
| ? [Vvar__0__P__25227] :
( cProp___24t(Vvar__0__P__25227)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__25227)
& Vvar__0___24Anonymous__25205 = c_24__prop__25235___24a2(Vvar__0___24Anonymous__25205,Vvar__0__P__25227) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX25095] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX25095)
=> ( VX25095 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__25096] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__25096)
& ? [Vvar__1___24Anonymous__25097] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__25097)
& VX25095 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__25096,Vvar__1___24Anonymous__25097) ) )
| ? [Vvar__0___24Anonymous__25098] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__25098)
& ? [Vvar__1___24Anonymous__25099] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__25099)
& VX25095 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__25098,Vvar__1___24Anonymous__25099) ) )
| ? [Vvar__0___24Anonymous__25100] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__25100)
& ? [Vvar__1___24Anonymous__25101] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__25101)
& ? [Vvar__2___24Anonymous__25102] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__25102)
& VX25095 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__25100,Vvar__1___24Anonymous__25101,Vvar__2___24Anonymous__25102) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
! [Vvar__0__x__30438,Vvar__1___24Anonymous__30439] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__30438)
=> ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__30439)
=> ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__30438,Vvar__1___24Anonymous__30439)
=> ( ? [Vvar__1__c__30442] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__30442)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__30438,Vvar__1__c__30442)
& Vvar__1___24Anonymous__30439 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__30442) )
| ? [Vvar__1__p__30445] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__30445)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__30438,Vvar__1__p__30445)
& ? [Vvar__3__j__30447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__30447)
& Vvar__1___24Anonymous__30439 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__30447,Vvar__1__p__30445) ) )
| ? [Vvar__1__p__30449] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__30449)
& ? [Vvar__2__q__30450] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__30450)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__30438,Vvar__1__p__30449)
& cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__30438,Vvar__2__q__30450)
& ? [Vvar__5__j__30453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__30453)
& Vvar__1___24Anonymous__30439 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__30449,Vvar__5__j__30453,Vvar__2__q__30450) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__26985,Vvar__1__env__26986,Vvar__2__env_27__26989,Vvar__3__x__26992] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__26985)
=> ( c_24__type__27013___24t(Vvar__0__fr__26985,Vvar__1__env__26986,Vvar__2__env_27__26989,Vvar__3__x__26992,Vvar__1__env__26986)
=> ( c_24__type__27022___24t(Vvar__0__fr__26985,Vvar__1__env__26986,Vvar__2__env_27__26989,Vvar__3__x__26992,Vvar__2__env_27__26989)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__26992)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__26985,Vvar__1__env__26986,Vvar__2__env_27__26989,Vvar__3__x__26992)
=> ( happ(Vvar__1__env__26986,Vvar__3__x__26992) = happ(Vvar__2__env_27__26989,Vvar__3__x__26992)
& happ(Vvar__1__env__26986,Vvar__3__x__26992) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__26989,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__26985,Vvar__3__x__26992))),happ(Vvar__2__env_27__26989,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__26985,Vvar__3__x__26992))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__26989,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__26985,Vvar__3__x__26992))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__26989,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__26985,Vvar__3__x__26992))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__1992,VX1993] :
( cType___24t(Vvar__0__C__1992)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,VX1993)
=> ( VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__1992)
| VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__1992)
| ? [Vvar__1___24Anonymous__1997] :
( t(Vvar__1___24Anonymous__1997,Vvar__0__C__1992)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__1992,Vvar__1___24Anonymous__1997) )
| ? [Vvar__1___24Anonymous__1999] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1999)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__1992,Vvar__1___24Anonymous__1999) )
| ? [Vvar__1___24Anonymous__2001] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2001)
& ? [Vvar__2___24Anonymous__2002] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__2___24Anonymous__2002)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__1992,Vvar__1___24Anonymous__2001,Vvar__2___24Anonymous__2002) ) )
| ? [Vvar__1___24Anonymous__2004] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2004)
& ? [Vvar__2___24Anonymous__2005] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__2___24Anonymous__2005)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__1992,Vvar__1___24Anonymous__2004,Vvar__2___24Anonymous__2005) ) )
| ? [Vvar__1___24Anonymous__2007] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2007)
& ? [Vvar__2___24Anonymous__2008] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__2___24Anonymous__2008)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__1992,Vvar__1___24Anonymous__2007,Vvar__2___24Anonymous__2008) ) )
| ? [Vvar__1___24Anonymous__2010] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2010)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__1992,Vvar__1___24Anonymous__2010) )
| ? [Vvar__1___24Anonymous__2012] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2012)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__1992,Vvar__1___24Anonymous__2012) )
| ? [Vvar__1___24Anonymous__2014] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2014)
& ? [Vvar__2___24Anonymous__2015] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__2___24Anonymous__2015)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__1992,Vvar__1___24Anonymous__2014,Vvar__2___24Anonymous__2015) ) )
| ? [Vvar__1___24Anonymous__2017] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__1992,Vvar__1___24Anonymous__2017)
& ? [Vvar__2___24Anonymous__2018] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2018)
& VX1993 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__1992,Vvar__1___24Anonymous__2017,Vvar__2___24Anonymous__2018) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187] :
( cType___24t(Vvar__0__R__1158)
=> ( t(Vvar__1__rO__1159,Vvar__0__R__1158)
=> ( t(Vvar__2__rI__1160,Vvar__0__R__1158)
=> ( c_24__type__1352___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__3__radd__1161)
=> ( c_24__type__1445___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__4__rmul__1166)
=> ( c_24__type__1538___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__5__rsub__1171)
=> ( c_24__type__1620___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__6__ropp__1176)
=> ( c_24__type__1713___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__7__rdiv__1179)
=> ( c_24__type__1795___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__8__rinv__1184)
=> ( c_24__type__1888___24t(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187,Vvar__9__req__1187)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__7__rdiv__1179,Vvar__8__rinv__1184,Vvar__9__req__1187)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__1158,Vvar__1__rO__1159,Vvar__2__rI__1160,Vvar__3__radd__1161,Vvar__4__rmul__1166,Vvar__5__rsub__1171,Vvar__6__ropp__1176,Vvar__9__req__1187)
& ~ p(happ(happ(Vvar__9__req__1187,Vvar__2__rI__1160),Vvar__1__rO__1159))
& ! [Vvar__var__var__var__var__var__var__12__p__1230__1232__1239__1241__1243__1245__1247] :
( t(Vvar__var__var__var__var__var__var__12__p__1230__1232__1239__1241__1243__1245__1247,Vvar__0__R__1158)
=> ! [Vvar__var__var__var__var__var__var__13__q__1231__1233__1240__1242__1244__1246__1248] :
( t(Vvar__var__var__var__var__var__var__13__q__1231__1233__1240__1242__1244__1246__1248,Vvar__0__R__1158)
=> p(happ(happ(Vvar__9__req__1187,happ(happ(Vvar__7__rdiv__1179,Vvar__var__var__var__var__var__var__12__p__1230__1232__1239__1241__1243__1245__1247),Vvar__var__var__var__var__var__var__13__q__1231__1233__1240__1242__1244__1246__1248)),happ(happ(Vvar__4__rmul__1166,Vvar__var__var__var__var__var__var__12__p__1230__1232__1239__1241__1243__1245__1247),happ(Vvar__8__rinv__1184,Vvar__var__var__var__var__var__var__13__q__1231__1233__1240__1242__1244__1246__1248)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__1235__1237__1249__1251__1253__1255__1257__1259] :
( t(Vvar__var__var__var__var__var__var__var__13__p__1235__1237__1249__1251__1253__1255__1257__1259,Vvar__0__R__1158)
=> ( ~ p(happ(happ(Vvar__9__req__1187,Vvar__var__var__var__var__var__var__var__13__p__1235__1237__1249__1251__1253__1255__1257__1259),Vvar__1__rO__1159))
=> p(happ(happ(Vvar__9__req__1187,happ(happ(Vvar__4__rmul__1166,happ(Vvar__8__rinv__1184,Vvar__var__var__var__var__var__var__var__13__p__1235__1237__1249__1251__1253__1255__1257__1259)),Vvar__var__var__var__var__var__var__var__13__p__1235__1237__1249__1251__1253__1255__1257__1259)),Vvar__2__rI__1160)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990] :
( cType___24t(Vvar__0__R__22961)
=> ( t(Vvar__1__rO__22962,Vvar__0__R__22961)
=> ( t(Vvar__2__rI__22963,Vvar__0__R__22961)
=> ( c_24__type__23155___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__3__radd__22964)
=> ( c_24__type__23248___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__4__rmul__22969)
=> ( c_24__type__23341___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__5__rsub__22974)
=> ( c_24__type__23423___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__6__ropp__22979)
=> ( c_24__type__23516___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__7__rdiv__22982)
=> ( c_24__type__23598___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__8__rinv__22987)
=> ( c_24__type__23691___24t(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990,Vvar__9__req__22990)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__7__rdiv__22982,Vvar__8__rinv__22987,Vvar__9__req__22990)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__22961,Vvar__1__rO__22962,Vvar__2__rI__22963,Vvar__3__radd__22964,Vvar__4__rmul__22969,Vvar__5__rsub__22974,Vvar__6__ropp__22979,Vvar__9__req__22990)
& ~ p(happ(happ(Vvar__9__req__22990,Vvar__2__rI__22963),Vvar__1__rO__22962))
& ! [Vvar__var__var__var__var__var__var__12__p__23033__23035__23042__23044__23046__23048__23050] :
( t(Vvar__var__var__var__var__var__var__12__p__23033__23035__23042__23044__23046__23048__23050,Vvar__0__R__22961)
=> ! [Vvar__var__var__var__var__var__var__13__q__23034__23036__23043__23045__23047__23049__23051] :
( t(Vvar__var__var__var__var__var__var__13__q__23034__23036__23043__23045__23047__23049__23051,Vvar__0__R__22961)
=> p(happ(happ(Vvar__9__req__22990,happ(happ(Vvar__7__rdiv__22982,Vvar__var__var__var__var__var__var__12__p__23033__23035__23042__23044__23046__23048__23050),Vvar__var__var__var__var__var__var__13__q__23034__23036__23043__23045__23047__23049__23051)),happ(happ(Vvar__4__rmul__22969,Vvar__var__var__var__var__var__var__12__p__23033__23035__23042__23044__23046__23048__23050),happ(Vvar__8__rinv__22987,Vvar__var__var__var__var__var__var__13__q__23034__23036__23043__23045__23047__23049__23051)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__23038__23040__23052__23054__23056__23058__23060__23062] :
( t(Vvar__var__var__var__var__var__var__var__13__p__23038__23040__23052__23054__23056__23058__23060__23062,Vvar__0__R__22961)
=> ( ~ p(happ(happ(Vvar__9__req__22990,Vvar__var__var__var__var__var__var__var__13__p__23038__23040__23052__23054__23056__23058__23060__23062),Vvar__1__rO__22962))
=> p(happ(happ(Vvar__9__req__22990,happ(happ(Vvar__4__rmul__22969,happ(Vvar__8__rinv__22987,Vvar__var__var__var__var__var__var__var__13__p__23038__23040__23052__23054__23056__23058__23060__23062)),Vvar__var__var__var__var__var__var__var__13__p__23038__23040__23052__23054__23056__23058__23060__23062)),Vvar__2__rI__22963)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__2610,VX2611] :
( cType___24t(Vvar__0__C__2610)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__2610,VX2611)
=> ? [Vvar__1__num__2613] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2610,Vvar__1__num__2613)
& ? [Vvar__2__denum__2614] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2610,Vvar__2__denum__2614)
& ? [Vvar__3__condition__2615] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__2610),Vvar__3__condition__2615)
& VX2611 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__2610,Vvar__1__num__2613,Vvar__2__denum__2614,Vvar__3__condition__2615) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__2899,VX2900] :
( cType___24t(Vvar__0__C__2899)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__2899,VX2900)
=> ? [Vvar__1__rsplit__left__2902] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2899,Vvar__1__rsplit__left__2902)
& ? [Vvar__2__rsplit__common__2903] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2899,Vvar__2__rsplit__common__2903)
& ? [Vvar__3__rsplit__right__2904] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__2899,Vvar__3__rsplit__right__2904)
& VX2900 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__2899,Vvar__1__rsplit__left__2902,Vvar__2__rsplit__common__2903,Vvar__3__rsplit__right__2904) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919] :
( cType___24t(Vvar__0__R__11898)
=> ( t(Vvar__1__rO__11899,Vvar__0__R__11898)
=> ( t(Vvar__2__rI__11900,Vvar__0__R__11898)
=> ( c_24__type__12046___24t(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919,Vvar__3__radd__11901)
=> ( c_24__type__12109___24t(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919,Vvar__4__rmul__11906)
=> ( c_24__type__12172___24t(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919,Vvar__5__rdiv__11911)
=> ( c_24__type__12226___24t(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919,Vvar__6__rinv__11916)
=> ( c_24__type__12289___24t(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919,Vvar__7__req__11919)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__5__rdiv__11911,Vvar__6__rinv__11916,Vvar__7__req__11919)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__11898,Vvar__1__rO__11899,Vvar__2__rI__11900,Vvar__3__radd__11901,Vvar__4__rmul__11906,Vvar__7__req__11919)
& ~ p(happ(happ(Vvar__7__req__11919,Vvar__2__rI__11900),Vvar__1__rO__11899))
& ! [Vvar__var__var__var__var__var__var__10__p__11954__11956__11963__11965__11967__11969__11971] :
( t(Vvar__var__var__var__var__var__var__10__p__11954__11956__11963__11965__11967__11969__11971,Vvar__0__R__11898)
=> ! [Vvar__var__var__var__var__var__var__11__q__11955__11957__11964__11966__11968__11970__11972] :
( t(Vvar__var__var__var__var__var__var__11__q__11955__11957__11964__11966__11968__11970__11972,Vvar__0__R__11898)
=> p(happ(happ(Vvar__7__req__11919,happ(happ(Vvar__5__rdiv__11911,Vvar__var__var__var__var__var__var__10__p__11954__11956__11963__11965__11967__11969__11971),Vvar__var__var__var__var__var__var__11__q__11955__11957__11964__11966__11968__11970__11972)),happ(happ(Vvar__4__rmul__11906,Vvar__var__var__var__var__var__var__10__p__11954__11956__11963__11965__11967__11969__11971),happ(Vvar__6__rinv__11916,Vvar__var__var__var__var__var__var__11__q__11955__11957__11964__11966__11968__11970__11972)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__11959__11961__11973__11975__11977__11979__11981__11983] :
( t(Vvar__var__var__var__var__var__var__var__11__p__11959__11961__11973__11975__11977__11979__11981__11983,Vvar__0__R__11898)
=> ( ~ p(happ(happ(Vvar__7__req__11919,Vvar__var__var__var__var__var__var__var__11__p__11959__11961__11973__11975__11977__11979__11981__11983),Vvar__1__rO__11899))
=> p(happ(happ(Vvar__7__req__11919,happ(happ(Vvar__4__rmul__11906,happ(Vvar__6__rinv__11916,Vvar__var__var__var__var__var__var__var__11__p__11959__11961__11973__11975__11977__11979__11981__11983)),Vvar__var__var__var__var__var__var__var__11__p__11959__11961__11973__11975__11977__11979__11981__11983)),Vvar__2__rI__11900)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
! [VX25530] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX25530)
=> ? [Vvar__0__hypo__type__25531] :
( cType___24t(Vvar__0__hypo__type__25531)
& ? [Vvar__1__hypo__proof__25532] :
( t(Vvar__1__hypo__proof__25532,Vvar__0__hypo__type__25531)
& VX25530 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__25531,Vvar__1__hypo__proof__25532) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX3620] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX3620)
=> ( VX3620 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__3621] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3621)
& ? [Vvar__1___24Anonymous__3622] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__3622)
& VX3620 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__3621,Vvar__1___24Anonymous__3622) ) )
| ? [Vvar__0___24Anonymous__3623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3623)
& ? [Vvar__1___24Anonymous__3624] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__3624)
& VX3620 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__3623,Vvar__1___24Anonymous__3624) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__3641,VX3642] :
( cType___24t(Vvar__0__C__3641)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,VX3642)
=> ( VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__3641)
| VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__3641)
| ? [Vvar__1___24Anonymous__3646] :
( t(Vvar__1___24Anonymous__3646,Vvar__0__C__3641)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__3641,Vvar__1___24Anonymous__3646) )
| ? [Vvar__1___24Anonymous__3648] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3648)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__3641,Vvar__1___24Anonymous__3648) )
| ? [Vvar__1___24Anonymous__3650] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__1___24Anonymous__3650)
& ? [Vvar__2___24Anonymous__3651] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__2___24Anonymous__3651)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__3641,Vvar__1___24Anonymous__3650,Vvar__2___24Anonymous__3651) ) )
| ? [Vvar__1___24Anonymous__3653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__1___24Anonymous__3653)
& ? [Vvar__2___24Anonymous__3654] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__2___24Anonymous__3654)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__3641,Vvar__1___24Anonymous__3653,Vvar__2___24Anonymous__3654) ) )
| ? [Vvar__1___24Anonymous__3656] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__1___24Anonymous__3656)
& ? [Vvar__2___24Anonymous__3657] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__2___24Anonymous__3657)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__3641,Vvar__1___24Anonymous__3656,Vvar__2___24Anonymous__3657) ) )
| ? [Vvar__1___24Anonymous__3659] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__1___24Anonymous__3659)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__3641,Vvar__1___24Anonymous__3659) )
| ? [Vvar__1___24Anonymous__3661] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__3641,Vvar__1___24Anonymous__3661)
& ? [Vvar__2___24Anonymous__3662] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3662)
& VX3642 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__3641,Vvar__1___24Anonymous__3661,Vvar__2___24Anonymous__3662) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__3441,VX3442] :
( cType___24t(Vvar__0__C__3441)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__3441,VX3442)
=> ( ? [Vvar__1___24Anonymous__3444] :
( t(Vvar__1___24Anonymous__3444,Vvar__0__C__3441)
& VX3442 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__3441,Vvar__1___24Anonymous__3444) )
| ? [Vvar__1___24Anonymous__3446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3446)
& ? [Vvar__2___24Anonymous__3447] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__3441,Vvar__2___24Anonymous__3447)
& VX3442 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__3441,Vvar__1___24Anonymous__3446,Vvar__2___24Anonymous__3447) ) )
| ? [Vvar__1___24Anonymous__3449] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__3441,Vvar__1___24Anonymous__3449)
& ? [Vvar__2___24Anonymous__3450] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3450)
& ? [Vvar__3___24Anonymous__3451] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__3441,Vvar__3___24Anonymous__3451)
& VX3442 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__3441,Vvar__1___24Anonymous__3449,Vvar__2___24Anonymous__3450,Vvar__3___24Anonymous__3451) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267] :
( cType___24t(Vvar__0__R__5246)
=> ( t(Vvar__1__rO__5247,Vvar__0__R__5246)
=> ( t(Vvar__2__rI__5248,Vvar__0__R__5246)
=> ( c_24__type__5495___24t(Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267,Vvar__3__radd__5249)
=> ( c_24__type__5558___24t(Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267,Vvar__4__rmul__5254)
=> ( c_24__type__5621___24t(Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267,Vvar__5__rsub__5259)
=> ( c_24__type__5675___24t(Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267,Vvar__6__ropp__5264)
=> ( c_24__type__5738___24t(Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267,Vvar__7__req__5267)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__5246,Vvar__1__rO__5247,Vvar__2__rI__5248,Vvar__3__radd__5249,Vvar__4__rmul__5254,Vvar__5__rsub__5259,Vvar__6__ropp__5264,Vvar__7__req__5267)
=> ( ! [Vvar__var__var__var__var__var__8__x__5300__5301__5354__5355__5356__5357] :
( t(Vvar__var__var__var__var__var__8__x__5300__5301__5354__5355__5356__5357,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__3__radd__5249,Vvar__1__rO__5247),Vvar__var__var__var__var__var__8__x__5300__5301__5354__5355__5356__5357)),Vvar__var__var__var__var__var__8__x__5300__5301__5354__5355__5356__5357)) )
& ! [Vvar__var__var__var__var__9__x__5303__5305__5358__5360__5362] :
( t(Vvar__var__var__var__var__9__x__5303__5305__5358__5360__5362,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__10__y__5304__5306__5359__5361__5363] :
( t(Vvar__var__var__var__var__10__y__5304__5306__5359__5361__5363,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__9__x__5303__5305__5358__5360__5362),Vvar__var__var__var__var__10__y__5304__5306__5359__5361__5363)),happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__10__y__5304__5306__5359__5361__5363),Vvar__var__var__var__var__9__x__5303__5305__5358__5360__5362))) ) )
& ! [Vvar__var__var__var__var__10__x__5308__5311__5364__5367__5370] :
( t(Vvar__var__var__var__var__10__x__5308__5311__5364__5367__5370,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__11__y__5309__5312__5365__5368__5371] :
( t(Vvar__var__var__var__var__11__y__5309__5312__5365__5368__5371,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__12__z__5310__5313__5366__5369__5372] :
( t(Vvar__var__var__var__var__12__z__5310__5313__5366__5369__5372,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__10__x__5308__5311__5364__5367__5370),happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__11__y__5309__5312__5365__5368__5371),Vvar__var__var__var__var__12__z__5310__5313__5366__5369__5372))),happ(happ(Vvar__3__radd__5249,happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__10__x__5308__5311__5364__5367__5370),Vvar__var__var__var__var__11__y__5309__5312__5365__5368__5371)),Vvar__var__var__var__var__12__z__5310__5313__5366__5369__5372))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__5315__5316__5373__5374__5375__5376] :
( t(Vvar__var__var__var__var__var__11__x__5315__5316__5373__5374__5375__5376,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__4__rmul__5254,Vvar__2__rI__5248),Vvar__var__var__var__var__var__11__x__5315__5316__5373__5374__5375__5376)),Vvar__var__var__var__var__var__11__x__5315__5316__5373__5374__5375__5376)) )
& ! [Vvar__var__var__var__var__var__12__x__5318__5319__5377__5378__5379__5380] :
( t(Vvar__var__var__var__var__var__12__x__5318__5319__5377__5378__5379__5380,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__4__rmul__5254,Vvar__1__rO__5247),Vvar__var__var__var__var__var__12__x__5318__5319__5377__5378__5379__5380)),Vvar__1__rO__5247)) )
& ! [Vvar__var__var__var__var__13__x__5321__5323__5381__5383__5385] :
( t(Vvar__var__var__var__var__13__x__5321__5323__5381__5383__5385,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__14__y__5322__5324__5382__5384__5386] :
( t(Vvar__var__var__var__var__14__y__5322__5324__5382__5384__5386,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__13__x__5321__5323__5381__5383__5385),Vvar__var__var__var__var__14__y__5322__5324__5382__5384__5386)),happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__14__y__5322__5324__5382__5384__5386),Vvar__var__var__var__var__13__x__5321__5323__5381__5383__5385))) ) )
& ! [Vvar__var__var__var__var__14__x__5326__5329__5387__5390__5393] :
( t(Vvar__var__var__var__var__14__x__5326__5329__5387__5390__5393,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__15__y__5327__5330__5388__5391__5394] :
( t(Vvar__var__var__var__var__15__y__5327__5330__5388__5391__5394,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__16__z__5328__5331__5389__5392__5395] :
( t(Vvar__var__var__var__var__16__z__5328__5331__5389__5392__5395,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__14__x__5326__5329__5387__5390__5393),happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__15__y__5327__5330__5388__5391__5394),Vvar__var__var__var__var__16__z__5328__5331__5389__5392__5395))),happ(happ(Vvar__4__rmul__5254,happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__14__x__5326__5329__5387__5390__5393),Vvar__var__var__var__var__15__y__5327__5330__5388__5391__5394)),Vvar__var__var__var__var__16__z__5328__5331__5389__5392__5395))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__5333__5336__5396__5399__5402__5405] :
( t(Vvar__var__var__var__var__var__15__x__5333__5336__5396__5399__5402__5405,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__var__16__y__5334__5337__5397__5400__5403__5406] :
( t(Vvar__var__var__var__var__var__16__y__5334__5337__5397__5400__5403__5406,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__var__17__z__5335__5338__5398__5401__5404__5407] :
( t(Vvar__var__var__var__var__var__17__z__5335__5338__5398__5401__5404__5407,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__4__rmul__5254,happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__var__15__x__5333__5336__5396__5399__5402__5405),Vvar__var__var__var__var__var__16__y__5334__5337__5397__5400__5403__5406)),Vvar__var__var__var__var__var__17__z__5335__5338__5398__5401__5404__5407)),happ(happ(Vvar__3__radd__5249,happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__var__15__x__5333__5336__5396__5399__5402__5405),Vvar__var__var__var__var__var__17__z__5335__5338__5398__5401__5404__5407)),happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__var__16__y__5334__5337__5397__5400__5403__5406),Vvar__var__var__var__var__var__17__z__5335__5338__5398__5401__5404__5407)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__5340__5342__5408__5410__5412__5414] :
( t(Vvar__var__var__var__var__var__16__x__5340__5342__5408__5410__5412__5414,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__var__17__y__5341__5343__5409__5411__5413__5415] :
( t(Vvar__var__var__var__var__var__17__y__5341__5343__5409__5411__5413__5415,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(Vvar__6__ropp__5264,happ(happ(Vvar__4__rmul__5254,Vvar__var__var__var__var__var__16__x__5340__5342__5408__5410__5412__5414),Vvar__var__var__var__var__var__17__y__5341__5343__5409__5411__5413__5415))),happ(happ(Vvar__4__rmul__5254,happ(Vvar__6__ropp__5264,Vvar__var__var__var__var__var__16__x__5340__5342__5408__5410__5412__5414)),Vvar__var__var__var__var__var__17__y__5341__5343__5409__5411__5413__5415))) ) )
& ! [Vvar__var__var__var__var__var__17__x__5345__5347__5416__5418__5420__5422] :
( t(Vvar__var__var__var__var__var__17__x__5345__5347__5416__5418__5420__5422,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__var__18__y__5346__5348__5417__5419__5421__5423] :
( t(Vvar__var__var__var__var__var__18__y__5346__5348__5417__5419__5421__5423,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(Vvar__6__ropp__5264,happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__var__17__x__5345__5347__5416__5418__5420__5422),Vvar__var__var__var__var__var__18__y__5346__5348__5417__5419__5421__5423))),happ(happ(Vvar__3__radd__5249,happ(Vvar__6__ropp__5264,Vvar__var__var__var__var__var__17__x__5345__5347__5416__5418__5420__5422)),happ(Vvar__6__ropp__5264,Vvar__var__var__var__var__var__18__y__5346__5348__5417__5419__5421__5423)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__5350__5352__5424__5426__5428__5430__5432] :
( t(Vvar__var__var__var__var__var__var__18__x__5350__5352__5424__5426__5428__5430__5432,Vvar__0__R__5246)
=> ! [Vvar__var__var__var__var__var__var__19__y__5351__5353__5425__5427__5429__5431__5433] :
( t(Vvar__var__var__var__var__var__var__19__y__5351__5353__5425__5427__5429__5431__5433,Vvar__0__R__5246)
=> p(happ(happ(Vvar__7__req__5267,happ(happ(Vvar__5__rsub__5259,Vvar__var__var__var__var__var__var__18__x__5350__5352__5424__5426__5428__5430__5432),Vvar__var__var__var__var__var__var__19__y__5351__5353__5425__5427__5429__5431__5433)),happ(happ(Vvar__3__radd__5249,Vvar__var__var__var__var__var__var__18__x__5350__5352__5424__5426__5428__5430__5432),happ(Vvar__6__ropp__5264,Vvar__var__var__var__var__var__var__19__y__5351__5353__5425__5427__5429__5431__5433)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842] :
( cType___24t(Vvar__0__R__8822)
=> ( c_24__type__8962___24t(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842,Vvar__1__req__8823)
=> ( cType___24t(Vvar__2__C__8828)
=> ( c_24__type__9012___24t(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842,Vvar__3__cadd__8829)
=> ( c_24__type__9062___24t(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842,Vvar__4__cmul__8834)
=> ( c_24__type__9104___24t(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842,Vvar__5__phi__8839)
=> ( c_24__type__9154___24t(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842,Vvar__6__cdiv__8842)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__8874__8879__8884__8889__8894__8899__8904__8909] :
( t(Vvar__var__var__var__var__var__var__var__7__a__8874__8879__8884__8889__8894__8899__8904__8909,Vvar__2__C__8828)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__8875__8880__8885__8890__8895__8900__8905__8910] :
( t(Vvar__var__var__var__var__var__var__var__8__b__8875__8880__8885__8890__8895__8900__8905__8910,Vvar__2__C__8828)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_249217___24a9(Vvar__0__R__8822,Vvar__1__req__8823,Vvar__2__C__8828,Vvar__3__cadd__8829,Vvar__4__cmul__8834,Vvar__5__phi__8839,Vvar__6__cdiv__8842,Vvar__var__var__var__var__var__var__var__7__a__8874__8879__8884__8889__8894__8899__8904__8909,Vvar__var__var__var__var__var__var__var__8__b__8875__8880__8885__8890__8895__8900__8905__8910) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__3__req__9244,Vvar__4__Cpow__9249,Vvar__5__Cp__phi__9250,Vvar__6__rpow__9253] :
( cType___24t(Vvar__0__R__9237)
=> ( t(Vvar__1__rI__9238,Vvar__0__R__9237)
=> ( c_24__type__9339___24t(Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__3__req__9244,Vvar__4__Cpow__9249,Vvar__5__Cp__phi__9250,Vvar__6__rpow__9253,Vvar__2__rmul__9239)
=> ( c_24__type__9383___24t(Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__3__req__9244,Vvar__4__Cpow__9249,Vvar__5__Cp__phi__9250,Vvar__6__rpow__9253,Vvar__3__req__9244)
=> ( cType___24t(Vvar__4__Cpow__9249)
=> ( c_24__type__9419___24t(Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__3__req__9244,Vvar__4__Cpow__9249,Vvar__5__Cp__phi__9250,Vvar__6__rpow__9253,Vvar__5__Cp__phi__9250)
=> ( c_24__type__9463___24t(Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__3__req__9244,Vvar__4__Cpow__9249,Vvar__5__Cp__phi__9250,Vvar__6__rpow__9253,Vvar__6__rpow__9253)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__3__req__9244,Vvar__4__Cpow__9249,Vvar__5__Cp__phi__9250,Vvar__6__rpow__9253)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__9281__9283__9285__9287__9289__9291__9293__9295] :
( t(Vvar__var__var__var__var__var__var__var__7__r__9281__9283__9285__9287__9289__9291__9293__9295,Vvar__0__R__9237)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__9282__9284__9286__9288__9290__9292__9294__9296] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__9282__9284__9286__9288__9290__9292__9294__9296)
=> p(happ(happ(Vvar__3__req__9244,happ(happ(Vvar__6__rpow__9253,Vvar__var__var__var__var__var__var__var__7__r__9281__9283__9285__9287__9289__9291__9293__9295),happ(Vvar__5__Cp__phi__9250,Vvar__var__var__var__var__var__var__var__8__n__9282__9284__9286__9288__9290__9292__9294__9296))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__9237,Vvar__1__rI__9238,Vvar__2__rmul__9239,Vvar__var__var__var__var__var__var__var__7__r__9281__9283__9285__9287__9289__9291__9293__9295,Vvar__var__var__var__var__var__var__var__8__n__9282__9284__9286__9288__9290__9292__9294__9296))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854] :
( cType___24t(Vvar__0__R__5840)
=> ( c_24__type__5945___24t(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854,Vvar__1__radd__5841)
=> ( c_24__type__5975___24t(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854,Vvar__2__rmul__5846)
=> ( c_24__type__5999___24t(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854,Vvar__3__ropp__5851)
=> ( c_24__type__6029___24t(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854,Vvar__4__req__5854)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6059___24a5(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__5840,c_24__type__6083___24a5(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854),Vvar__4__req__5854,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__5840,Vvar__0__R__5840,Vvar__4__req__5854,Vvar__4__req__5854)),Vvar__1__radd__5841)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6116___24a5(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__5840,c_24__type__6140___24a5(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854),Vvar__4__req__5854,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__5840,Vvar__0__R__5840,Vvar__4__req__5854,Vvar__4__req__5854)),Vvar__2__rmul__5846)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__6167___24a5(Vvar__0__R__5840,Vvar__1__radd__5841,Vvar__2__rmul__5846,Vvar__3__ropp__5851,Vvar__4__req__5854),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__5840,Vvar__0__R__5840,Vvar__4__req__5854,Vvar__4__req__5854),Vvar__3__ropp__5851)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX26595] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX26595)
=> ( VX26595 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__26596] :
( cType___24t(Vvar__0__R__26596)
& ? [Vvar__1__req__26597] :
( c_24__type__1915___24t(Vvar__0__R__26596,Vvar__1__req__26597)
& ? [Vvar__2__reqb__26602] :
( c_24__type__2987___24t(Vvar__0__R__26596,Vvar__2__reqb__26602)
& ! [Vvar__var__3__x__26608__26611] :
( t(Vvar__var__3__x__26608__26611,Vvar__0__R__26596)
=> ! [Vvar__var__4__y__26609__26612] :
( t(Vvar__var__4__y__26609__26612,Vvar__0__R__26596)
=> ( happ(happ(Vvar__2__reqb__26602,Vvar__var__3__x__26608__26611),Vvar__var__4__y__26609__26612) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__26597,Vvar__var__3__x__26608__26611),Vvar__var__4__y__26609__26612)) ) ) )
& VX26595 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__26596,Vvar__1__req__26597,Vvar__2__reqb__26602) ) ) )
| ? [Vvar__0__R__26614] :
( cType___24t(Vvar__0__R__26614)
& ? [Vvar__1__rO__26615] :
( t(Vvar__1__rO__26615,Vvar__0__R__26614)
& ? [Vvar__2__rI__26616] :
( t(Vvar__2__rI__26616,Vvar__0__R__26614)
& ? [Vvar__3__radd__26617] :
( c_24__type__1897___24t(Vvar__0__R__26614,Vvar__3__radd__26617)
& ? [Vvar__4__rmul__26622] :
( c_24__type__1897___24t(Vvar__0__R__26614,Vvar__4__rmul__26622)
& ? [Vvar__5__rsub__26627] :
( c_24__type__1897___24t(Vvar__0__R__26614,Vvar__5__rsub__26627)
& ? [Vvar__6__ropp__26632] :
( c_24__type__1906___24t(Vvar__0__R__26614,Vvar__6__ropp__26632)
& ? [Vvar__7__req__26635] :
( c_24__type__1915___24t(Vvar__0__R__26614,Vvar__7__req__26635)
& ? [Vvar__8__C__26640] :
( cType___24t(Vvar__8__C__26640)
& ? [Vvar__9__cO__26641] :
( t(Vvar__9__cO__26641,Vvar__8__C__26640)
& ? [Vvar__10__cI__26642] :
( t(Vvar__10__cI__26642,Vvar__8__C__26640)
& ? [Vvar__11__cadd__26643] :
( c_24__type__3011___24t(Vvar__0__R__26614,Vvar__8__C__26640,Vvar__11__cadd__26643)
& ? [Vvar__12__cmul__26648] :
( c_24__type__3011___24t(Vvar__0__R__26614,Vvar__8__C__26640,Vvar__12__cmul__26648)
& ? [Vvar__13__csub__26653] :
( c_24__type__3011___24t(Vvar__0__R__26614,Vvar__8__C__26640,Vvar__13__csub__26653)
& ? [Vvar__14__copp__26658] :
( c_24__type__3025___24t(Vvar__0__R__26614,Vvar__8__C__26640,Vvar__14__copp__26658)
& ? [Vvar__15__ceqb__26661] :
( c_24__type__3032___24t(Vvar__0__R__26614,Vvar__8__C__26640,Vvar__15__ceqb__26661)
& ? [Vvar__16__phi__26666] :
( c_24__type__2594___24t(Vvar__0__R__26614,Vvar__8__C__26640,Vvar__16__phi__26666)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__26614,Vvar__1__rO__26615,Vvar__2__rI__26616,Vvar__3__radd__26617,Vvar__4__rmul__26622,Vvar__5__rsub__26627,Vvar__6__ropp__26632,Vvar__7__req__26635,Vvar__8__C__26640,Vvar__9__cO__26641,Vvar__10__cI__26642,Vvar__11__cadd__26643,Vvar__12__cmul__26648,Vvar__13__csub__26653,Vvar__14__copp__26658,Vvar__15__ceqb__26661,Vvar__16__phi__26666)
& VX26595 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__26614,Vvar__1__rO__26615,Vvar__2__rI__26616,Vvar__3__radd__26617,Vvar__4__rmul__26622,Vvar__5__rsub__26627,Vvar__6__ropp__26632,Vvar__7__req__26635,Vvar__8__C__26640,Vvar__9__cO__26641,Vvar__10__cI__26642,Vvar__11__cadd__26643,Vvar__12__cmul__26648,Vvar__13__csub__26653,Vvar__14__copp__26658,Vvar__15__ceqb__26661,Vvar__16__phi__26666) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222] :
( cType___24t(Vvar__0__R__6170)
=> ( t(Vvar__1__rO__6171,Vvar__0__R__6170)
=> ( t(Vvar__2__rI__6172,Vvar__0__R__6170)
=> ( c_24__type__6566___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__3__radd__6173)
=> ( c_24__type__6779___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__4__rmul__6178)
=> ( c_24__type__6992___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__5__rsub__6183)
=> ( c_24__type__7187___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__6__ropp__6188)
=> ( c_24__type__7400___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__7__req__6191)
=> ( cType___24t(Vvar__8__C__6196)
=> ( t(Vvar__9__cO__6197,Vvar__8__C__6196)
=> ( t(Vvar__10__cI__6198,Vvar__8__C__6196)
=> ( c_24__type__7613___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__11__cadd__6199)
=> ( c_24__type__7826___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__12__cmul__6204)
=> ( c_24__type__8039___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__13__csub__6209)
=> ( c_24__type__8234___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__14__copp__6214)
=> ( c_24__type__8447___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__15__ceqb__6217)
=> ( c_24__type__8642___24t(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222,Vvar__16__phi__6222)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__6170,Vvar__1__rO__6171,Vvar__2__rI__6172,Vvar__3__radd__6173,Vvar__4__rmul__6178,Vvar__5__rsub__6183,Vvar__6__ropp__6188,Vvar__7__req__6191,Vvar__8__C__6196,Vvar__9__cO__6197,Vvar__10__cI__6198,Vvar__11__cadd__6199,Vvar__12__cmul__6204,Vvar__13__csub__6209,Vvar__14__copp__6214,Vvar__15__ceqb__6217,Vvar__16__phi__6222)
=> ( p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,Vvar__9__cO__6197)),Vvar__1__rO__6171))
& p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,Vvar__10__cI__6198)),Vvar__2__rI__6172))
& ! [Vvar__var__var__var__var__var__var__19__x__6284__6286__6308__6310__6312__6314__6316] :
( t(Vvar__var__var__var__var__var__var__19__x__6284__6286__6308__6310__6312__6314__6316,Vvar__8__C__6196)
=> ! [Vvar__var__var__var__var__var__var__20__y__6285__6287__6309__6311__6313__6315__6317] :
( t(Vvar__var__var__var__var__var__var__20__y__6285__6287__6309__6311__6313__6315__6317,Vvar__8__C__6196)
=> p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,happ(happ(Vvar__11__cadd__6199,Vvar__var__var__var__var__var__var__19__x__6284__6286__6308__6310__6312__6314__6316),Vvar__var__var__var__var__var__var__20__y__6285__6287__6309__6311__6313__6315__6317))),happ(happ(Vvar__3__radd__6173,happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__19__x__6284__6286__6308__6310__6312__6314__6316)),happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__20__y__6285__6287__6309__6311__6313__6315__6317)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__6289__6291__6318__6320__6322__6324__6326] :
( t(Vvar__var__var__var__var__var__var__20__x__6289__6291__6318__6320__6322__6324__6326,Vvar__8__C__6196)
=> ! [Vvar__var__var__var__var__var__var__21__y__6290__6292__6319__6321__6323__6325__6327] :
( t(Vvar__var__var__var__var__var__var__21__y__6290__6292__6319__6321__6323__6325__6327,Vvar__8__C__6196)
=> p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,happ(happ(Vvar__13__csub__6209,Vvar__var__var__var__var__var__var__20__x__6289__6291__6318__6320__6322__6324__6326),Vvar__var__var__var__var__var__var__21__y__6290__6292__6319__6321__6323__6325__6327))),happ(happ(Vvar__5__rsub__6183,happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__20__x__6289__6291__6318__6320__6322__6324__6326)),happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__21__y__6290__6292__6319__6321__6323__6325__6327)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__6294__6296__6328__6330__6332__6334__6336] :
( t(Vvar__var__var__var__var__var__var__21__x__6294__6296__6328__6330__6332__6334__6336,Vvar__8__C__6196)
=> ! [Vvar__var__var__var__var__var__var__22__y__6295__6297__6329__6331__6333__6335__6337] :
( t(Vvar__var__var__var__var__var__var__22__y__6295__6297__6329__6331__6333__6335__6337,Vvar__8__C__6196)
=> p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,happ(happ(Vvar__12__cmul__6204,Vvar__var__var__var__var__var__var__21__x__6294__6296__6328__6330__6332__6334__6336),Vvar__var__var__var__var__var__var__22__y__6295__6297__6329__6331__6333__6335__6337))),happ(happ(Vvar__4__rmul__6178,happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__21__x__6294__6296__6328__6330__6332__6334__6336)),happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__22__y__6295__6297__6329__6331__6333__6335__6337)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__6299__6300__6338__6339__6340__6341__6342] :
( t(Vvar__var__var__var__var__var__var__22__x__6299__6300__6338__6339__6340__6341__6342,Vvar__8__C__6196)
=> p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,happ(Vvar__14__copp__6214,Vvar__var__var__var__var__var__var__22__x__6299__6300__6338__6339__6340__6341__6342))),happ(Vvar__6__ropp__6188,happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__var__22__x__6299__6300__6338__6339__6340__6341__6342)))) )
& ! [Vvar__var__var__var__var__var__23__x__6302__6305__6343__6346__6349__6352] :
( t(Vvar__var__var__var__var__var__23__x__6302__6305__6343__6346__6349__6352,Vvar__8__C__6196)
=> ! [Vvar__var__var__var__var__var__24__y__6303__6306__6344__6347__6350__6353] :
( t(Vvar__var__var__var__var__var__24__y__6303__6306__6344__6347__6350__6353,Vvar__8__C__6196)
=> ( happ(happ(Vvar__15__ceqb__6217,Vvar__var__var__var__var__var__23__x__6302__6305__6343__6346__6349__6352),Vvar__var__var__var__var__var__24__y__6303__6306__6344__6347__6350__6353) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__6191,happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__23__x__6302__6305__6343__6346__6349__6352)),happ(Vvar__16__phi__6222,Vvar__var__var__var__var__var__24__y__6303__6306__6344__6347__6350__6353))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989] :
( cType___24t(Vvar__0__R__23968)
=> ( t(Vvar__1__rO__23969,Vvar__0__R__23968)
=> ( t(Vvar__2__rI__23970,Vvar__0__R__23968)
=> ( c_24__type__24192___24t(Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989,Vvar__3__radd__23971)
=> ( c_24__type__24255___24t(Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989,Vvar__4__rmul__23976)
=> ( c_24__type__24318___24t(Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989,Vvar__5__rsub__23981)
=> ( c_24__type__24372___24t(Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989,Vvar__6__ropp__23986)
=> ( c_24__type__24435___24t(Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989,Vvar__7__req__23989)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__23968,Vvar__1__rO__23969,Vvar__2__rI__23970,Vvar__3__radd__23971,Vvar__4__rmul__23976,Vvar__5__rsub__23981,Vvar__6__ropp__23986,Vvar__7__req__23989)
=> ( ! [Vvar__var__var__var__var__var__8__x__24022__24023__24066__24067__24068__24069] :
( t(Vvar__var__var__var__var__var__8__x__24022__24023__24066__24067__24068__24069,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__3__radd__23971,Vvar__1__rO__23969),Vvar__var__var__var__var__var__8__x__24022__24023__24066__24067__24068__24069)),Vvar__var__var__var__var__var__8__x__24022__24023__24066__24067__24068__24069)) )
& ! [Vvar__var__var__var__var__9__x__24025__24027__24070__24072__24074] :
( t(Vvar__var__var__var__var__9__x__24025__24027__24070__24072__24074,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__10__y__24026__24028__24071__24073__24075] :
( t(Vvar__var__var__var__var__10__y__24026__24028__24071__24073__24075,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__9__x__24025__24027__24070__24072__24074),Vvar__var__var__var__var__10__y__24026__24028__24071__24073__24075)),happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__10__y__24026__24028__24071__24073__24075),Vvar__var__var__var__var__9__x__24025__24027__24070__24072__24074))) ) )
& ! [Vvar__var__var__var__var__10__x__24030__24033__24076__24079__24082] :
( t(Vvar__var__var__var__var__10__x__24030__24033__24076__24079__24082,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__11__y__24031__24034__24077__24080__24083] :
( t(Vvar__var__var__var__var__11__y__24031__24034__24077__24080__24083,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__12__z__24032__24035__24078__24081__24084] :
( t(Vvar__var__var__var__var__12__z__24032__24035__24078__24081__24084,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__10__x__24030__24033__24076__24079__24082),happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__11__y__24031__24034__24077__24080__24083),Vvar__var__var__var__var__12__z__24032__24035__24078__24081__24084))),happ(happ(Vvar__3__radd__23971,happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__10__x__24030__24033__24076__24079__24082),Vvar__var__var__var__var__11__y__24031__24034__24077__24080__24083)),Vvar__var__var__var__var__12__z__24032__24035__24078__24081__24084))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__24037__24038__24085__24086__24087__24088] :
( t(Vvar__var__var__var__var__var__11__x__24037__24038__24085__24086__24087__24088,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__4__rmul__23976,Vvar__2__rI__23970),Vvar__var__var__var__var__var__11__x__24037__24038__24085__24086__24087__24088)),Vvar__var__var__var__var__var__11__x__24037__24038__24085__24086__24087__24088)) )
& ! [Vvar__var__var__var__var__12__x__24040__24042__24089__24091__24093] :
( t(Vvar__var__var__var__var__12__x__24040__24042__24089__24091__24093,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__13__y__24041__24043__24090__24092__24094] :
( t(Vvar__var__var__var__var__13__y__24041__24043__24090__24092__24094,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__12__x__24040__24042__24089__24091__24093),Vvar__var__var__var__var__13__y__24041__24043__24090__24092__24094)),happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__13__y__24041__24043__24090__24092__24094),Vvar__var__var__var__var__12__x__24040__24042__24089__24091__24093))) ) )
& ! [Vvar__var__var__var__var__13__x__24045__24048__24095__24098__24101] :
( t(Vvar__var__var__var__var__13__x__24045__24048__24095__24098__24101,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__14__y__24046__24049__24096__24099__24102] :
( t(Vvar__var__var__var__var__14__y__24046__24049__24096__24099__24102,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__15__z__24047__24050__24097__24100__24103] :
( t(Vvar__var__var__var__var__15__z__24047__24050__24097__24100__24103,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__13__x__24045__24048__24095__24098__24101),happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__14__y__24046__24049__24096__24099__24102),Vvar__var__var__var__var__15__z__24047__24050__24097__24100__24103))),happ(happ(Vvar__4__rmul__23976,happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__13__x__24045__24048__24095__24098__24101),Vvar__var__var__var__var__14__y__24046__24049__24096__24099__24102)),Vvar__var__var__var__var__15__z__24047__24050__24097__24100__24103))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__24052__24055__24104__24107__24110__24113] :
( t(Vvar__var__var__var__var__var__14__x__24052__24055__24104__24107__24110__24113,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__var__15__y__24053__24056__24105__24108__24111__24114] :
( t(Vvar__var__var__var__var__var__15__y__24053__24056__24105__24108__24111__24114,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__var__16__z__24054__24057__24106__24109__24112__24115] :
( t(Vvar__var__var__var__var__var__16__z__24054__24057__24106__24109__24112__24115,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__4__rmul__23976,happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__var__14__x__24052__24055__24104__24107__24110__24113),Vvar__var__var__var__var__var__15__y__24053__24056__24105__24108__24111__24114)),Vvar__var__var__var__var__var__16__z__24054__24057__24106__24109__24112__24115)),happ(happ(Vvar__3__radd__23971,happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__var__14__x__24052__24055__24104__24107__24110__24113),Vvar__var__var__var__var__var__16__z__24054__24057__24106__24109__24112__24115)),happ(happ(Vvar__4__rmul__23976,Vvar__var__var__var__var__var__15__y__24053__24056__24105__24108__24111__24114),Vvar__var__var__var__var__var__16__z__24054__24057__24106__24109__24112__24115)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__24059__24061__24116__24118__24120__24122__24124] :
( t(Vvar__var__var__var__var__var__var__15__x__24059__24061__24116__24118__24120__24122__24124,Vvar__0__R__23968)
=> ! [Vvar__var__var__var__var__var__var__16__y__24060__24062__24117__24119__24121__24123__24125] :
( t(Vvar__var__var__var__var__var__var__16__y__24060__24062__24117__24119__24121__24123__24125,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__5__rsub__23981,Vvar__var__var__var__var__var__var__15__x__24059__24061__24116__24118__24120__24122__24124),Vvar__var__var__var__var__var__var__16__y__24060__24062__24117__24119__24121__24123__24125)),happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__var__var__15__x__24059__24061__24116__24118__24120__24122__24124),happ(Vvar__6__ropp__23986,Vvar__var__var__var__var__var__var__16__y__24060__24062__24117__24119__24121__24123__24125)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__24064__24065__24126__24127__24128__24129__24130] :
( t(Vvar__var__var__var__var__var__var__16__x__24064__24065__24126__24127__24128__24129__24130,Vvar__0__R__23968)
=> p(happ(happ(Vvar__7__req__23989,happ(happ(Vvar__3__radd__23971,Vvar__var__var__var__var__var__var__16__x__24064__24065__24126__24127__24128__24129__24130),happ(Vvar__6__ropp__23986,Vvar__var__var__var__var__var__var__16__x__24064__24065__24126__24127__24128__24129__24130))),Vvar__1__rO__23969)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632] :
( cType___24t(Vvar__0__R__25596)
=> ( t(Vvar__1__rO__25597,Vvar__0__R__25596)
=> ( t(Vvar__2__rI__25598,Vvar__0__R__25596)
=> ( c_24__type__25849___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__3__radd__25599)
=> ( c_24__type__25974___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__4__rmul__25604)
=> ( c_24__type__26099___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__5__req__25609)
=> ( cType___24t(Vvar__6__C__25614)
=> ( t(Vvar__7__cO__25615,Vvar__6__C__25614)
=> ( t(Vvar__8__cI__25616,Vvar__6__C__25614)
=> ( c_24__type__26224___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__9__cadd__25617)
=> ( c_24__type__26349___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__10__cmul__25622)
=> ( c_24__type__26474___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__11__ceqb__25627)
=> ( c_24__type__26585___24t(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632,Vvar__12__phi__25632)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__25596,Vvar__1__rO__25597,Vvar__2__rI__25598,Vvar__3__radd__25599,Vvar__4__rmul__25604,Vvar__5__req__25609,Vvar__6__C__25614,Vvar__7__cO__25615,Vvar__8__cI__25616,Vvar__9__cadd__25617,Vvar__10__cmul__25622,Vvar__11__ceqb__25627,Vvar__12__phi__25632)
=> ( p(happ(happ(Vvar__5__req__25609,happ(Vvar__12__phi__25632,Vvar__7__cO__25615)),Vvar__1__rO__25597))
& p(happ(happ(Vvar__5__req__25609,happ(Vvar__12__phi__25632,Vvar__8__cI__25616)),Vvar__2__rI__25598))
& ! [Vvar__var__var__var__var__var__var__15__x__25678__25680__25694__25696__25698__25700__25702] :
( t(Vvar__var__var__var__var__var__var__15__x__25678__25680__25694__25696__25698__25700__25702,Vvar__6__C__25614)
=> ! [Vvar__var__var__var__var__var__var__16__y__25679__25681__25695__25697__25699__25701__25703] :
( t(Vvar__var__var__var__var__var__var__16__y__25679__25681__25695__25697__25699__25701__25703,Vvar__6__C__25614)
=> p(happ(happ(Vvar__5__req__25609,happ(Vvar__12__phi__25632,happ(happ(Vvar__9__cadd__25617,Vvar__var__var__var__var__var__var__15__x__25678__25680__25694__25696__25698__25700__25702),Vvar__var__var__var__var__var__var__16__y__25679__25681__25695__25697__25699__25701__25703))),happ(happ(Vvar__3__radd__25599,happ(Vvar__12__phi__25632,Vvar__var__var__var__var__var__var__15__x__25678__25680__25694__25696__25698__25700__25702)),happ(Vvar__12__phi__25632,Vvar__var__var__var__var__var__var__16__y__25679__25681__25695__25697__25699__25701__25703)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__25683__25685__25704__25706__25708__25710__25712] :
( t(Vvar__var__var__var__var__var__var__16__x__25683__25685__25704__25706__25708__25710__25712,Vvar__6__C__25614)
=> ! [Vvar__var__var__var__var__var__var__17__y__25684__25686__25705__25707__25709__25711__25713] :
( t(Vvar__var__var__var__var__var__var__17__y__25684__25686__25705__25707__25709__25711__25713,Vvar__6__C__25614)
=> p(happ(happ(Vvar__5__req__25609,happ(Vvar__12__phi__25632,happ(happ(Vvar__10__cmul__25622,Vvar__var__var__var__var__var__var__16__x__25683__25685__25704__25706__25708__25710__25712),Vvar__var__var__var__var__var__var__17__y__25684__25686__25705__25707__25709__25711__25713))),happ(happ(Vvar__4__rmul__25604,happ(Vvar__12__phi__25632,Vvar__var__var__var__var__var__var__16__x__25683__25685__25704__25706__25708__25710__25712)),happ(Vvar__12__phi__25632,Vvar__var__var__var__var__var__var__17__y__25684__25686__25705__25707__25709__25711__25713)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__25688__25691__25714__25717__25720__25723] :
( t(Vvar__var__var__var__var__var__17__x__25688__25691__25714__25717__25720__25723,Vvar__6__C__25614)
=> ! [Vvar__var__var__var__var__var__18__y__25689__25692__25715__25718__25721__25724] :
( t(Vvar__var__var__var__var__var__18__y__25689__25692__25715__25718__25721__25724,Vvar__6__C__25614)
=> ( happ(happ(Vvar__11__ceqb__25627,Vvar__var__var__var__var__var__17__x__25688__25691__25714__25717__25720__25723),Vvar__var__var__var__var__var__18__y__25689__25692__25715__25718__25721__25724) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__25609,happ(Vvar__12__phi__25632,Vvar__var__var__var__var__var__17__x__25688__25691__25714__25717__25720__25723)),happ(Vvar__12__phi__25632,Vvar__var__var__var__var__var__18__y__25689__25692__25715__25718__25721__25724))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__23704,Vvar__1__rO__23705,Vvar__2__rI__23706,Vvar__3__radd__23707,Vvar__4__rmul__23712,Vvar__5__req__23717] :
( cType___24t(Vvar__0__R__23704)
=> ( t(Vvar__1__rO__23705,Vvar__0__R__23704)
=> ( t(Vvar__2__rI__23706,Vvar__0__R__23704)
=> ( c_24__type__23872___24t(Vvar__0__R__23704,Vvar__1__rO__23705,Vvar__2__rI__23706,Vvar__3__radd__23707,Vvar__4__rmul__23712,Vvar__5__req__23717,Vvar__3__radd__23707)
=> ( c_24__type__23911___24t(Vvar__0__R__23704,Vvar__1__rO__23705,Vvar__2__rI__23706,Vvar__3__radd__23707,Vvar__4__rmul__23712,Vvar__5__req__23717,Vvar__4__rmul__23712)
=> ( c_24__type__23950___24t(Vvar__0__R__23704,Vvar__1__rO__23705,Vvar__2__rI__23706,Vvar__3__radd__23707,Vvar__4__rmul__23712,Vvar__5__req__23717,Vvar__5__req__23717)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__23704,Vvar__1__rO__23705,Vvar__2__rI__23706,Vvar__3__radd__23707,Vvar__4__rmul__23712,Vvar__5__req__23717)
=> ( ! [Vvar__var__var__var__var__var__6__n__23742__23743__23781__23782__23783__23784] :
( t(Vvar__var__var__var__var__var__6__n__23742__23743__23781__23782__23783__23784,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__3__radd__23707,Vvar__1__rO__23705),Vvar__var__var__var__var__var__6__n__23742__23743__23781__23782__23783__23784)),Vvar__var__var__var__var__var__6__n__23742__23743__23781__23782__23783__23784)) )
& ! [Vvar__var__var__var__var__7__n__23745__23747__23785__23787__23789] :
( t(Vvar__var__var__var__var__7__n__23745__23747__23785__23787__23789,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__8__m__23746__23748__23786__23788__23790] :
( t(Vvar__var__var__var__var__8__m__23746__23748__23786__23788__23790,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__3__radd__23707,Vvar__var__var__var__var__7__n__23745__23747__23785__23787__23789),Vvar__var__var__var__var__8__m__23746__23748__23786__23788__23790)),happ(happ(Vvar__3__radd__23707,Vvar__var__var__var__var__8__m__23746__23748__23786__23788__23790),Vvar__var__var__var__var__7__n__23745__23747__23785__23787__23789))) ) )
& ! [Vvar__var__var__var__var__8__n__23750__23753__23791__23794__23797] :
( t(Vvar__var__var__var__var__8__n__23750__23753__23791__23794__23797,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__9__m__23751__23754__23792__23795__23798] :
( t(Vvar__var__var__var__var__9__m__23751__23754__23792__23795__23798,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__10__p__23752__23755__23793__23796__23799] :
( t(Vvar__var__var__var__var__10__p__23752__23755__23793__23796__23799,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__3__radd__23707,Vvar__var__var__var__var__8__n__23750__23753__23791__23794__23797),happ(happ(Vvar__3__radd__23707,Vvar__var__var__var__var__9__m__23751__23754__23792__23795__23798),Vvar__var__var__var__var__10__p__23752__23755__23793__23796__23799))),happ(happ(Vvar__3__radd__23707,happ(happ(Vvar__3__radd__23707,Vvar__var__var__var__var__8__n__23750__23753__23791__23794__23797),Vvar__var__var__var__var__9__m__23751__23754__23792__23795__23798)),Vvar__var__var__var__var__10__p__23752__23755__23793__23796__23799))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__23757__23758__23800__23801__23802__23803] :
( t(Vvar__var__var__var__var__var__9__n__23757__23758__23800__23801__23802__23803,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__4__rmul__23712,Vvar__2__rI__23706),Vvar__var__var__var__var__var__9__n__23757__23758__23800__23801__23802__23803)),Vvar__var__var__var__var__var__9__n__23757__23758__23800__23801__23802__23803)) )
& ! [Vvar__var__var__var__var__var__10__n__23760__23761__23804__23805__23806__23807] :
( t(Vvar__var__var__var__var__var__10__n__23760__23761__23804__23805__23806__23807,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__4__rmul__23712,Vvar__1__rO__23705),Vvar__var__var__var__var__var__10__n__23760__23761__23804__23805__23806__23807)),Vvar__1__rO__23705)) )
& ! [Vvar__var__var__var__var__11__n__23763__23765__23808__23810__23812] :
( t(Vvar__var__var__var__var__11__n__23763__23765__23808__23810__23812,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__12__m__23764__23766__23809__23811__23813] :
( t(Vvar__var__var__var__var__12__m__23764__23766__23809__23811__23813,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__11__n__23763__23765__23808__23810__23812),Vvar__var__var__var__var__12__m__23764__23766__23809__23811__23813)),happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__12__m__23764__23766__23809__23811__23813),Vvar__var__var__var__var__11__n__23763__23765__23808__23810__23812))) ) )
& ! [Vvar__var__var__var__var__12__n__23768__23771__23814__23817__23820] :
( t(Vvar__var__var__var__var__12__n__23768__23771__23814__23817__23820,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__13__m__23769__23772__23815__23818__23821] :
( t(Vvar__var__var__var__var__13__m__23769__23772__23815__23818__23821,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__14__p__23770__23773__23816__23819__23822] :
( t(Vvar__var__var__var__var__14__p__23770__23773__23816__23819__23822,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__12__n__23768__23771__23814__23817__23820),happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__13__m__23769__23772__23815__23818__23821),Vvar__var__var__var__var__14__p__23770__23773__23816__23819__23822))),happ(happ(Vvar__4__rmul__23712,happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__12__n__23768__23771__23814__23817__23820),Vvar__var__var__var__var__13__m__23769__23772__23815__23818__23821)),Vvar__var__var__var__var__14__p__23770__23773__23816__23819__23822))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__23775__23778__23823__23826__23829__23832] :
( t(Vvar__var__var__var__var__var__13__n__23775__23778__23823__23826__23829__23832,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__var__14__m__23776__23779__23824__23827__23830__23833] :
( t(Vvar__var__var__var__var__var__14__m__23776__23779__23824__23827__23830__23833,Vvar__0__R__23704)
=> ! [Vvar__var__var__var__var__var__15__p__23777__23780__23825__23828__23831__23834] :
( t(Vvar__var__var__var__var__var__15__p__23777__23780__23825__23828__23831__23834,Vvar__0__R__23704)
=> p(happ(happ(Vvar__5__req__23717,happ(happ(Vvar__4__rmul__23712,happ(happ(Vvar__3__radd__23707,Vvar__var__var__var__var__var__13__n__23775__23778__23823__23826__23829__23832),Vvar__var__var__var__var__var__14__m__23776__23779__23824__23827__23830__23833)),Vvar__var__var__var__var__var__15__p__23777__23780__23825__23828__23831__23834)),happ(happ(Vvar__3__radd__23707,happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__var__13__n__23775__23778__23823__23826__23829__23832),Vvar__var__var__var__var__var__15__p__23777__23780__23825__23828__23831__23834)),happ(happ(Vvar__4__rmul__23712,Vvar__var__var__var__var__var__14__m__23776__23779__23824__23827__23830__23833),Vvar__var__var__var__var__var__15__p__23777__23780__23825__23828__23831__23834)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__8728,Vvar__1__copp__8729,Vvar__2__ceqb__8732,Vvar__3__get__sign__8737] :
( cType___24t(Vvar__0__C__8728)
=> ( c_24__type__8784___24t(Vvar__0__C__8728,Vvar__1__copp__8729,Vvar__2__ceqb__8732,Vvar__3__get__sign__8737,Vvar__1__copp__8729)
=> ( c_24__type__8803___24t(Vvar__0__C__8728,Vvar__1__copp__8729,Vvar__2__ceqb__8732,Vvar__3__get__sign__8737,Vvar__2__ceqb__8732)
=> ( c_24__type__8817___24t(Vvar__0__C__8728,Vvar__1__copp__8729,Vvar__2__ceqb__8732,Vvar__3__get__sign__8737,Vvar__3__get__sign__8737)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__8728,Vvar__1__copp__8729,Vvar__2__ceqb__8732,Vvar__3__get__sign__8737)
=> ( ! [Vvar__var__var__var__var__var__4__c__8754__8757__8760__8763__8766__8769] :
( t(Vvar__var__var__var__var__var__4__c__8754__8757__8760__8763__8766__8769,Vvar__0__C__8728)
=> ! [Vvar__var__var__var__var__var__5__c_27__8755__8758__8761__8764__8767__8770] :
( t(Vvar__var__var__var__var__var__5__c_27__8755__8758__8761__8764__8767__8770,Vvar__0__C__8728)
=> ( happ(Vvar__3__get__sign__8737,Vvar__var__var__var__var__var__4__c__8754__8757__8760__8763__8766__8769) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__8728,Vvar__var__var__var__var__var__5__c_27__8755__8758__8761__8764__8767__8770)
=> happ(happ(Vvar__2__ceqb__8732,Vvar__var__var__var__var__var__4__c__8754__8757__8760__8763__8766__8769),happ(Vvar__1__copp__8729,Vvar__var__var__var__var__var__5__c_27__8755__8758__8761__8764__8767__8770)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741] :
( cType___24t(Vvar__0__R__20730)
=> ( c_24__type__20816___24t(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741,Vvar__1__radd__20731)
=> ( c_24__type__20839___24t(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741,Vvar__2__rmul__20736)
=> ( c_24__type__20862___24t(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741,Vvar__3__req__20741)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__20885___24a4(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20730,c_24__type__20903___24a4(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741),Vvar__3__req__20741,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20730,Vvar__0__R__20730,Vvar__3__req__20741,Vvar__3__req__20741)),Vvar__1__radd__20731)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__20929___24a4(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20730,c_24__type__20947___24a4(Vvar__0__R__20730,Vvar__1__radd__20731,Vvar__2__rmul__20736,Vvar__3__req__20741),Vvar__3__req__20741,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__20730,Vvar__0__R__20730,Vvar__3__req__20741,Vvar__3__req__20741)),Vvar__2__rmul__20736)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [VX25571] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX25571)
=> ( VX25571 = cHammer_2eTactics_2eReconstr_2eEmpty
| VX25571 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).
fof('$_inversion_Lambda.Terms.lambda',axiom,
! [VX73] :
( cLambda_2eTerms_2elambda___24t(VX73)
=> ( ? [Vvar__0___24Anonymous__74] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__74)
& VX73 = cLambda_2eTerms_2eRef___24a1(Vvar__0___24Anonymous__74) )
| ? [Vvar__0___24Anonymous__75] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__75)
& VX73 = cLambda_2eTerms_2eAbs___24a1(Vvar__0___24Anonymous__75) )
| ? [Vvar__0___24Anonymous__76] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__76)
& ? [Vvar__1___24Anonymous__77] :
( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__77)
& VX73 = cLambda_2eTerms_2eApp___24a2(Vvar__0___24Anonymous__76,Vvar__1___24Anonymous__77) ) ) ) ) ).
fof('$_inversion_Reduction.par_red',axiom,
! [Vvar__0___24Anonymous__31290,Vvar__1___24Anonymous__31291] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__31290)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__31291)
=> ( cReduction_2epar__red___24a2(Vvar__0___24Anonymous__31290,Vvar__1___24Anonymous__31291)
=> ( ? [Vvar__0__M__31293] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__31293)
& ? [Vvar__1__N__31294] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__31294)
& cReduction_2epar__red1___24a2(Vvar__0__M__31293,Vvar__1__N__31294)
& Vvar__1___24Anonymous__31291 = Vvar__1__N__31294
& Vvar__0___24Anonymous__31290 = Vvar__0__M__31293 ) )
| ? [Vvar__0__M__31296] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__31296)
& ? [Vvar__1__N__31297] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__31297)
& ? [Vvar__2__P__31298] :
( cLambda_2eTerms_2elambda___24t(Vvar__2__P__31298)
& cReduction_2epar__red___24a2(Vvar__0__M__31296,Vvar__1__N__31297)
& cReduction_2epar__red___24a2(Vvar__1__N__31297,Vvar__2__P__31298)
& Vvar__1___24Anonymous__31291 = Vvar__2__P__31298
& Vvar__0___24Anonymous__31290 = Vvar__0__M__31296 ) ) ) ) ) ) ) ).
fof('$_inversion_Reduction.par_red1',axiom,
! [Vvar__0___24Anonymous__30940,Vvar__1___24Anonymous__30941] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__30940)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__30941)
=> ( cReduction_2epar__red1___24a2(Vvar__0___24Anonymous__30940,Vvar__1___24Anonymous__30941)
=> ( ? [Vvar__0__M__30943] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__30943)
& ? [Vvar__1__M_27__30944] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__M_27__30944)
& cReduction_2epar__red1___24a2(Vvar__0__M__30943,Vvar__1__M_27__30944)
& ? [Vvar__3__N__30946] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__N__30946)
& ? [Vvar__4__N_27__30947] :
( cLambda_2eTerms_2elambda___24t(Vvar__4__N_27__30947)
& cReduction_2epar__red1___24a2(Vvar__3__N__30946,Vvar__4__N_27__30947)
& Vvar__1___24Anonymous__30941 = c_24__case__Lambda_2eTerms_2elambda_24673___24a4(Vvar__0___24Anonymous__30940,Vvar__1___24Anonymous__30941,Vvar__1__M_27__30944,Vvar__4__N_27__30947)
& Vvar__0___24Anonymous__30940 = cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__30943),Vvar__3__N__30946) ) ) ) )
| ? [Vvar__0__n__30954] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__30954)
& Vvar__1___24Anonymous__30941 = cLambda_2eTerms_2eRef___24a1(Vvar__0__n__30954)
& Vvar__0___24Anonymous__30940 = cLambda_2eTerms_2eRef___24a1(Vvar__0__n__30954) )
| ? [Vvar__0__M__30955] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__30955)
& ? [Vvar__1__M_27__30956] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__M_27__30956)
& cReduction_2epar__red1___24a2(Vvar__0__M__30955,Vvar__1__M_27__30956)
& Vvar__1___24Anonymous__30941 = cLambda_2eTerms_2eAbs___24a1(Vvar__1__M_27__30956)
& Vvar__0___24Anonymous__30940 = cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__30955) ) )
| ? [Vvar__0__M__30958] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__30958)
& ? [Vvar__1__M_27__30959] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__M_27__30959)
& cReduction_2epar__red1___24a2(Vvar__0__M__30958,Vvar__1__M_27__30959)
& ? [Vvar__3__N__30961] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__N__30961)
& ? [Vvar__4__N_27__30962] :
( cLambda_2eTerms_2elambda___24t(Vvar__4__N_27__30962)
& cReduction_2epar__red1___24a2(Vvar__3__N__30961,Vvar__4__N_27__30962)
& Vvar__1___24Anonymous__30941 = cLambda_2eTerms_2eApp___24a2(Vvar__1__M_27__30959,Vvar__4__N_27__30962)
& Vvar__0___24Anonymous__30940 = cLambda_2eTerms_2eApp___24a2(Vvar__0__M__30958,Vvar__3__N__30961) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Reduction.red',axiom,
! [Vvar__0___24Anonymous__308,Vvar__1___24Anonymous__309] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__308)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__309)
=> ( cReduction_2ered___24a2(Vvar__0___24Anonymous__308,Vvar__1___24Anonymous__309)
=> ( ? [Vvar__0__M__311] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__311)
& ? [Vvar__1__N__312] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__312)
& cReduction_2ered1___24a2(Vvar__0__M__311,Vvar__1__N__312)
& Vvar__1___24Anonymous__309 = Vvar__1__N__312
& Vvar__0___24Anonymous__308 = Vvar__0__M__311 ) )
| ? [Vvar__0__M__314] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__314)
& Vvar__1___24Anonymous__309 = Vvar__0__M__314
& Vvar__0___24Anonymous__308 = Vvar__0__M__314 )
| ? [Vvar__0__M__315] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__315)
& ? [Vvar__1__N__316] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__316)
& ? [Vvar__2__P__317] :
( cLambda_2eTerms_2elambda___24t(Vvar__2__P__317)
& cReduction_2ered___24a2(Vvar__0__M__315,Vvar__1__N__316)
& cReduction_2ered___24a2(Vvar__1__N__316,Vvar__2__P__317)
& Vvar__1___24Anonymous__309 = Vvar__2__P__317
& Vvar__0___24Anonymous__308 = Vvar__0__M__315 ) ) ) ) ) ) ) ).
fof('$_inversion_Reduction.red1',axiom,
! [Vvar__0___24Anonymous__337,Vvar__1___24Anonymous__338] :
( cLambda_2eTerms_2elambda___24t(Vvar__0___24Anonymous__337)
=> ( cLambda_2eTerms_2elambda___24t(Vvar__1___24Anonymous__338)
=> ( cReduction_2ered1___24a2(Vvar__0___24Anonymous__337,Vvar__1___24Anonymous__338)
=> ( ? [Vvar__0__M__340] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__340)
& ? [Vvar__1__N__341] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__341)
& Vvar__1___24Anonymous__338 = c_24__case__Lambda_2eTerms_2elambda_24673___24a4(Vvar__0___24Anonymous__337,Vvar__1___24Anonymous__338,Vvar__0__M__340,Vvar__1__N__341)
& Vvar__0___24Anonymous__337 = cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__340),Vvar__1__N__341) ) )
| ? [Vvar__0__M__347] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M__347)
& ? [Vvar__1__N__348] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N__348)
& cReduction_2ered1___24a2(Vvar__0__M__347,Vvar__1__N__348)
& Vvar__1___24Anonymous__338 = cLambda_2eTerms_2eAbs___24a1(Vvar__1__N__348)
& Vvar__0___24Anonymous__337 = cLambda_2eTerms_2eAbs___24a1(Vvar__0__M__347) ) )
| ? [Vvar__0__M1__350] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M1__350)
& ? [Vvar__1__N1__351] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N1__351)
& cReduction_2ered1___24a2(Vvar__0__M1__350,Vvar__1__N1__351)
& ? [Vvar__3__M2__353] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__M2__353)
& Vvar__1___24Anonymous__338 = cLambda_2eTerms_2eApp___24a2(Vvar__1__N1__351,Vvar__3__M2__353)
& Vvar__0___24Anonymous__337 = cLambda_2eTerms_2eApp___24a2(Vvar__0__M1__350,Vvar__3__M2__353) ) ) )
| ? [Vvar__0__M2__354] :
( cLambda_2eTerms_2elambda___24t(Vvar__0__M2__354)
& ? [Vvar__1__N2__355] :
( cLambda_2eTerms_2elambda___24t(Vvar__1__N2__355)
& cReduction_2ered1___24a2(Vvar__0__M2__354,Vvar__1__N2__355)
& ? [Vvar__3__M1__357] :
( cLambda_2eTerms_2elambda___24t(Vvar__3__M1__357)
& Vvar__1___24Anonymous__338 = cLambda_2eTerms_2eApp___24a2(Vvar__3__M1__357,Vvar__1__N2__355)
& Vvar__0___24Anonymous__337 = cLambda_2eTerms_2eApp___24a2(Vvar__3__M1__357,Vvar__0__M2__354) ) ) ) ) ) ) ) ).
fof('$_lam_29393',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29393___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_29401',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29401___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('$_lam_29409',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29409___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_29417',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29417___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('$_lam_29490',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29490___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_29498',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29498___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_29506',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29506___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_29514',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__29514___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_30510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__30510___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_30532',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__30532___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_30636',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__30636___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30637] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30637)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30637)
& c_24__lam__30636___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__30637) ) ) ) ).
fof('$_lam_30643',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__30643___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__30644] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30644)
& Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30644)
& c_24__lam__30643___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__30644) ) ) ) ).
fof('$_lam_30647',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__lam__30647___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__30648] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30648)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30648)
& c_24__lam__30647___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_prop_25229',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__S__25207,Vvar__1__x__25208,Vvar__2__y__25209] :
( p(c_24__prop__25229___24a4(Vvar__0___24Anonymous__25205,Vvar__0__S__25207,Vvar__1__x__25208,Vvar__2__y__25209))
<=> Vvar__1__x__25208 = Vvar__2__y__25209 ) ).
fof('$_prop_25230',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__x__25210,Vvar__1__y__25211] :
( p(c_24__prop__25230___24a3(Vvar__0___24Anonymous__25205,Vvar__0__x__25210,Vvar__1__y__25211))
<=> Vvar__0__x__25210 = Vvar__1__y__25211 ) ).
fof('$_prop_25231',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__x__25212,Vvar__1__s__25213] :
( p(c_24__prop__25231___24a3(Vvar__0___24Anonymous__25205,Vvar__0__x__25212,Vvar__1__s__25213))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__25212,Vvar__1__s__25213) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_25232',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__P__25214,Vvar__1__Q__25215] :
( p(c_24__prop__25232___24a3(Vvar__0___24Anonymous__25205,Vvar__0__P__25214,Vvar__1__Q__25215))
<=> ( p(Vvar__0__P__25214)
& p(Vvar__1__Q__25215) ) ) ).
fof('$_prop_25233',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__P__25218,Vvar__1__Q__25219] :
( p(c_24__prop__25233___24a3(Vvar__0___24Anonymous__25205,Vvar__0__P__25218,Vvar__1__Q__25219))
<=> ( p(Vvar__0__P__25218)
| p(Vvar__1__Q__25219) ) ) ).
fof('$_prop_25234',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__P__25222,Vvar__1__Q__25223] :
( p(c_24__prop__25234___24a3(Vvar__0___24Anonymous__25205,Vvar__0__P__25222,Vvar__1__Q__25223))
<=> ( p(Vvar__0__P__25222)
=> p(Vvar__1__Q__25223) ) ) ).
fof('$_prop_25235',axiom,
! [Vvar__0___24Anonymous__25205,Vvar__0__P__25227] :
( p(c_24__prop__25235___24a2(Vvar__0___24Anonymous__25205,Vvar__0__P__25227))
<=> ~ p(Vvar__0__P__25227) ) ).
fof('$_prop_27107',axiom,
! [Vvar__0___24Anonymous__27094,Vvar__0__s__27098] :
( p(c_24__prop__27107___24a2(Vvar__0___24Anonymous__27094,Vvar__0__s__27098))
<=> ! [Vvar__1__a__27099] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__27099)
=> ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__27099,Vvar__0__s__27098) ) ) ).
fof('$_prop_27108',axiom,
! [Vvar__0___24Anonymous__27094,Vvar__0__s1__27100,Vvar__1__s2__27101] :
( p(c_24__prop__27108___24a3(Vvar__0___24Anonymous__27094,Vvar__0__s1__27100,Vvar__1__s2__27101))
<=> ! [Vvar__2__a__27102] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__27102)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__27102,Vvar__0__s1__27100)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__27102,Vvar__1__s2__27101) ) ) ) ).
fof('$_prop_27109',axiom,
! [Vvar__0___24Anonymous__27094,Vvar__0__s1__27104,Vvar__1__s2__27105] :
( p(c_24__prop__27109___24a3(Vvar__0___24Anonymous__27094,Vvar__0__s1__27104,Vvar__1__s2__27105))
<=> ! [Vvar__2__a__27106] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__27106)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__27106,Vvar__0__s1__27104)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__27106,Vvar__1__s2__27105) ) ) ) ).
fof('$_prop_30696',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__30696___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_type_10',axiom,
! [Vvar__11] :
( c_24__type__10___24t(Vvar__11)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__11,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1030',axiom,
! [Vvar__1031] :
( c_24__type__1030___24t(Vvar__1031)
<=> ! [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__1031,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10427',axiom,
! [Vvar__10428] :
( c_24__type__10427___24t(Vvar__10428)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10428,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10431',axiom,
! [Vvar__10432] :
( c_24__type__10431___24t(Vvar__10432)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__10432,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10435',axiom,
! [Vvar__10436] :
( c_24__type__10435___24t(Vvar__10436)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10436,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10447',axiom,
! [Vvar__10448] :
( c_24__type__10447___24t(Vvar__10448)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10448,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10452',axiom,
! [Vvar__10453] :
( c_24__type__10452___24t(Vvar__10453)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(Vvar__10453,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10454',axiom,
! [Vvar__10455] :
( c_24__type__10454___24t(Vvar__10455)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__10455,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10494',axiom,
! [Vvar__10495] :
( c_24__type__10494___24t(Vvar__10495)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__10495,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_10549',axiom,
! [Vv__CANONICAL__0,Vvar__10550] :
( c_24__type__10549___24t(Vv__CANONICAL__0,Vvar__10550)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__10550,Vv__CANONICAL__1)) ) ) ).
fof('$_type_10562',axiom,
! [Vvar__10563] :
( c_24__type__10562___24t(Vvar__10563)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__10563,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10564',axiom,
! [Vvar__10565] :
( c_24__type__10564___24t(Vvar__10565)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__10565,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10566',axiom,
! [Vvar__10567] :
( c_24__type__10566___24t(Vvar__10567)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10567,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10703',axiom,
! [Vvar__10704] :
( c_24__type__10703___24t(Vvar__10704)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__10704,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1075',axiom,
! [Vvar__1076] :
( c_24__type__1075___24t(Vvar__1076)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1076,Vv__CANONICAL__0)) ) ) ).
fof('$_type_108',axiom,
! [Vv__CANONICAL__0,Vvar__109] :
( c_24__type__108___24t(Vv__CANONICAL__0,Vvar__109)
<=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__109,Vv__CANONICAL__1)) ) ) ).
fof('$_type_1083',axiom,
! [Vvar__1084] :
( c_24__type__1083___24t(Vvar__1084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1084,Vv__CANONICAL__0)) ) ) ).
fof('$_type_10875',axiom,
! [Vvar__10876] :
( c_24__type__10875___24t(Vvar__10876)
<=> ! [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__10876,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10930',axiom,
! [Vvar__10931] :
( c_24__type__10930___24t(Vvar__10931)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(Vvar__10931,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1102',axiom,
! [Vvar__1103] :
( c_24__type__1102___24t(Vvar__1103)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1103,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1118',axiom,
! [Vvar__1119] :
( c_24__type__1118___24t(Vvar__1119)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__1119,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1138',axiom,
! [Vvar__1139] :
( c_24__type__1138___24t(Vvar__1139)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1139,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1143',axiom,
! [Vvar__1144] :
( c_24__type__1143___24t(Vvar__1144)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__1144,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1155',axiom,
! [Vvar__1156] :
( c_24__type__1155___24t(Vvar__1156)
<=> ! [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__1156,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11716',axiom,
! [Vvar__11717] :
( c_24__type__11716___24t(Vvar__11717)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__11717,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11719',axiom,
! [Vvar__11720] :
( c_24__type__11719___24t(Vvar__11720)
<=> ! [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__11720,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11724',axiom,
! [Vvar__11725] :
( c_24__type__11724___24t(Vvar__11725)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__11725,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_11727',axiom,
! [Vvar__11728] :
( c_24__type__11727___24t(Vvar__11728)
<=> ! [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__11728,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12046',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12047] :
( c_24__type__12046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12047)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12047,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12109',axiom,
! [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__12110] :
( c_24__type__12109___24t(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__12110)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12110,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12173] :
( c_24__type__12172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12173)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__12173,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_12226',axiom,
! [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__12227] :
( c_24__type__12226___24t(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__12227)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__12227,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_12289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12290] :
( c_24__type__12289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__12290)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12290,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_12365',axiom,
! [Vvar__12366] :
( c_24__type__12365___24t(Vvar__12366)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__12366,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12423',axiom,
! [Vvar__12424] :
( c_24__type__12423___24t(Vvar__12424)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1906___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__12424,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_12490',axiom,
! [Vvar__12491] :
( c_24__type__12490___24t(Vvar__12491)
<=> ! [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__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__12491,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_12621',axiom,
! [Vvar__12622] :
( c_24__type__12621___24t(Vvar__12622)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__12622,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12646',axiom,
! [Vvar__12647] :
( c_24__type__12646___24t(Vvar__12647)
<=> ! [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__12647,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12797',axiom,
! [Vvar__12798] :
( c_24__type__12797___24t(Vvar__12798)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__12798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12806',axiom,
! [Vvar__12807] :
( c_24__type__12806___24t(Vvar__12807)
<=> ! [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__12807,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12814',axiom,
! [Vvar__12815] :
( c_24__type__12814___24t(Vvar__12815)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__12815,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__13256] :
( c_24__type__13255___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__13256)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13256,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13356',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__13357] :
( c_24__type__13356___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__13357)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13357,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13457',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__13458] :
( c_24__type__13457___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__13458)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__13458,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1352',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1353] :
( c_24__type__1352___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1353)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1353,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__13548] :
( c_24__type__13547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__13548)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__13548,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_13648',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__13649] :
( c_24__type__13648___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__13649)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13649,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_13749',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__13750] :
( c_24__type__13749___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__13750)
<=> ! [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__13750,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_13850',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__13851] :
( c_24__type__13850___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__13851)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__13851,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_14054',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__14055] :
( c_24__type__14054___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__14055)
<=> ! [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__14055,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_14073',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__14074] :
( c_24__type__14073___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__14074)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__14074,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_14093',axiom,
! [Vvar__14094] :
( c_24__type__14093___24t(Vvar__14094)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1915___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__14094,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_14218',axiom,
! [Vvar__14219] :
( c_24__type__14218___24t(Vvar__14219)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__14219,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14223',axiom,
! [Vvar__14224] :
( c_24__type__14223___24t(Vvar__14224)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__14224,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14228',axiom,
! [Vvar__14229] :
( c_24__type__14228___24t(Vvar__14229)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__14229,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14273',axiom,
! [Vvar__14274] :
( c_24__type__14273___24t(Vvar__14274)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14274,Vv__CANONICAL__0)) ) ) ).
fof('$_type_144',axiom,
! [Vvar__145] :
( c_24__type__144___24t(Vvar__145)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__146___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__154___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__166___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__145,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_14434',axiom,
! [Vvar__14435] :
( c_24__type__14434___24t(Vvar__14435)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__14435,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14436',axiom,
! [Vvar__14437] :
( c_24__type__14436___24t(Vvar__14437)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__14437,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14439',axiom,
! [Vvar__14440] :
( c_24__type__14439___24t(Vvar__14440)
<=> ! [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__14440,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14446',axiom,
! [Vvar__14447] :
( c_24__type__14446___24t(Vvar__14447)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__14447,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1445',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__1446] :
( c_24__type__1445___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__1446)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1446,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_14494',axiom,
! [Vvar__14495] :
( c_24__type__14494___24t(Vvar__14495)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__14495,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14511',axiom,
! [Vvar__14512] :
( c_24__type__14511___24t(Vvar__14512)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__14512,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14536',axiom,
! [Vvar__14537] :
( c_24__type__14536___24t(Vvar__14537)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__14537,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_14539',axiom,
! [Vv__CANONICAL__0,Vvar__14540] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vvar__14540)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14540,Vv__CANONICAL__1)) ) ) ).
fof('$_type_14564',axiom,
! [Vvar__14565] :
( c_24__type__14564___24t(Vvar__14565)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__14565,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_146',axiom,
! [Vvar__147] :
( c_24__type__146___24t(Vvar__147)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__147,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14685] :
( c_24__type__14684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14685)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__14685,Vv__CANONICAL__6)) ) ) ).
fof('$_type_14713',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14714] :
( c_24__type__14713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14714)
<=> ! [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__14714,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_14750',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14751] :
( c_24__type__14750___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14751)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
=> cProp___24t(happ(happ(happ(Vvar__14751,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).
fof('$_type_14753',axiom,
! [Vv__CANONICAL__0,Vvar__14754] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vvar__14754)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__14754,Vv__CANONICAL__1)) ) ) ).
fof('$_type_14848',axiom,
! [Vvar__14849] :
( c_24__type__14848___24t(Vvar__14849)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__14849,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_149',axiom,
! [Vv__CANONICAL__0,Vvar__150] :
( c_24__type__149___24t(Vv__CANONICAL__0,Vvar__150)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__150,Vv__CANONICAL__1),happ(Vv__CANONICAL__0,cLambda_2eTerms_2eRef___24a1(Vv__CANONICAL__1))) ) ) ).
fof('$_type_1538',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1539] :
( c_24__type__1538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1539)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1539,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_154',axiom,
! [Vv__CANONICAL__0,Vvar__155] :
( c_24__type__154___24t(Vv__CANONICAL__0,Vvar__155)
<=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__155,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cLambda_2eTerms_2eAbs___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_15427',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15428] :
( c_24__type__15427___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__15428)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15428,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15773',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__15774] :
( c_24__type__15773___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__15774)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15774,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_16119',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__16120] :
( c_24__type__16119___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__16120)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__16120,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__1621] :
( c_24__type__1620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__1621)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__1621,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_16442',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__16443] :
( c_24__type__16442___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__16443)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__16443,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_166',axiom,
! [Vv__CANONICAL__0,Vvar__167] :
( c_24__type__166___24t(Vv__CANONICAL__0,Vvar__167)
<=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__3] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
=> t(happ(happ(happ(happ(Vvar__167,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cLambda_2eTerms_2eApp___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ) ) ).
fof('$_type_16788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__16789] :
( c_24__type__16788___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__16789)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__16789,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_168',axiom,
! [Vvar__169] :
( c_24__type__168___24t(Vvar__169)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__169,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1713',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1714] :
( c_24__type__1713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1714)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1714,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__17135] :
( c_24__type__17134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__17135)
<=> ! [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__17135,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_17480',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__17481] :
( c_24__type__17480___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__17481)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__17481,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_17826',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__17827] :
( c_24__type__17826___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__17827)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__17827,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_1795',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1796] :
( c_24__type__1795___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1796)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__1796,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_18172',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__18173] :
( c_24__type__18172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__18173)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__18173,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_18495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__18496] :
( c_24__type__18495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__18496)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__18496,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_18841',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__18842] :
( c_24__type__18841___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__18842)
<=> ! [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__18842,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_1888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1889] :
( c_24__type__1888___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__1889)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1889,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_1897',axiom,
! [Vv__CANONICAL__0,Vvar__1898] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vvar__1898)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__1898,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_1906',axiom,
! [Vv__CANONICAL__0,Vvar__1907] :
( c_24__type__1906___24t(Vv__CANONICAL__0,Vvar__1907)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__1907,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_1915',axiom,
! [Vv__CANONICAL__0,Vvar__1916] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vvar__1916)
<=> ! [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__1916,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_19187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19188] :
( c_24__type__19187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19188)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__19188,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_19510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__19511] :
( c_24__type__19510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__19511)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__19511,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_19833',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19834] :
( c_24__type__19833___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19834)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__19834,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_20179',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__20180] :
( c_24__type__20179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__20180)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__20180,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20698',axiom,
! [Vvar__20699] :
( c_24__type__20698___24t(Vvar__20699)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(happ(happ(Vvar__20699,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20701',axiom,
! [Vvar__20702] :
( c_24__type__20701___24t(Vvar__20702)
<=> ! [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__20702,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20707',axiom,
! [Vvar__20708] :
( c_24__type__20707___24t(Vvar__20708)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__20708,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_20725',axiom,
! [Vvar__20726] :
( c_24__type__20725___24t(Vvar__20726)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1897___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__20726,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_20816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20817] :
( c_24__type__20816___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20817)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20817,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20839',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20840] :
( c_24__type__20839___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20840)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20840,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20862',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20863] :
( c_24__type__20862___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20863)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20863,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_20885',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20886] :
( c_24__type__20885___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20886)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20886,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20903',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20904] :
( c_24__type__20903___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20904)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__20904,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_20929',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20930] :
( c_24__type__20929___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20930)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20930,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20947',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20948] :
( c_24__type__20947___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__20948)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__20948,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_20963',axiom,
! [Vvar__20964] :
( c_24__type__20963___24t(Vvar__20964)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20964,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_20974',axiom,
! [Vvar__20975] :
( c_24__type__20974___24t(Vvar__20975)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__20975,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_21033',axiom,
! [Vvar__21034] :
( c_24__type__21033___24t(Vvar__21034)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1915___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__21043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__21034,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21044] :
( c_24__type__21043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21044)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__21044,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_21083',axiom,
! [Vvar__21084] :
( c_24__type__21083___24t(Vvar__21084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__21093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__21043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__21084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_21093',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21094] :
( c_24__type__21093___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21094)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__21094,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_21114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21115] :
( c_24__type__21114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21115)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__21115,Vv__CANONICAL__2)) ) ) ).
fof('$_type_21118',axiom,
! [Vvar__21119] :
( c_24__type__21118___24t(Vvar__21119)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__21119,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21136',axiom,
! [Vvar__21137] :
( c_24__type__21136___24t(Vvar__21137)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___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__21137,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_21153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21154] :
( c_24__type__21153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__21154)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__21154,Vv__CANONICAL__2)) ) ) ).
fof('$_type_21157',axiom,
! [Vvar__21158] :
( c_24__type__21157___24t(Vvar__21158)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__21158,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21175',axiom,
! [Vvar__21176] :
( c_24__type__21175___24t(Vvar__21176)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__21176,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21560',axiom,
! [Vvar__21561] :
( c_24__type__21560___24t(Vvar__21561)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__21561,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_21577',axiom,
! [Vvar__21578] :
( c_24__type__21577___24t(Vvar__21578)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__21578,Vv__CANONICAL__0)) ) ) ).
fof('$_type_222',axiom,
! [Vvar__223] :
( c_24__type__222___24t(Vvar__223)
<=> ! [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)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(Vvar__223,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22258',axiom,
! [Vvar__22259] :
( c_24__type__22258___24t(Vvar__22259)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__22259,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22275',axiom,
! [Vvar__22276] :
( c_24__type__22275___24t(Vvar__22276)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__22276,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22295',axiom,
! [Vvar__22296] :
( c_24__type__22295___24t(Vvar__22296)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__22296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22304',axiom,
! [Vvar__22305] :
( c_24__type__22304___24t(Vvar__22305)
<=> ! [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__22305,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22344',axiom,
! [Vvar__22345] :
( c_24__type__22344___24t(Vvar__22345)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__22345,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22359',axiom,
! [Vvar__22360] :
( c_24__type__22359___24t(Vvar__22360)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__22360,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22394',axiom,
! [Vvar__22395] :
( c_24__type__22394___24t(Vvar__22395)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22359___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22359___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22395,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22424',axiom,
! [Vvar__22425] :
( c_24__type__22424___24t(Vvar__22425)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__22425,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22443',axiom,
! [Vvar__22444] :
( c_24__type__22443___24t(Vvar__22444)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vv__CANONICAL__2)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(happ(happ(happ(Vvar__22444,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_22489',axiom,
! [Vvar__22490] :
( c_24__type__22489___24t(Vvar__22490)
<=> ! [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__22490,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22718',axiom,
! [Vvar__22719] :
( c_24__type__22718___24t(Vvar__22719)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__22719,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22755',axiom,
! [Vvar__22756] :
( c_24__type__22755___24t(Vvar__22756)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__22756,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22759',axiom,
! [Vvar__22760] :
( c_24__type__22759___24t(Vvar__22760)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__22760,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22764',axiom,
! [Vvar__22765] :
( c_24__type__22764___24t(Vvar__22765)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__22765,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22767',axiom,
! [Vvar__22768] :
( c_24__type__22767___24t(Vvar__22768)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__22768,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22782',axiom,
! [Vvar__22783] :
( c_24__type__22782___24t(Vvar__22783)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__22783,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22839',axiom,
! [Vvar__22840] :
( c_24__type__22839___24t(Vvar__22840)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__22840,Vv__CANONICAL__0)) ) ) ).
fof('$_type_22876',axiom,
! [Vvar__22877] :
( c_24__type__22876___24t(Vvar__22877)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__22877,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_22906',axiom,
! [Vv__CANONICAL__0,Vvar__22907] :
( c_24__type__22906___24t(Vv__CANONICAL__0,Vvar__22907)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__22907,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_22951',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__22952] :
( c_24__type__22951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__22952)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__22952,Vv__CANONICAL__6)) ) ) ).
fof('$_type_23',axiom,
! [Vvar__24] :
( c_24__type__23___24t(Vvar__24)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__24,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23155',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23156] :
( c_24__type__23155___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23156)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23156,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23248',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23249] :
( c_24__type__23248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23249)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23249,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_233',axiom,
! [Vvar__234] :
( c_24__type__233___24t(Vvar__234)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___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)
=> cLambda_2eTerms_2elambda___24t(happ(happ(happ(Vvar__234,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23341',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23342] :
( c_24__type__23341___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23342)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23342,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23423',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23424] :
( c_24__type__23423___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23424)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__23424,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_23516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23517] :
( c_24__type__23516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__23517)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23517,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23598',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23599] :
( c_24__type__23598___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23599)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__23599,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_236',axiom,
! [Vvar__237] :
( c_24__type__236___24t(Vvar__237)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> cLambda_2eTerms_2elambda___24t(happ(happ(Vvar__237,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_23691',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__23692] :
( c_24__type__23691___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__23692)
<=> ! [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__23692,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_23872',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__23873] :
( c_24__type__23872___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__23873)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23873,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23911',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__23912] :
( c_24__type__23911___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__23912)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23912,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23950',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__23951] :
( c_24__type__23950___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__23951)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23951,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_24192',axiom,
! [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__24193] :
( c_24__type__24192___24t(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__24193)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24193,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24256] :
( c_24__type__24255___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24256)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24256,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24318',axiom,
! [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__24319] :
( c_24__type__24318___24t(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__24319)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24319,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24372',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24373] :
( c_24__type__24372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24373)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__24373,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_24435',axiom,
! [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__24436] :
( c_24__type__24435___24t(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__24436)
<=> ! [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__24436,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_24479',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24480] :
( c_24__type__24479___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24480)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__24480,Vv__CANONICAL__3)) ) ) ).
fof('$_type_24487',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24488] :
( c_24__type__24487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24488)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__24488,Vv__CANONICAL__3)) ) ) ).
fof('$_type_24495',axiom,
! [Vvar__24496] :
( c_24__type__24495___24t(Vvar__24496)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__24496,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24535',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24536] :
( c_24__type__24535___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24536)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24536,Vv__CANONICAL__3)) ) ) ).
fof('$_type_24543',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24544] :
( c_24__type__24543___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__24544)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__24544,Vv__CANONICAL__3)) ) ) ).
fof('$_type_24551',axiom,
! [Vvar__24552] :
( c_24__type__24551___24t(Vvar__24552)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__24552,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_24630',axiom,
! [Vvar__24631] :
( c_24__type__24630___24t(Vvar__24631)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__24631,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25092] :
( c_24__type__25091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25092)
<=> ! [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__25092,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_25255',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25256] :
( c_24__type__25255___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25256)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__25256,Vv__CANONICAL__3)) ) ) ).
fof('$_type_25276',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25277] :
( c_24__type__25276___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__25277)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__25277,Vv__CANONICAL__3)) ) ) ).
fof('$_type_25311',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25312] :
( c_24__type__25311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25312)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__25312,Vv__CANONICAL__5)) ) ) ).
fof('$_type_25319',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25320] :
( c_24__type__25319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__25320)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> cProp___24t(happ(Vvar__25320,Vv__CANONICAL__5)) ) ) ).
fof('$_type_25324',axiom,
! [Vvar__25325] :
( c_24__type__25324___24t(Vvar__25325)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__25325,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_25350',axiom,
! [Vvar__25351] :
( c_24__type__25350___24t(Vvar__25351)
<=> ! [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__25351,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25460',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__25461] :
( c_24__type__25460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__25461)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__25461,Vv__CANONICAL__6)) ) ) ).
fof('$_type_25487',axiom,
! [Vvar__25488] :
( c_24__type__25487___24t(Vvar__25488)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1897___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__25488,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_25537',axiom,
! [Vvar__25538] :
( c_24__type__25537___24t(Vvar__25538)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__25538,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25569',axiom,
! [Vvar__25570] :
( c_24__type__25569___24t(Vvar__25570)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__25570,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25573',axiom,
! [Vvar__25574] :
( c_24__type__25573___24t(Vvar__25574)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25574,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_25591',axiom,
! [Vvar__25592] :
( c_24__type__25591___24t(Vvar__25592)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1897___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__25592,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_25849',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__25850] :
( c_24__type__25849___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__25850)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25850,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2594',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2595] :
( c_24__type__2594___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2595)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__2595,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_25974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__25975] :
( c_24__type__25974___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__25975)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25975,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__26100] :
( c_24__type__26099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__26100)
<=> ! [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__26100,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_26224',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26225] :
( c_24__type__26224___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26225)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__26225,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_26349',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__26350] :
( c_24__type__26349___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__26350)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__26350,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_26474',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26475] :
( c_24__type__26474___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26475)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26475,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_26585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__26586] :
( c_24__type__26585___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__26586)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__26586,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_26805',axiom,
! [Vvar__26806] :
( c_24__type__26805___24t(Vvar__26806)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__26806,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_26847',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__26848] :
( c_24__type__26847___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__26848)
<=> ! [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__26848,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_26882',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26883] :
( c_24__type__26882___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26883)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26883,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_26915',axiom,
! [Vvar__26916] :
( c_24__type__26915___24t(Vvar__26916)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1915___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__26925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__21043___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__26916,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_26925',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26926] :
( c_24__type__26925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__26926)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26926,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_26982',axiom,
! [Vvar__26983] :
( c_24__type__26982___24t(Vvar__26983)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ( p(c_24False)
=> t(happ(Vvar__26983,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27013',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27014] :
( c_24__type__27013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27014)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__27014,Vv__CANONICAL__4)) ) ) ).
fof('$_type_27022',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27023] :
( c_24__type__27022___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27023)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__27023,Vv__CANONICAL__4)) ) ) ).
fof('$_type_27061',axiom,
! [Vvar__27062] :
( c_24__type__27061___24t(Vvar__27062)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__27062,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27114',axiom,
! [Vvar__27115] :
( c_24__type__27114___24t(Vvar__27115)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__27115,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27126',axiom,
! [Vvar__27127] :
( c_24__type__27126___24t(Vvar__27127)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__27127,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_27143',axiom,
! [Vvar__27144] :
( c_24__type__27143___24t(Vvar__27144)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1897___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__27144,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_27205',axiom,
! [Vvar__27206] :
( c_24__type__27205___24t(Vvar__27206)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__27206,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27231',axiom,
! [Vvar__27232] :
( c_24__type__27231___24t(Vvar__27232)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__27232,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27261',axiom,
! [Vvar__27262] :
( c_24__type__27261___24t(Vvar__27262)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__7)
=> cCoq_2eStrings_2eAscii_2eascii___24t(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__27262,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).
fof('$_type_27266',axiom,
! [Vvar__27267] :
( c_24__type__27266___24t(Vvar__27267)
<=> ! [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__27267,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27273',axiom,
! [Vvar__27274] :
( c_24__type__27273___24t(Vvar__27274)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__27274,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27276',axiom,
! [Vvar__27277] :
( c_24__type__27276___24t(Vvar__27277)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__27278___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(Vv__CANONICAL__1)
=> t(happ(happ(Vvar__27277,Vv__CANONICAL__0),Vv__CANONICAL__1),happ(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27278',axiom,
! [Vvar__27279] :
( c_24__type__27278___24t(Vvar__27279)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__27279,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27280',axiom,
! [Vvar__27281] :
( c_24__type__27280___24t(Vvar__27281)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__27281,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27286',axiom,
! [Vv__CANONICAL__0,Vvar__27287] :
( c_24__type__27286___24t(Vv__CANONICAL__0,Vvar__27287)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__27287,Vv__CANONICAL__1)) ) ) ).
fof('$_type_27299',axiom,
! [Vvar__27300] :
( c_24__type__27299___24t(Vvar__27300)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12365___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__27304___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__27300,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27304',axiom,
! [Vv__CANONICAL__0,Vvar__27305] :
( c_24__type__27304___24t(Vv__CANONICAL__0,Vvar__27305)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__27305,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_27309',axiom,
! [Vvar__27310] :
( c_24__type__27309___24t(Vvar__27310)
<=> ! [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__27310,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27314',axiom,
! [Vvar__27315] :
( c_24__type__27314___24t(Vvar__27315)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__27315,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27326',axiom,
! [Vvar__27327] :
( c_24__type__27326___24t(Vvar__27327)
<=> ! [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__27327,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_27352',axiom,
! [Vvar__27353] :
( c_24__type__27352___24t(Vvar__27353)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__27361___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__27353,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ) ) ) ).
fof('$_type_27361',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27362] :
( c_24__type__27361___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27362)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__27362,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27363',axiom,
! [Vvar__27364] :
( c_24__type__27363___24t(Vvar__27364)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__27364,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27376',axiom,
! [Vvar__27377] :
( c_24__type__27376___24t(Vvar__27377)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__27377,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27379',axiom,
! [Vvar__27380] :
( c_24__type__27379___24t(Vvar__27380)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__27380,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27384',axiom,
! [Vvar__27385] :
( c_24__type__27384___24t(Vvar__27385)
<=> ! [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__27385,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27392',axiom,
! [Vvar__27393] :
( c_24__type__27392___24t(Vvar__27393)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__27393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27395',axiom,
! [Vvar__27396] :
( c_24__type__27395___24t(Vvar__27396)
<=> ! [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__27396,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27408',axiom,
! [Vvar__27409] :
( c_24__type__27408___24t(Vvar__27409)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cProp___24t(happ(happ(happ(happ(Vvar__27409,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27417',axiom,
! [Vvar__27418] :
( c_24__type__27417___24t(Vvar__27418)
<=> ! [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__27418,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_27419',axiom,
! [Vvar__27420] :
( c_24__type__27419___24t(Vvar__27420)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(Vvar__27420,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27424',axiom,
! [Vv__CANONICAL__0,Vvar__27425] :
( c_24__type__27424___24t(Vv__CANONICAL__0,Vvar__27425)
<=> ! [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__27425,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_27435',axiom,
! [Vvar__27436] :
( c_24__type__27435___24t(Vvar__27436)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__27424___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__27436,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_27453',axiom,
! [Vvar__27454] :
( c_24__type__27453___24t(Vvar__27454)
<=> ! [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__27454,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_27458',axiom,
! [Vvar__27459] :
( c_24__type__27458___24t(Vvar__27459)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__27459,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27469',axiom,
! [Vvar__27470] :
( c_24__type__27469___24t(Vvar__27470)
<=> ! [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__27470,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_27478',axiom,
! [Vvar__27479] :
( c_24__type__27478___24t(Vvar__27479)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__27479,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_275',axiom,
! [Vvar__276] :
( c_24__type__275___24t(Vvar__276)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cLambda_2eTerms_2elambda___24t(happ(happ(happ(Vvar__276,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_27502',axiom,
! [Vvar__27503] :
( c_24__type__27502___24t(Vvar__27503)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__27503,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_27526',axiom,
! [Vvar__27527] :
( c_24__type__27526___24t(Vvar__27527)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9482___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__27527,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_27555',axiom,
! [Vvar__27556] :
( c_24__type__27555___24t(Vvar__27556)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__27562___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__27556,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_27562',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27563] :
( c_24__type__27562___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27563)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27563,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27602',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27603] :
( c_24__type__27602___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27603)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__27603,Vv__CANONICAL__3)) ) ) ).
fof('$_type_27626',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27627] :
( c_24__type__27626___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27627)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__27627,Vv__CANONICAL__3)) ) ) ).
fof('$_type_27673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27674] :
( c_24__type__27673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__27674)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__27674,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_27708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27709] :
( c_24__type__27708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__27709)
<=> ! [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__27709,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_27745',axiom,
! [Vvar__27746] :
( c_24__type__27745___24t(Vvar__27746)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__27746,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_27768',axiom,
! [Vvar__27769] :
( c_24__type__27768___24t(Vvar__27769)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12814___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12814___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__27769,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28603',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28604] :
( c_24__type__28603___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28604)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28604,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_28628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28629] :
( c_24__type__28628___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28629)
<=> ! [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__28629,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_28700',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28701] :
( c_24__type__28700___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28701)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28701,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_28725',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28726] :
( c_24__type__28725___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__28726)
<=> ! [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__28726,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_28767',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28768] :
( c_24__type__28767___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28768)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28768,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28818',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28819] :
( c_24__type__28818___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28819)
<=> ! [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__28819,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28916',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28917] :
( c_24__type__28916___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28917)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__28917,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_29381',axiom,
! [Vvar__29382] :
( c_24__type__29381___24t(Vvar__29382)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2987___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__29382,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_29460',axiom,
! [Vvar__29461] :
( c_24__type__29460___24t(Vvar__29461)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__29461,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_29472',axiom,
! [Vvar__29473] :
( c_24__type__29472___24t(Vvar__29473)
<=> ! [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__29473,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29474',axiom,
! [Vvar__29475] :
( c_24__type__29474___24t(Vvar__29475)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vv__CANONICAL__0,happ(Vvar__29475,Vv__CANONICAL__0)) ) ) ).
fof('$_type_295',axiom,
! [Vvar__296] :
( c_24__type__295___24t(Vvar__296)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29551',axiom,
! [Vvar__29552] :
( c_24__type__29551___24t(Vvar__29552)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__29552,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_29563',axiom,
! [Vvar__29564] :
( c_24__type__29563___24t(Vvar__29564)
<=> ! [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__29564,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29568',axiom,
! [Vvar__29569] :
( c_24__type__29568___24t(Vvar__29569)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__29569,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29576',axiom,
! [Vvar__29577] :
( c_24__type__29576___24t(Vvar__29577)
<=> ! [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__29577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_29579',axiom,
! [Vvar__29580] :
( c_24__type__29579___24t(Vvar__29580)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__29580,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29584',axiom,
! [Vvar__29585] :
( c_24__type__29584___24t(Vvar__29585)
<=> ! [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__29585,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29804] :
( c_24__type__29803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29804)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29804,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_29846',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29847] :
( c_24__type__29846___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29847)
<=> ! [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__29847,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_2987',axiom,
! [Vv__CANONICAL__0,Vvar__2988] :
( c_24__type__2987___24t(Vv__CANONICAL__0,Vvar__2988)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__2988,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_29885',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29886] :
( c_24__type__29885___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29886)
<=> ! [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__29886,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_29920',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29921] :
( c_24__type__29920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29921)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__29921,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_29955',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29956] :
( c_24__type__29955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29956)
<=> ! [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__29956,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_29975',axiom,
! [Vvar__29976] :
( c_24__type__29975___24t(Vvar__29976)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14539___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__29976,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_29997',axiom,
! [Vvar__29998] :
( c_24__type__29997___24t(Vvar__29998)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14753___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esigT2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__29998,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_30015',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30016] :
( c_24__type__30015___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30016)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30016,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30021',axiom,
! [Vvar__30022] :
( c_24__type__30021___24t(Vvar__30022)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14539___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__30022,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_30038',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30039] :
( c_24__type__30038___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__30039)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__30039,Vv__CANONICAL__2)) ) ) ).
fof('$_type_30044',axiom,
! [Vvar__30045] :
( c_24__type__30044___24t(Vvar__30045)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14753___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__30045,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_30050',axiom,
! [Vvar__30051] :
( c_24__type__30050___24t(Vvar__30051)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__30051,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30055',axiom,
! [Vvar__30056] :
( c_24__type__30055___24t(Vvar__30056)
<=> ! [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__30056,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_30058',axiom,
! [Vvar__30059] :
( c_24__type__30058___24t(Vvar__30059)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__30059,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30066',axiom,
! [Vvar__30067] :
( c_24__type__30066___24t(Vvar__30067)
<=> ! [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__30067,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30084',axiom,
! [Vvar__30085] :
( c_24__type__30084___24t(Vvar__30085)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__30085,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_30101',axiom,
! [Vvar__30102] :
( c_24__type__30101___24t(Vvar__30102)
<=> ! [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__30102,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3011',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3012] :
( c_24__type__3011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3012)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__3012,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_30134',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30135] :
( c_24__type__30134___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30135)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30135,Vv__CANONICAL__4)) ) ) ).
fof('$_type_30164',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30165] :
( c_24__type__30164___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__30165)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__30165,Vv__CANONICAL__4)) ) ) ).
fof('$_type_30230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30231] :
( c_24__type__30230___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30231)
<=> ! [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__30231,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_3025',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3026] :
( c_24__type__3025___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3026)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__3026,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_30286',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30287] :
( c_24__type__30286___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30287)
<=> ! [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__30287,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_30292',axiom,
! [Vvar__30293] :
( c_24__type__30292___24t(Vvar__30293)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__1915___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30293,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30304',axiom,
! [Vvar__30305] :
( c_24__type__30304___24t(Vvar__30305)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__30307___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__30305,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30307',axiom,
! [Vv__CANONICAL__0,Vvar__30308] :
( c_24__type__30307___24t(Vv__CANONICAL__0,Vvar__30308)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__30308,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3032',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3033] :
( c_24__type__3032___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3033)
<=> ! [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__3033,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_30485',axiom,
! [Vvar__30486] :
( c_24__type__30485___24t(Vvar__30486)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__30486,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30522',axiom,
! [Vvar__30523] :
( c_24__type__30522___24t(Vvar__30523)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__30527___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__30523,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_30527',axiom,
! [Vv__CANONICAL__0,Vvar__30528] :
( c_24__type__30527___24t(Vv__CANONICAL__0,Vvar__30528)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30528,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30544',axiom,
! [Vvar__30545] :
( c_24__type__30544___24t(Vvar__30545)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__30549___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__30545,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_30549',axiom,
! [Vv__CANONICAL__0,Vvar__30550] :
( c_24__type__30549___24t(Vv__CANONICAL__0,Vvar__30550)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30550,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30562',axiom,
! [Vvar__30563] :
( c_24__type__30562___24t(Vvar__30563)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__30563,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30574',axiom,
! [Vvar__30575] :
( c_24__type__30574___24t(Vvar__30575)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__30575,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30600',axiom,
! [Vvar__30601] :
( c_24__type__30600___24t(Vvar__30601)
<=> ! [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__30601,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30620',axiom,
! [Vvar__30621] :
( c_24__type__30620___24t(Vvar__30621)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__30621,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30650',axiom,
! [Vvar__30651] :
( c_24__type__30650___24t(Vvar__30651)
<=> ! [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__30651,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30657',axiom,
! [Vvar__30658] :
( c_24__type__30657___24t(Vvar__30658)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__30658,Vv__CANONICAL__0)) ) ) ).
fof('$_type_30683',axiom,
! [Vvar__30684] :
( c_24__type__30683___24t(Vvar__30684)
<=> ! [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__30684,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30689',axiom,
! [Vvar__30690] :
( c_24__type__30689___24t(Vvar__30690)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30690,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30706',axiom,
! [Vvar__30707] :
( c_24__type__30706___24t(Vvar__30707)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__22782___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__22782___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__30707,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3438',axiom,
! [Vvar__3439] :
( c_24__type__3438___24t(Vvar__3439)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3439,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3615',axiom,
! [Vvar__3616] :
( c_24__type__3615___24t(Vvar__3616)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__2987___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__3616,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3864',axiom,
! [Vvar__3865] :
( c_24__type__3864___24t(Vvar__3865)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__3865,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3869',axiom,
! [Vvar__3870] :
( c_24__type__3869___24t(Vvar__3870)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [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__3870,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5241',axiom,
! [Vvar__5242] :
( c_24__type__5241___24t(Vvar__5242)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__1897___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__5242,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_53',axiom,
! [Vvar__54] :
( c_24__type__53___24t(Vvar__54)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__54,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5495',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5496] :
( c_24__type__5495___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5496)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5496,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5558',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5559] :
( c_24__type__5558___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5559)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5559,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5621',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5622] :
( c_24__type__5621___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5622)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5622,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5675',axiom,
! [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__5676] :
( c_24__type__5675___24t(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__5676)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__5676,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_5738',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5739] :
( c_24__type__5738___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5739)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5739,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_5945',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__5946] :
( c_24__type__5945___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__5946)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5946,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5975',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__5976] :
( c_24__type__5975___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__5976)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5976,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5999',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6000] :
( c_24__type__5999___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6000)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__6000,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_6',axiom,
! [Vvar__7] :
( c_24__type__6___24t(Vvar__7)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__7,Vv__CANONICAL__0)) ) ) ).
fof('$_type_6029',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6030] :
( c_24__type__6029___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6030)
<=> ! [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__6030,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_6059',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6060] :
( c_24__type__6059___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6060)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6060,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6083',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6084] :
( c_24__type__6083___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6084)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__6084,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_6116',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6117] :
( c_24__type__6116___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6117)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6117,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6140',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6141] :
( c_24__type__6140___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6141)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__6141,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_6167',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6168] :
( c_24__type__6167___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__6168)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__6168,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_6566',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__6567] :
( c_24__type__6566___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__6567)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6567,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6779',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__6780] :
( c_24__type__6779___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__6780)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6780,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_6992',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__6993] :
( c_24__type__6992___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__6993)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6993,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7188] :
( c_24__type__7187___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7188)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__7188,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_7400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__7401] :
( c_24__type__7400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__7401)
<=> ! [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__7401,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_7613',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7614] :
( c_24__type__7613___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7614)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__7614,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_7826',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__7827] :
( c_24__type__7826___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__7827)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__7827,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_8039',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8040] :
( c_24__type__8039___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8040)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__8040,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_8234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__8235] :
( c_24__type__8234___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,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__8235)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__8235,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_8447',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8448] :
( c_24__type__8447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8448)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8448,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_852',axiom,
! [Vvar__853] :
( c_24__type__852___24t(Vvar__853)
<=> ! [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__853,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_855',axiom,
! [Vvar__856] :
( c_24__type__855___24t(Vvar__856)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__856,Vv__CANONICAL__0)) ) ) ).
fof('$_type_858',axiom,
! [Vvar__859] :
( c_24__type__858___24t(Vvar__859)
<=> ! [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__859,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8642',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8643] :
( c_24__type__8642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8643)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__8643,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_8784',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__8785] :
( c_24__type__8784___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__8785)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__8785,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_8803',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__8804] :
( c_24__type__8803___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__8804)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8804,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_8817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__8818] :
( c_24__type__8817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__8818)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__8818,Vv__CANONICAL__4)) ) ) ).
fof('$_type_890',axiom,
! [Vvar__891] :
( c_24__type__890___24t(Vvar__891)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__891,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_896',axiom,
! [Vvar__897] :
( c_24__type__896___24t(Vvar__897)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__897,Vv__CANONICAL__0)) ) ) ).
fof('$_type_8962',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__8963] :
( c_24__type__8962___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__8963)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8963,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_9012',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9013] :
( c_24__type__9012___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9013)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__9013,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_9062',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9063] :
( c_24__type__9062___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9063)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__9063,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_909',axiom,
! [Vvar__910] :
( c_24__type__909___24t(Vvar__910)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__910,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9104',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9105] :
( c_24__type__9104___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9105)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__9105,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_9154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9155] :
( c_24__type__9154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9155)
<=> ! [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__9155,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_9230',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9231] :
( c_24__type__9230___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9231)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__9231,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_933',axiom,
! [Vvar__934] :
( c_24__type__933___24t(Vvar__934)
<=> ! [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__934,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9339',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9340] :
( c_24__type__9339___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9340)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9340,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9383',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9384] :
( c_24__type__9383___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9384)
<=> ! [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__9384,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_94',axiom,
! [Vvar__95] :
( c_24__type__94___24t(Vvar__95)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cLambda_2eTerms_2elambda___24t(happ(Vvar__95,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9420] :
( c_24__type__9419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9420)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__9420,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_945',axiom,
! [Vvar__946] :
( c_24__type__945___24t(Vvar__946)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__946,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_9463',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9464] :
( c_24__type__9463___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__9464)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__9464,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9482',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9483] :
( c_24__type__9482___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9483)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__9483,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_950',axiom,
! [Vvar__951] :
( c_24__type__950___24t(Vvar__951)
<=> ! [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__951,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_9539',axiom,
! [Vvar__9540] :
( c_24__type__9539___24t(Vvar__9540)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__9540,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9553',axiom,
! [Vvar__9554] :
( c_24__type__9553___24t(Vvar__9554)
<=> ! [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__9554,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9592',axiom,
! [Vvar__9593] :
( c_24__type__9592___24t(Vvar__9593)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__9593,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_96',axiom,
! [Vvar__97] :
( c_24__type__96___24t(Vvar__97)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> cLambda_2eTerms_2elambda___24t(happ(Vvar__97,Vv__CANONICAL__0)) ) ) ).
fof('$_type_976',axiom,
! [Vvar__977] :
( c_24__type__976___24t(Vvar__977)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__977,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9776',axiom,
! [Vvar__9777] :
( c_24__type__9776___24t(Vvar__9777)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__9777,Vv__CANONICAL__0)) ) ) ).
fof('$_type_989',axiom,
! [Vvar__990] :
( c_24__type__989___24t(Vvar__990)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__990,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_99',axiom,
! [Vvar__100] :
( c_24__type__99___24t(Vvar__100)
<=> ! [Vv__CANONICAL__0] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cLambda_2eTerms_2elambda___24t(Vv__CANONICAL__1)
=> cLambda_2eTerms_2elambda___24t(happ(happ(Vvar__100,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__27266___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__10___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__30562___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__10___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
c_24__type__10___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__27768___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
c_24__type__10___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
c_24__type__10___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__30544___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
c_24__type__933___24t(cCoq_2eArith_2ePlus_2etail__plus) ).
fof('$_typeof_Coq.Arith.Wf_nat.gtof',axiom,
c_24__type__30304___24t(cCoq_2eArith_2eWf__nat_2egtof) ).
fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
c_24__type__30304___24t(cCoq_2eArith_2eWf__nat_2eltof) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__10435___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__10427___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
c_24__type__25324___24t(cCoq_2eBool_2eBool_2eifb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__22876___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
c_24__type__12365___24t(cCoq_2eBool_2eBvector_2eBvector) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__12814___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__9553___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__22718___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__22443___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Subset',axiom,
c_24__type__9553___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eSubset) ).
fof('$_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__9553___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__22489___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_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('$_typeof_Coq.Init.Byte.byte_of_byte',axiom,
c_24__type__27273___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).
fof('$_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__10564___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__25350___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set) ).
fof('$_typeof_Coq.Init.Datatypes.Empty_set_rect',axiom,
c_24__type__27276___24t(cCoq_2eInit_2eDatatypes_2eEmpty__set__rect) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__10454___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__6___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__10452___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__10427___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__1155___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__1143___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__10494___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.id',axiom,
cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).
fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
c_24__type__10427___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).
fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
c_24__type__27309___24t(cCoq_2eInit_2eDatatypes_2einl) ).
fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
c_24__type__27314___24t(cCoq_2eInit_2eDatatypes_2einr) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__10562___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__1083___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nat_rect',axiom,
c_24__type__27299___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__10431___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__1138___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__1083___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__10427___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__1118___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__1102___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.prod_curry',axiom,
c_24__type__27352___24t(cCoq_2eInit_2eDatatypes_2eprod__curry) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__27326___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__1102___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__10427___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Decimal.D0',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD0) ).
fof('$_typeof_Coq.Init.Decimal.D1',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD1) ).
fof('$_typeof_Coq.Init.Decimal.D2',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD2) ).
fof('$_typeof_Coq.Init.Decimal.D3',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD3) ).
fof('$_typeof_Coq.Init.Decimal.D4',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD4) ).
fof('$_typeof_Coq.Init.Decimal.D5',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD5) ).
fof('$_typeof_Coq.Init.Decimal.D6',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD6) ).
fof('$_typeof_Coq.Init.Decimal.D7',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD7) ).
fof('$_typeof_Coq.Init.Decimal.D8',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD8) ).
fof('$_typeof_Coq.Init.Decimal.D9',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2eD9) ).
fof('$_typeof_Coq.Init.Decimal.Neg',axiom,
c_24__type__27363___24t(cCoq_2eInit_2eDecimal_2eNeg) ).
fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).
fof('$_typeof_Coq.Init.Decimal.Pos',axiom,
c_24__type__27363___24t(cCoq_2eInit_2eDecimal_2ePos) ).
fof('$_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__27376___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).
fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2enzhead) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
c_24__type__10703___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).
fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
c_24__type__25537___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__933___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__12806___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__12797___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__12814___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__933___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.leb',axiom,
c_24__type__12797___24t(cCoq_2eInit_2eNat_2eleb) ).
fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
c_24__type__27745___24t(cCoq_2eInit_2eNat_2elog2__iter) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__933___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__933___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__933___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__933___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sqrt_iter',axiom,
c_24__type__27745___24t(cCoq_2eInit_2eNat_2esqrt__iter) ).
fof('$_typeof_Coq.Init.Nat.square',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2esquare) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__933___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.succ',axiom,
c_24__type__6___24t(cCoq_2eInit_2eNat_2esucc) ).
fof('$_typeof_Coq.Init.Nat.t',axiom,
cType___24t(cCoq_2eInit_2eNat_2et) ).
fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
c_24__type__933___24t(cCoq_2eInit_2eNat_2etail__add) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__12797___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__10447___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__10___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__10___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__10___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.Exc',axiom,
c_24__type__1083___24t(cCoq_2eInit_2eSpecif_2eExc) ).
fof('$_typeof_Coq.Init.Specif.except',axiom,
c_24__type__26982___24t(cCoq_2eInit_2eSpecif_2eexcept) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__21136___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.exist2',axiom,
c_24__type__29975___24t(cCoq_2eInit_2eSpecif_2eexist2) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__21175___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.existT2',axiom,
c_24__type__29997___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__30050___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__30055___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__945___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__30021___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__30044___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__950___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__21118___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__24495___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__21157___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__24551___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__23___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__53___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__30292___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__12621___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__27526___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__27555___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.hd',axiom,
c_24__type__27469___24t(cCoq_2eLists_2eList_2ehd) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__27502___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__12646___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.List.tl',axiom,
c_24__type__27478___24t(cCoq_2eLists_2eList_2etl) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_op',axiom,
c_24__type__21083___24t(cCoq_2eLists_2eSetoidList_2ecompat__op) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__21033___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
c_24__type__21033___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
c_24__type__26915___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
c_24__type__26915___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__10566___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__27408___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
c_24__type__25537___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__27417___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__852___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
c_24__type__852___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__22394___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__852___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__852___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__30522___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__976___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__22295___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
c_24__type__22275___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__22275___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__22304___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__22359___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.land',axiom,
c_24__type__976___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eland) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
c_24__type__976___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__976___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__976___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__976___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__22275___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__22275___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_pos',axiom,
c_24__type__30485___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__22304___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__22344___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).
fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
c_24__type__27768___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).
fof('$_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__9776___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__909___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__909___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__1075___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__1075___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
c_24__type__27205___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
c_24__type__989___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__989___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__989___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__30683___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).
fof('$_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__27114___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__30600___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
c_24__type__1075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2_up',axiom,
c_24__type__1075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
c_24__type__30620___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__27126___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__27143___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__9592___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__9592___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__9592___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__30657___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__30657___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size',axiom,
c_24__type__1075___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
c_24__type__30574___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__9592___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__1075___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__30650___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__14228___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__14218___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
c_24__type__14223___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__14273___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_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('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__14511___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).
fof('$_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('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__3438___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__3438___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__14273___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__3438___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__3438___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__14494___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__14273___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__14494___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__25569___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__14848___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__26805___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__1083___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__26805___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__26805___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__26805___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__1083___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
c_24__type__27261___24t(cCoq_2eStrings_2eAscii_2eAscii) ).
fof('$_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__30058___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__27435___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).
fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
c_24__type__27435___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__14093___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__852___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
c_24__type__852___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__10___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__10___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
c_24__type__989___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__989___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
c_24__type__989___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
c_24__type__989___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
c_24__type__989___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__30689___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__890___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
c_24__type__890___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).
fof('$_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('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__12365___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__21577___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__21560___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__22839___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__890___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
c_24__type__890___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__30706___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__890___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__890___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__890___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__890___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__855___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
c_24__type__22759___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
c_24__type__22755___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__1030___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
c_24__type__22782___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__9539___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
c_24__type__22782___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__22767___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__22764___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.one',axiom,
cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eone) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__855___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__855___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__858___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__855___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__22759___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
c_24__type__22755___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__27231___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__9539___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zcomplements.floor_pos',axiom,
c_24__type__1075___24t(cCoq_2eZArith_2eZcomplements_2efloor__pos) ).
fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
c_24__type__896___24t(cCoq_2eZArith_2eZeven_2eZeven) ).
fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
c_24__type__896___24t(cCoq_2eZArith_2eZeven_2eZodd) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
c_24__type__22424___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).
fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
c_24__type__909___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).
fof('$_typeof_Coq.ZArith.Znat.neq',axiom,
c_24__type__10___24t(cCoq_2eZArith_2eZnat_2eneq) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__14848___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__27061___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__10875___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__27379___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__27392___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__10930___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__27384___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).
fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
c_24__type__27395___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__27395___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('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
c_24__type__14446___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).
fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
c_24__type__14439___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).
fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
c_24__type__14439___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).
fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
c_24__type__14446___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).
fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
c_24__type__14439___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).
fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
c_24__type__14434___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).
fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
c_24__type__14436___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__14564___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__14536___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__1083___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('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzC',axiom,
c_24__type__29472___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzC) ).
fof('$_typeof_Coq.micromega.RingMicromega.PsatzZ',axiom,
c_24__type__29474___24t(cCoq_2emicromega_2eRingMicromega_2ePsatzZ) ).
fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).
fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
c_24__type__29381___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__29460___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__29551___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
c_24__type__12797___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__30101___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__30066___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__24630___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
c_24__type__24630___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__30066___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__30084___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__1102___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__1083___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZCoeff.gen_order_phi_Z',axiom,
c_24__type__12423___24t(cCoq_2emicromega_2eZCoeff_2egen__order__phi__Z) ).
fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).
fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
c_24__type__22258___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).
fof('$_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('$_typeof_Coq.micromega.ZMicromega.isZ0',axiom,
c_24__type__22782___24t(cCoq_2emicromega_2eZMicromega_2eisZ0) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
c_24__type__22767___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).
fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
c_24__type__22764___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
c_24__type__909___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).
fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
c_24__type__909___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).
fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
c_24__type__22344___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEI',axiom,
c_24__type__27419___24t(cCoq_2esetoid__ring_2eField__theory_2eFEI) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEO',axiom,
c_24__type__27419___24t(cCoq_2esetoid__ring_2eField__theory_2eFEO) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__11719___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__11716___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__11727___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__11724___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__1083___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__1083___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__1083___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__22275___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('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__12490___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__25487___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__25487___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__12423___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.hypo_type',axiom,
c_24__type__27458___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo__type) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.mkhypo',axiom,
c_24__type__27453___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__10427___24t(cCoq_2esetoid__ring_2eRing_2ebool__eq) ).
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__29579___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
c_24__type__29579___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__3864___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__3869___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__20701___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__3869___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__20707___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__29584___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__3869___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__1083___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
c_24__type__29576___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
c_24__type__29563___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__3615___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
c_24__type__29568___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__1083___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
c_24__type__25591___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
c_24__type__20698___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
c_24__type__20698___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('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__20963___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__20963___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__20974___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__22275___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__5241___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__20725___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).
fof('$_typeof_Hammer.Tactics.Reconstr.AllHyps',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).
fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).
fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).
fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
c_24__type__25573___24t(cHammer_2eTactics_2eReconstr_2erdone) ).
fof('$_typeof_Hammer.Tactics.Tactics.default',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2edefault) ).
fof('$_typeof_Hammer.Tactics.Tactics.hints',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2ehints) ).
fof('$_typeof_Hammer.Tactics.Tactics.logic',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2elogic) ).
fof('$_typeof_Hammer.Tactics.Tactics.nohints',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2enohints) ).
fof('$_typeof_Hammer.Tactics.Tactics.none',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cHammer_2eTactics_2eTactics_2enone) ).
fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
c_24__type__25573___24t(cHammer_2eTactics_2eTactics_2erdone) ).
fof('$_typeof_Lambda.Terms.Abs',axiom,
c_24__type__96___24t(cLambda_2eTerms_2eAbs) ).
fof('$_typeof_Lambda.Terms.App',axiom,
c_24__type__99___24t(cLambda_2eTerms_2eApp) ).
fof('$_typeof_Lambda.Terms.Ref',axiom,
c_24__type__94___24t(cLambda_2eTerms_2eRef) ).
fof('$_typeof_Lambda.Terms.lambda',axiom,
cType___24t(cLambda_2eTerms_2elambda) ).
fof('$_typeof_Lambda.Terms.lambda_rec',axiom,
c_24__type__144___24t(cLambda_2eTerms_2elambda__rec) ).
fof('$_typeof_Lambda.Terms.lambda_rect',axiom,
c_24__type__144___24t(cLambda_2eTerms_2elambda__rect) ).
fof('$_typeof_Lambda.Terms.lift',axiom,
c_24__type__236___24t(cLambda_2eTerms_2elift) ).
fof('$_typeof_Lambda.Terms.lift_rec',axiom,
c_24__type__233___24t(cLambda_2eTerms_2elift__rec) ).
fof('$_typeof_Lambda.Terms.relocate',axiom,
c_24__type__222___24t(cLambda_2eTerms_2erelocate) ).
fof('$_typeof_Lambda.Terms.subst',axiom,
c_24__type__99___24t(cLambda_2eTerms_2esubst) ).
fof('$_typeof_Lambda.Terms.subst_rec',axiom,
c_24__type__275___24t(cLambda_2eTerms_2esubst__rec) ).
fof('Coq.Arith.PeanoNat.Nat.A\'A_left',axiom,
! [V0__A] :
( c_24__type__10447___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [Vvar__4__m__30554] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__m__30554)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__4__m__30554,V1__z))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V2__n,Vvar__4__m__30554))
=> p(happ(V0__A,Vvar__4__m__30554)) ) ) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V1__z))
=> p(happ(V0__A,V3__n)) ) ) ) ) ) ).
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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ( p(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)
=> p(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)
=> ( ~ p(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)
=> p(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_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> p(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
=> p(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)
=> p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_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)
=> ( p(cCoq_2eInit_2ePeano_2ele___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.le_refl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p))
=> 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)
| p(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)
=> p(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)
=> ( p(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__10___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__10447___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.Bool.Bool.absurd_eq_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( p(c_24False)
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.trans_eq_bool',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Init.Datatypes.Empty_set_ind',axiom,
! [V0__P] :
( c_24__type__27280___24t(V0__P)
=> ! [V1__e] :
( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(V1__e)
=> p(happ(V0__P,V1__e)) ) ) ).
fof('Coq.Init.Datatypes.Empty_set_sind',axiom,
! [V0__P] :
( c_24__type__27280___24t(V0__P)
=> ! [V1__e] :
( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(V1__e)
=> p(happ(V0__P,V1__e)) ) ) ).
fof('Coq.Init.Datatypes.idProp',axiom,
p(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__10549___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ).
fof('Coq.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__10447___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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.nat_case',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__P] :
( c_24__type__10447___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__m))) )
=> p(happ(V1__P,V0__n)) ) ) ) ) ).
fof('Coq.Init.Peano.nat_double_ind',axiom,
! [V0__R] :
( c_24__type__10___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.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',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.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__14753___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.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.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.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.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__22424___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_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__1906___24t(V1__A,V2__f)
=> ! [V3__Inv] :
( c_24__type__14539___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.QArith.QArith_base.Qeq_refl',axiom,
! [V0__x] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__x)
=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V0__x,V0__x) ) ).
fof('Coq.Reals.RIneq.Rge_refl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r,V0__r) ) ).
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.Reals.RIneq.Rle_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V2__r3) ) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.Raxioms.Rlt_trans',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ! [V2__r3] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r3)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V2__r3)
=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V2__r3) ) ) ) ) ) ).
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__896___24t(V0__A)
=> ! [V1__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [Vvar__4__m__30697] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__m__30697)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vvar__4__m__30697,V1__z))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__n,Vvar__4__m__30697))
=> p(happ(V0__A,Vvar__4__m__30697)) ) ) ) )
=> ! [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_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( 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.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ 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.Private_Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).
fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__30696___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.eq_sym_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
<=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( 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_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
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.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__890,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__896,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),c_3c_3d_3e)),cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.ZArith.BinInt.Z.lt_1_2',axiom,
p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)))) ).
fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_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_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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__1897___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__1897___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__1897___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__1915___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__1915___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.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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_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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),V1__rO)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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.ARdistr_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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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,happ(happ(V3__radd,V9__x),V10__y)),V11__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V9__x),V11__z)),happ(happ(V4__rmul,V10__y),V11__z)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.mk_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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__1897___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__1906___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__1915___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__1897___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__1897___24t(V0__R,V4__rmul)
=> ! [V5__req] :
( c_24__type__1915___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('Lambda.Terms.lambda_ind',axiom,
! [V0__P] :
( c_24__type__168___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> p(happ(V0__P,cLambda_2eTerms_2eRef___24a1(V1__n))) )
=> ( ! [V2__l] :
( cLambda_2eTerms_2elambda___24t(V2__l)
=> ( p(happ(V0__P,V2__l))
=> p(happ(V0__P,cLambda_2eTerms_2eAbs___24a1(V2__l))) ) )
=> ( ! [V3__l] :
( cLambda_2eTerms_2elambda___24t(V3__l)
=> ( p(happ(V0__P,V3__l))
=> ! [V5__l] :
( cLambda_2eTerms_2elambda___24t(V5__l)
=> ( p(happ(V0__P,V5__l))
=> p(happ(V0__P,cLambda_2eTerms_2eApp___24a2(V3__l,V5__l))) ) ) ) )
=> ! [V4__l] :
( cLambda_2eTerms_2elambda___24t(V4__l)
=> p(happ(V0__P,V4__l)) ) ) ) ) ) ).
fof('Reduction.abs_par_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ( cReduction_2epar__red1___24a2(V0__M,V1__M_27)
=> cReduction_2epar__red1___24a2(cLambda_2eTerms_2eAbs___24a1(V0__M),cLambda_2eTerms_2eAbs___24a1(V1__M_27)) ) ) ) ).
fof('Reduction.abs_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ( cReduction_2ered1___24a2(V0__M,V1__N)
=> cReduction_2ered1___24a2(cLambda_2eTerms_2eAbs___24a1(V0__M),cLambda_2eTerms_2eAbs___24a1(V1__N)) ) ) ) ).
fof('Reduction.app_par_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ( cReduction_2epar__red1___24a2(V0__M,V1__M_27)
=> ! [V3__N] :
( cLambda_2eTerms_2elambda___24t(V3__N)
=> ! [V4__N_27] :
( cLambda_2eTerms_2elambda___24t(V4__N_27)
=> ( cReduction_2epar__red1___24a2(V3__N,V4__N_27)
=> cReduction_2epar__red1___24a2(cLambda_2eTerms_2eApp___24a2(V0__M,V3__N),cLambda_2eTerms_2eApp___24a2(V1__M_27,V4__N_27)) ) ) ) ) ) ) ).
fof('Reduction.app_red_l',axiom,
! [V0__M1] :
( cLambda_2eTerms_2elambda___24t(V0__M1)
=> ! [V1__N1] :
( cLambda_2eTerms_2elambda___24t(V1__N1)
=> ( cReduction_2ered1___24a2(V0__M1,V1__N1)
=> ! [V3__M2] :
( cLambda_2eTerms_2elambda___24t(V3__M2)
=> cReduction_2ered1___24a2(cLambda_2eTerms_2eApp___24a2(V0__M1,V3__M2),cLambda_2eTerms_2eApp___24a2(V1__N1,V3__M2)) ) ) ) ) ).
fof('Reduction.app_red_r',axiom,
! [V0__M2] :
( cLambda_2eTerms_2elambda___24t(V0__M2)
=> ! [V1__N2] :
( cLambda_2eTerms_2elambda___24t(V1__N2)
=> ( cReduction_2ered1___24a2(V0__M2,V1__N2)
=> ! [V3__M1] :
( cLambda_2eTerms_2elambda___24t(V3__M1)
=> cReduction_2ered1___24a2(cLambda_2eTerms_2eApp___24a2(V3__M1,V0__M2),cLambda_2eTerms_2eApp___24a2(V3__M1,V1__N2)) ) ) ) ) ).
fof('Reduction.beta',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> cReduction_2ered1___24a2(cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(V0__M),V1__N),cLambda_2eTerms_2esubst___24a2(V1__N,V0__M)) ) ) ).
fof('Reduction.one_step_par_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ( cReduction_2epar__red1___24a2(V0__M,V1__N)
=> cReduction_2epar__red___24a2(V0__M,V1__N) ) ) ) ).
fof('Reduction.one_step_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ( cReduction_2ered1___24a2(V0__M,V1__N)
=> cReduction_2ered___24a2(V0__M,V1__N) ) ) ) ).
fof('Reduction.par_beta',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ( cReduction_2epar__red1___24a2(V0__M,V1__M_27)
=> ! [V3__N] :
( cLambda_2eTerms_2elambda___24t(V3__N)
=> ! [V4__N_27] :
( cLambda_2eTerms_2elambda___24t(V4__N_27)
=> ( cReduction_2epar__red1___24a2(V3__N,V4__N_27)
=> cReduction_2epar__red1___24a2(cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(V0__M),V3__N),cLambda_2eTerms_2esubst___24a2(V4__N_27,V1__M_27)) ) ) ) ) ) ) ).
fof('Reduction.par_red_ind',axiom,
! [V0__P] :
( c_24__type__295___24t(V0__P)
=> ( ! [V1__M] :
( cLambda_2eTerms_2elambda___24t(V1__M)
=> ! [V2__N] :
( cLambda_2eTerms_2elambda___24t(V2__N)
=> ( cReduction_2epar__red1___24a2(V1__M,V2__N)
=> p(happ(happ(V0__P,V1__M),V2__N)) ) ) )
=> ( ! [V2__M] :
( cLambda_2eTerms_2elambda___24t(V2__M)
=> ! [V3__N] :
( cLambda_2eTerms_2elambda___24t(V3__N)
=> ! [V4__P] :
( cLambda_2eTerms_2elambda___24t(V4__P)
=> ( cReduction_2epar__red___24a2(V2__M,V3__N)
=> ( p(happ(happ(V0__P,V2__M),V3__N))
=> ( cReduction_2epar__red___24a2(V3__N,V4__P)
=> ( p(happ(happ(V0__P,V3__N),V4__P))
=> p(happ(happ(V0__P,V2__M),V4__P)) ) ) ) ) ) ) )
=> ! [V3__l] :
( cLambda_2eTerms_2elambda___24t(V3__l)
=> ! [V4__l] :
( cLambda_2eTerms_2elambda___24t(V4__l)
=> ( cReduction_2epar__red___24a2(V3__l,V4__l)
=> p(happ(happ(V0__P,V3__l),V4__l)) ) ) ) ) ) ) ).
fof('Reduction.red1_par_red1',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ( cReduction_2ered1___24a2(V0__M,V1__N)
=> cReduction_2epar__red1___24a2(V0__M,V1__N) ) ) ) ).
fof('Reduction.red_abs',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ( cReduction_2ered___24a2(V0__M,V1__M_27)
=> cReduction_2ered___24a2(cLambda_2eTerms_2eAbs___24a1(V0__M),cLambda_2eTerms_2eAbs___24a1(V1__M_27)) ) ) ) ).
fof('Reduction.red_app',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ! [V2__N] :
( cLambda_2eTerms_2elambda___24t(V2__N)
=> ! [V3__N_27] :
( cLambda_2eTerms_2elambda___24t(V3__N_27)
=> ( cReduction_2ered___24a2(V0__M,V1__M_27)
=> ( cReduction_2ered___24a2(V2__N,V3__N_27)
=> cReduction_2ered___24a2(cLambda_2eTerms_2eApp___24a2(V0__M,V2__N),cLambda_2eTerms_2eApp___24a2(V1__M_27,V3__N_27)) ) ) ) ) ) ) ).
fof('Reduction.red_appl',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ( cReduction_2ered___24a2(V0__M,V1__M_27)
=> ! [V3__N] :
( cLambda_2eTerms_2elambda___24t(V3__N)
=> cReduction_2ered___24a2(cLambda_2eTerms_2eApp___24a2(V0__M,V3__N),cLambda_2eTerms_2eApp___24a2(V1__M_27,V3__N)) ) ) ) ) ).
fof('Reduction.red_appr',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ( cReduction_2ered___24a2(V0__M,V1__M_27)
=> ! [V3__N] :
( cLambda_2eTerms_2elambda___24t(V3__N)
=> cReduction_2ered___24a2(cLambda_2eTerms_2eApp___24a2(V3__N,V0__M),cLambda_2eTerms_2eApp___24a2(V3__N,V1__M_27)) ) ) ) ) ).
fof('Reduction.red_beta',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__M_27] :
( cLambda_2eTerms_2elambda___24t(V1__M_27)
=> ! [V2__N] :
( cLambda_2eTerms_2elambda___24t(V2__N)
=> ! [V3__N_27] :
( cLambda_2eTerms_2elambda___24t(V3__N_27)
=> ( cReduction_2ered___24a2(V0__M,V1__M_27)
=> ( cReduction_2ered___24a2(V2__N,V3__N_27)
=> cReduction_2ered___24a2(cLambda_2eTerms_2eApp___24a2(cLambda_2eTerms_2eAbs___24a1(V0__M),V2__N),cLambda_2eTerms_2esubst___24a2(V3__N_27,V1__M_27)) ) ) ) ) ) ) ).
fof('Reduction.red_ind',axiom,
! [V0__P] :
( c_24__type__295___24t(V0__P)
=> ( ! [V1__M] :
( cLambda_2eTerms_2elambda___24t(V1__M)
=> ! [V2__N] :
( cLambda_2eTerms_2elambda___24t(V2__N)
=> ( cReduction_2ered1___24a2(V1__M,V2__N)
=> p(happ(happ(V0__P,V1__M),V2__N)) ) ) )
=> ( ! [V2__M] :
( cLambda_2eTerms_2elambda___24t(V2__M)
=> p(happ(happ(V0__P,V2__M),V2__M)) )
=> ( ! [V3__M] :
( cLambda_2eTerms_2elambda___24t(V3__M)
=> ! [V4__N] :
( cLambda_2eTerms_2elambda___24t(V4__N)
=> ! [V5__P] :
( cLambda_2eTerms_2elambda___24t(V5__P)
=> ( cReduction_2ered___24a2(V3__M,V4__N)
=> ( p(happ(happ(V0__P,V3__M),V4__N))
=> ( cReduction_2ered___24a2(V4__N,V5__P)
=> ( p(happ(happ(V0__P,V4__N),V5__P))
=> p(happ(happ(V0__P,V3__M),V5__P)) ) ) ) ) ) ) )
=> ! [V4__l] :
( cLambda_2eTerms_2elambda___24t(V4__l)
=> ! [V5__l] :
( cLambda_2eTerms_2elambda___24t(V5__l)
=> ( cReduction_2ered___24a2(V4__l,V5__l)
=> p(happ(happ(V0__P,V4__l),V5__l)) ) ) ) ) ) ) ) ).
fof('Reduction.ref_par_red',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cReduction_2epar__red1___24a2(cLambda_2eTerms_2eRef___24a1(V0__n),cLambda_2eTerms_2eRef___24a1(V0__n)) ) ).
fof('Reduction.refl_par_red1',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> cReduction_2epar__red1___24a2(V0__M,V0__M) ) ).
fof('Reduction.refl_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> cReduction_2ered___24a2(V0__M,V0__M) ) ).
fof('Reduction.trans_par_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ! [V2__P] :
( cLambda_2eTerms_2elambda___24t(V2__P)
=> ( cReduction_2epar__red___24a2(V0__M,V1__N)
=> ( cReduction_2epar__red___24a2(V1__N,V2__P)
=> cReduction_2epar__red___24a2(V0__M,V2__P) ) ) ) ) ) ).
fof('Reduction.trans_red',axiom,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ! [V2__P] :
( cLambda_2eTerms_2elambda___24t(V2__P)
=> ( cReduction_2ered___24a2(V0__M,V1__N)
=> ( cReduction_2ered___24a2(V1__N,V2__P)
=> cReduction_2ered___24a2(V0__M,V2__P) ) ) ) ) ) ).
fof('$adef_$_prop_25231_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25231,V_24X1),V_24X2),V_24X3) = c_24__prop__25231___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eland,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eland___24a2(V_24X1,V_24X2) ).
fof('$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.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.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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_29506_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__29506,V_24X1),V_24X2) = c_24__lam__29506___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_$_lam_30636_$a1',axiom,
! [V_24X1] : happ(c_24__lam__30636,V_24X1) = c_24__lam__30636___24a1(V_24X1) ).
fof('$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.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.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_$_lam_30510_$a1',axiom,
! [V_24X1] : happ(c_24__lam__30510,V_24X1) = c_24__lam__30510___24a1(V_24X1) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$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('$adef_Reduction.red1_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cReduction_2ered1,V_24X1),V_24X2))
<=> cReduction_2ered1___24a2(V_24X1,V_24X2) ) ).
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('$adef_Lambda.Terms.lambda_rect_$a1',axiom,
! [V_24X1] : happ(cLambda_2eTerms_2elambda__rect,V_24X1) = cLambda_2eTerms_2elambda__rect___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$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('$adef_$_fix_29246_v_CANONICAL_1_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__29246__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__29246__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_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_Coq.micromega.RingMicromega.eval_op2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_29490_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29490,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29490___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Lambda.Terms.subst_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTerms_2esubst,V_24X1),V_24X2) = cLambda_2eTerms_2esubst___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Reals.RIneq.mkposreal_$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('$adef_Coq.Init.Datatypes.implb_$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('$adef_Coq.Init.Datatypes.prod_curry_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__curry,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eprod__curry___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_fix_769_v_CANONICAL_0_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__769__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__769__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_30696_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__30696,V_24X1),V_24X2) = c_24__prop__30696___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.RMicromega.CMult_$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('$adef_$_lam_29393_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29393,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29393___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_Lambda.Terms.Abs_$a1',axiom,
! [V_24X1] : happ(cLambda_2eTerms_2eAbs,V_24X1) = cLambda_2eTerms_2eAbs___24a1(V_24X1) ).
fof('$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_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_$_lam_29498_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29498,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29498___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$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('$adef_Coq.Init.Nat.compare_$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('$adef_Lambda.Terms.lambda_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cLambda_2eTerms_2elambda__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cLambda_2eTerms_2elambda__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$14841_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2414841___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('$adef_Coq.Init.Specif.sig_$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('$adef_Lambda.Terms.subst_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eTerms_2esubst__rec,V_24X1),V_24X2),V_24X3) = cLambda_2eTerms_2esubst__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.leb_$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('$adef_Reduction.red_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cReduction_2ered,V_24X1),V_24X2))
<=> cReduction_2ered___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('$adef_Coq.NArith.BinNat.N.peano_rect_$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('$adef_$_lam_29514_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29514,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29514___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_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.Init.Nat.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2egcd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.micromega.ZMicromega.isZ0_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eisZ0,V_24X1) = cCoq_2emicromega_2eZMicromega_2eisZ0___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Lambda.Terms.lift_rec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eTerms_2elift__rec,V_24X1),V_24X2),V_24X3) = cLambda_2eTerms_2elift__rec___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_30532_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__30532,V_24X1),V_24X2) = c_24__lam__30532___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
<=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$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('$adef_$_case_Lambda.Terms.lambda$673_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Lambda_2eTerms_2elambda_24673,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Lambda_2eTerms_2elambda_24673___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_25233_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25233,V_24X1),V_24X2),V_24X3) = c_24__prop__25233___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_30532_$a1',axiom,
! [V_24X1] : happ(c_24__lam__30532,V_24X1) = c_24__lam__30532___24a1(V_24X1) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$9217_$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_249217,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_249217___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
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('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$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('$adef_$_lam_29417_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29417,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29417___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_Reduction.par_red1_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cReduction_2epar__red1,V_24X1),V_24X2))
<=> cReduction_2epar__red1___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_Lambda.Terms.App_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTerms_2eApp,V_24X1),V_24X2) = cLambda_2eTerms_2eApp___24a2(V_24X1,V_24X2) ).
fof('$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_Lambda.Test.test_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTest_2etest,V_24X1),V_24X2) = cLambda_2eTest_2etest___24a2(V_24X1,V_24X2) ).
fof('$adef_Lambda.Terms.lift_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cLambda_2eTerms_2elift,V_24X1),V_24X2) = cLambda_2eTerms_2elift___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Lambda.Terms.lambda_rec_$a1',axiom,
! [V_24X1] : happ(cLambda_2eTerms_2elambda__rec,V_24X1) = cLambda_2eTerms_2elambda__rec___24a1(V_24X1) ).
fof('$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_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_$_fix_27202_v_CANONICAL_0_$a1',axiom,
! [V_24X1] : happ(c_24__fix__27202__v__CANONICAL__0,V_24X1) = c_24__fix__27202__v__CANONICAL__0___24a1(V_24X1) ).
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('$adef_$_case_Coq.Numbers.BinNums.Z$14836_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2414836,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2414836___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_25235_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__25235,V_24X1),V_24X2) = c_24__prop__25235___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_case_Coq.Numbers.BinNums.positive$27186_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2427186,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2427186___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.micromega.Tauto.FF_$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('$adef_Coq.Init.Datatypes.identity_$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('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
<=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$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('$adef_$_lam_29409_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__29409,V_24X1),V_24X2),V_24X3) = c_24__lam__29409___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).
fof('$adef_Coq.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_$_let_var_6_p_20711_20714_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__20711__20714,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__20711__20714___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_25232_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25232,V_24X1),V_24X2),V_24X3) = c_24__prop__25232___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_27107_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__27107,V_24X1),V_24X2) = c_24__prop__27107___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$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('$adef_Reduction.par_red_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cReduction_2epar__red,V_24X1),V_24X2))
<=> cReduction_2epar__red___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('$adef_$_prop_27108_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__27108,V_24X1),V_24X2),V_24X3) = c_24__prop__27108___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.list$29114_$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_2429114,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2429114___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.setoid_ring.Ring.bool_eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing_2ebool__eq,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing_2ebool__eq___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('$adef_Coq.micromega.Tauto.X_$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('$adef_Coq.Sorting.Sorted.Sorted_$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('$adef_$_lam_29393_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__29393,V_24X1),V_24X2),V_24X3) = c_24__lam__29393___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_$_lam_29401_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__29401,V_24X1),V_24X2),V_24X3) = c_24__lam__29401___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Lambda.Terms.Ref_$a1',axiom,
! [V_24X1] : happ(cLambda_2eTerms_2eRef,V_24X1) = cLambda_2eTerms_2eRef___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zcomplements.floor_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZcomplements_2efloor__pos,V_24X1) = cCoq_2eZArith_2eZcomplements_2efloor__pos___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Relations_1.Antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eAntisymmetric,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$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('$adef_$_prop_25229_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__25229,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__25229___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.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_$_case_Coq.Init.Datatypes.list$29201_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2429201,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2429201___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$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('$adef_$_prop_27109_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__27109,V_24X1),V_24X2),V_24X3) = c_24__prop__27109___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Init.Nat.sqrt_iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2esqrt__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_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_$_lam_30643_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__30643,V_24X1),V_24X2) = c_24__lam__30643___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$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('$adef_$_lam_29490_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__29490,V_24X1),V_24X2) = c_24__lam__29490___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_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_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_$_lam_29506_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29506,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29506___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_$_prop_25234_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25234,V_24X1),V_24X2),V_24X3) = c_24__prop__25234___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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_$_lam_30510_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__30510,V_24X1),V_24X2) = c_24__lam__30510___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_30643_$a1',axiom,
! [V_24X1] : happ(c_24__lam__30643,V_24X1) = c_24__lam__30643___24a1(V_24X1) ).
fof('$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.PArith.BinPosDef.Pos.div2_up_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2__up___24a1(V_24X1) ).
fof('$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.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.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_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_$_case_Coq.Init.Datatypes.nat$14819_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2414819,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2414819___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$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('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$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('$adef_$_lam_29417_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__29417,V_24X1),V_24X2),V_24X3) = c_24__lam__29417___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_29409_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29409,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29409___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Lambda.Terms.insert_Ref_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eTerms_2einsert__Ref,V_24X1),V_24X2),V_24X3) = cLambda_2eTerms_2einsert__Ref___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('$adef_Coq.Init.Nat.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emodulo,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_linear_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__linear,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Lists.List.fold_right_$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('$adef_Coq.Init.Nat.pow_$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('$adef_$_lam_29498_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__29498,V_24X1),V_24X2) = c_24__lam__29498___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.land_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eland,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eland___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_25230_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__25230,V_24X1),V_24X2),V_24X3) = c_24__prop__25230___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_29514_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__29514,V_24X1),V_24X2) = c_24__lam__29514___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.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.Logic.EqdepFacts.Eq_rect_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.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_$_let_var_6_p_20713_20715_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__20713__20715,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__20713__20715___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Relations_1.Order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eOrder,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.QArith.QArith_base.Qeq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eQArith_2eQArith__base_2eQeq,V_24X1),V_24X2))
<=> cCoq_2eQArith_2eQArith__base_2eQeq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$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('$adef_$_lam_30636_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__30636,V_24X1),V_24X2) = c_24__lam__30636___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_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_$_lam_30647_$a1',axiom,
! [V_24X1] : happ(c_24__lam__30647,V_24X1) = c_24__lam__30647___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.InitialRing.hypo_type_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eInitialRing_2ehypo__type,V_24X1) = cCoq_2esetoid__ring_2eInitialRing_2ehypo__type___24a1(V_24X1) ).
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('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$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('$adef_Lambda.Terms.relocate_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cLambda_2eTerms_2erelocate,V_24X1),V_24X2),V_24X3) = cLambda_2eTerms_2erelocate___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('$adef_$_lam_29401_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__29401,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__29401___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ).
fof('$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_$_type_5945',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__5945___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__5945___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_30084',axiom,
! [V_24Y] :
( c_24__type__30084___24t(V_24Y)
<=> t(V_24Y,c_24__type__30084) ) ).
fof('$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_$_type_24630',axiom,
! [V_24Y] :
( c_24__type__24630___24t(V_24Y)
<=> t(V_24Y,c_24__type__24630) ) ).
fof('$tdef_$_type_9539',axiom,
! [V_24Y] :
( c_24__type__9539___24t(V_24Y)
<=> t(V_24Y,c_24__type__9539) ) ).
fof('$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_8803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__8803___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__8803___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_24479',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24479___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24479___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_20839',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20839___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20839___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3032',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3032___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3032___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_22359',axiom,
! [V_24Y] :
( c_24__type__22359___24t(V_24Y)
<=> t(V_24Y,c_24__type__22359) ) ).
fof('$tdef_$_type_27602',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__27602___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__27602___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_12365',axiom,
! [V_24Y] :
( c_24__type__12365___24t(V_24Y)
<=> t(V_24Y,c_24__type__12365) ) ).
fof('$tdef_$_type_11727',axiom,
! [V_24Y] :
( c_24__type__11727___24t(V_24Y)
<=> t(V_24Y,c_24__type__11727) ) ).
fof('$tdef_$_type_5675',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5675___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__5675___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Lambda.Terms.lambda',axiom,
! [V_24Y] :
( cLambda_2eTerms_2elambda___24t(V_24Y)
<=> t(V_24Y,cLambda_2eTerms_2elambda) ) ).
fof('$tdef_$_type_30021',axiom,
! [V_24Y] :
( c_24__type__30021___24t(V_24Y)
<=> t(V_24Y,c_24__type__30021) ) ).
fof('$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_9230',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9230___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9230___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27435',axiom,
! [V_24Y] :
( c_24__type__27435___24t(V_24Y)
<=> t(V_24Y,c_24__type__27435) ) ).
fof('$tdef_$_type_2594',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2594___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2594___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_29576',axiom,
! [V_24Y] :
( c_24__type__29576___24t(V_24Y)
<=> t(V_24Y,c_24__type__29576) ) ).
fof('$tdef_$_type_27276',axiom,
! [V_24Y] :
( c_24__type__27276___24t(V_24Y)
<=> t(V_24Y,c_24__type__27276) ) ).
fof('$tdef_$_type_14848',axiom,
! [V_24Y] :
( c_24__type__14848___24t(V_24Y)
<=> t(V_24Y,c_24__type__14848) ) ).
fof('$tdef_$_type_14273',axiom,
! [V_24Y] :
( c_24__type__14273___24t(V_24Y)
<=> t(V_24Y,c_24__type__14273) ) ).
fof('$tdef_$_type_24192',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24192___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__24192___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
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_22718',axiom,
! [V_24Y] :
( c_24__type__22718___24t(V_24Y)
<=> t(V_24Y,c_24__type__22718) ) ).
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_$_type_20701',axiom,
! [V_24Y] :
( c_24__type__20701___24t(V_24Y)
<=> t(V_24Y,c_24__type__20701) ) ).
fof('$tdef_$_type_27363',axiom,
! [V_24Y] :
( c_24__type__27363___24t(V_24Y)
<=> t(V_24Y,c_24__type__27363) ) ).
fof('$tdef_$_type_23872',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__23872___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__23872___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_26349',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26349___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26349___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_23',axiom,
! [V_24Y] :
( c_24__type__23___24t(V_24Y)
<=> t(V_24Y,c_24__type__23) ) ).
fof('$tdef_$_type_22764',axiom,
! [V_24Y] :
( c_24__type__22764___24t(V_24Y)
<=> t(V_24Y,c_24__type__22764) ) ).
fof('$tdef_$_type_9553',axiom,
! [V_24Y] :
( c_24__type__9553___24t(V_24Y)
<=> t(V_24Y,c_24__type__9553) ) ).
fof('$tdef_$_type_27143',axiom,
! [V_24Y] :
( c_24__type__27143___24t(V_24Y)
<=> t(V_24Y,c_24__type__27143) ) ).
fof('$tdef_$_type_22876',axiom,
! [V_24Y] :
( c_24__type__22876___24t(V_24Y)
<=> t(V_24Y,c_24__type__22876) ) ).
fof('$tdef_$_type_20903',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20903___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20903___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_1143',axiom,
! [V_24Y] :
( c_24__type__1143___24t(V_24Y)
<=> t(V_24Y,c_24__type__1143) ) ).
fof('$tdef_$_type_24318',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24318___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__24318___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_25276',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25276___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25276___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_12172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12172___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12172___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_30058',axiom,
! [V_24Y] :
( c_24__type__30058___24t(V_24Y)
<=> t(V_24Y,c_24__type__30058) ) ).
fof('$tdef_$_type_9062',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9062___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9062___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30286',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__30286___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__30286___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_166',axiom,
! [V_24X1,V_24Y] :
( c_24__type__166___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__166___24a1(V_24X1)) ) ).
fof('$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_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_30549',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30549___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30549___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27280',axiom,
! [V_24Y] :
( c_24__type__27280___24t(V_24Y)
<=> t(V_24Y,c_24__type__27280) ) ).
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_13547',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__13547___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__13547___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_30689',axiom,
! [V_24Y] :
( c_24__type__30689___24t(V_24Y)
<=> t(V_24Y,c_24__type__30689) ) ).
fof('$tdef_$_type_22767',axiom,
! [V_24Y] :
( c_24__type__22767___24t(V_24Y)
<=> t(V_24Y,c_24__type__22767) ) ).
fof('$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('$tdef_$_type_26882',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__26882___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__26882___24a3(V_24X1,V_24X2,V_24X3)) ) ).
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_$_type_22424',axiom,
! [V_24Y] :
( c_24__type__22424___24t(V_24Y)
<=> t(V_24Y,c_24__type__22424) ) ).
fof('$tdef_$_type_21136',axiom,
! [V_24Y] :
( c_24__type__21136___24t(V_24Y)
<=> t(V_24Y,c_24__type__21136) ) ).
fof('$tdef_$_type_26585',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26585___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26585___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_20707',axiom,
! [V_24Y] :
( c_24__type__20707___24t(V_24Y)
<=> t(V_24Y,c_24__type__20707) ) ).
fof('$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_852',axiom,
! [V_24Y] :
( c_24__type__852___24t(V_24Y)
<=> t(V_24Y,c_24__type__852) ) ).
fof('$tdef_$_type_6140',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__6140___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__6140___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27326',axiom,
! [V_24Y] :
( c_24__type__27326___24t(V_24Y)
<=> t(V_24Y,c_24__type__27326) ) ).
fof('$tdef_$_type_29955',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29955___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29955___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22344',axiom,
! [V_24Y] :
( c_24__type__22344___24t(V_24Y)
<=> t(V_24Y,c_24__type__22344) ) ).
fof('$tdef_$_type_8447',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__8447___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__8447___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_29885',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29885___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29885___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
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_$_type_14446',axiom,
! [V_24Y] :
( c_24__type__14446___24t(V_24Y)
<=> t(V_24Y,c_24__type__14446) ) ).
fof('$tdef_$_type_149',axiom,
! [V_24X1,V_24Y] :
( c_24__type__149___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__149___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1795',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1795___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1795___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_108',axiom,
! [V_24X1,V_24Y] :
( c_24__type__108___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__108___24a1(V_24X1)) ) ).
fof('$tdef_$_type_53',axiom,
! [V_24Y] :
( c_24__type__53___24t(V_24Y)
<=> t(V_24Y,c_24__type__53) ) ).
fof('$tdef_$_type_28767',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28767___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28767___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_10452',axiom,
! [V_24Y] :
( c_24__type__10452___24t(V_24Y)
<=> t(V_24Y,c_24__type__10452) ) ).
fof('$tdef_$_type_23598',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__23598___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__23598___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_14223',axiom,
! [V_24Y] :
( c_24__type__14223___24t(V_24Y)
<=> t(V_24Y,c_24__type__14223) ) ).
fof('$tdef_$_type_10566',axiom,
! [V_24Y] :
( c_24__type__10566___24t(V_24Y)
<=> t(V_24Y,c_24__type__10566) ) ).
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_$_type_27408',axiom,
! [V_24Y] :
( c_24__type__27408___24t(V_24Y)
<=> t(V_24Y,c_24__type__27408) ) ).
fof('$tdef_$_type_27299',axiom,
! [V_24Y] :
( c_24__type__27299___24t(V_24Y)
<=> t(V_24Y,c_24__type__27299) ) ).
fof('$tdef_$_type_27526',axiom,
! [V_24Y] :
( c_24__type__27526___24t(V_24Y)
<=> t(V_24Y,c_24__type__27526) ) ).
fof('$tdef_$_type_12046',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12046___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12046___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_27453',axiom,
! [V_24Y] :
( c_24__type__27453___24t(V_24Y)
<=> t(V_24Y,c_24__type__27453) ) ).
fof('$tdef_$_type_6083',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__6083___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__6083___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27266',axiom,
! [V_24Y] :
( c_24__type__27266___24t(V_24Y)
<=> t(V_24Y,c_24__type__27266) ) ).
fof('$tdef_$_type_154',axiom,
! [V_24X1,V_24Y] :
( c_24__type__154___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__154___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16442',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__16442___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__16442___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_896',axiom,
! [V_24Y] :
( c_24__type__896___24t(V_24Y)
<=> t(V_24Y,c_24__type__896) ) ).
fof('$tdef_$_type_3615',axiom,
! [V_24Y] :
( c_24__type__3615___24t(V_24Y)
<=> t(V_24Y,c_24__type__3615) ) ).
fof('$tdef_$_type_30307',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30307___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30307___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27061',axiom,
! [V_24Y] :
( c_24__type__27061___24t(V_24Y)
<=> t(V_24Y,c_24__type__27061) ) ).
fof('$tdef_$_type_222',axiom,
! [V_24Y] :
( c_24__type__222___24t(V_24Y)
<=> t(V_24Y,c_24__type__222) ) ).
fof('$tdef_$_type_30620',axiom,
! [V_24Y] :
( c_24__type__30620___24t(V_24Y)
<=> t(V_24Y,c_24__type__30620) ) ).
fof('$tdef_$_type_30015',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30015___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30015___24a2(V_24X1,V_24X2)) ) ).
fof('$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_$_type_25537',axiom,
! [V_24Y] :
( c_24__type__25537___24t(V_24Y)
<=> t(V_24Y,c_24__type__25537) ) ).
fof('$tdef_$_type_8784',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__8784___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__8784___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29920',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29920___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29920___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29975',axiom,
! [V_24Y] :
( c_24__type__29975___24t(V_24Y)
<=> t(V_24Y,c_24__type__29975) ) ).
fof('$tdef_$_type_22443',axiom,
! [V_24Y] :
( c_24__type__22443___24t(V_24Y)
<=> t(V_24Y,c_24__type__22443) ) ).
fof('$tdef_$_type_16788',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__16788___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__16788___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_24487',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24487___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24487___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_30055',axiom,
! [V_24Y] :
( c_24__type__30055___24t(V_24Y)
<=> t(V_24Y,c_24__type__30055) ) ).
fof('$tdef_$_type_30050',axiom,
! [V_24Y] :
( c_24__type__30050___24t(V_24Y)
<=> t(V_24Y,c_24__type__30050) ) ).
fof('$tdef_$_type_9104',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9104___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9104___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_30574',axiom,
! [V_24Y] :
( c_24__type__30574___24t(V_24Y)
<=> t(V_24Y,c_24__type__30574) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_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_22906',axiom,
! [V_24X1,V_24Y] :
( c_24__type__22906___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__22906___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27395',axiom,
! [V_24Y] :
( c_24__type__27395___24t(V_24Y)
<=> t(V_24Y,c_24__type__27395) ) ).
fof('$tdef_$_type_10494',axiom,
! [V_24Y] :
( c_24__type__10494___24t(V_24Y)
<=> t(V_24Y,c_24__type__10494) ) ).
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_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_6059',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__6059___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__6059___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27261',axiom,
! [V_24Y] :
( c_24__type__27261___24t(V_24Y)
<=> t(V_24Y,c_24__type__27261) ) ).
fof('$tdef_$_type_8817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__8817___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__8817___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30066',axiom,
! [V_24Y] :
( c_24__type__30066___24t(V_24Y)
<=> t(V_24Y,c_24__type__30066) ) ).
fof('$tdef_$_type_10447',axiom,
! [V_24Y] :
( c_24__type__10447___24t(V_24Y)
<=> t(V_24Y,c_24__type__10447) ) ).
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_$_type_30706',axiom,
! [V_24Y] :
( c_24__type__30706___24t(V_24Y)
<=> t(V_24Y,c_24__type__30706) ) ).
fof('$tdef_$_type_22304',axiom,
! [V_24Y] :
( c_24__type__22304___24t(V_24Y)
<=> t(V_24Y,c_24__type__22304) ) ).
fof('$tdef_$_type_14564',axiom,
! [V_24Y] :
( c_24__type__14564___24t(V_24Y)
<=> t(V_24Y,c_24__type__14564) ) ).
fof('$tdef_$_type_5621',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5621___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__5621___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_20816',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20816___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20816___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_168',axiom,
! [V_24Y] :
( c_24__type__168___24t(V_24Y)
<=> t(V_24Y,c_24__type__168) ) ).
fof('$tdef_$_type_23248',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23248___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23248___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_28603',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28603___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28603___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_22755',axiom,
! [V_24Y] :
( c_24__type__22755___24t(V_24Y)
<=> t(V_24Y,c_24__type__22755) ) ).
fof('$tdef_$_type_22951',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__22951___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__22951___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_27562',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27562___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27562___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_26099',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__26099___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__26099___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_14753',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14753___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14753___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14436',axiom,
! [V_24Y] :
( c_24__type__14436___24t(V_24Y)
<=> t(V_24Y,c_24__type__14436) ) ).
fof('$tdef_$_type_24255',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24255___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__24255___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_25091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25091___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25091___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29579',axiom,
! [V_24Y] :
( c_24__type__29579___24t(V_24Y)
<=> t(V_24Y,c_24__type__29579) ) ).
fof('$tdef_$_type_24543',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24543___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24543___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_22258',axiom,
! [V_24Y] :
( c_24__type__22258___24t(V_24Y)
<=> t(V_24Y,c_24__type__22258) ) ).
fof('$tdef_$_type_19510',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__19510___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__19510___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_27376',axiom,
! [V_24Y] :
( c_24__type__27376___24t(V_24Y)
<=> t(V_24Y,c_24__type__27376) ) ).
fof('$tdef_$_type_25573',axiom,
! [V_24Y] :
( c_24__type__25573___24t(V_24Y)
<=> t(V_24Y,c_24__type__25573) ) ).
fof('$tdef_$_type_29997',axiom,
! [V_24Y] :
( c_24__type__29997___24t(V_24Y)
<=> t(V_24Y,c_24__type__29997) ) ).
fof('$tdef_$_type_9154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9154___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9154___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_10454',axiom,
! [V_24Y] :
( c_24__type__10454___24t(V_24Y)
<=> t(V_24Y,c_24__type__10454) ) ).
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_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_$_type_21083',axiom,
! [V_24Y] :
( c_24__type__21083___24t(V_24Y)
<=> t(V_24Y,c_24__type__21083) ) ).
fof('$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_$_type_9419',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9419___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9419___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_30650',axiom,
! [V_24Y] :
( c_24__type__30650___24t(V_24Y)
<=> t(V_24Y,c_24__type__30650) ) ).
fof('$tdef_$_type_27352',axiom,
! [V_24Y] :
( c_24__type__27352___24t(V_24Y)
<=> t(V_24Y,c_24__type__27352) ) ).
fof('$tdef_$_type_3025',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3025___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3025___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_20974',axiom,
! [V_24Y] :
( c_24__type__20974___24t(V_24Y)
<=> t(V_24Y,c_24__type__20974) ) ).
fof('$tdef_$_type_5999',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__5999___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__5999___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_1620',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__1620___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__1620___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_8642',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__8642___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__8642___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_8962',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__8962___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__8962___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
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_$_type_30304',axiom,
! [V_24Y] :
( c_24__type__30304___24t(V_24Y)
<=> t(V_24Y,c_24__type__30304) ) ).
fof('$tdef_$_type_27304',axiom,
! [V_24X1,V_24Y] :
( c_24__type__27304___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__27304___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13749',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__13749___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__13749___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_24535',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__24535___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__24535___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1138',axiom,
! [V_24Y] :
( c_24__type__1138___24t(V_24Y)
<=> t(V_24Y,c_24__type__1138) ) ).
fof('$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_9383',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9383___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9383___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_10930',axiom,
! [V_24Y] :
( c_24__type__10930___24t(V_24Y)
<=> t(V_24Y,c_24__type__10930) ) ).
fof('$tdef_$_type_19187',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__19187___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__19187___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_25460',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__25460___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__25460___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_5738',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5738___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__5738___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_18841',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__18841___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__18841___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_$_type_27126',axiom,
! [V_24Y] :
( c_24__type__27126___24t(V_24Y)
<=> t(V_24Y,c_24__type__27126) ) ).
fof('$tdef_$_type_1118',axiom,
! [V_24Y] :
( c_24__type__1118___24t(V_24Y)
<=> t(V_24Y,c_24__type__1118) ) ).
fof('$tdef_$_type_236',axiom,
! [V_24Y] :
( c_24__type__236___24t(V_24Y)
<=> t(V_24Y,c_24__type__236) ) ).
fof('$tdef_$_type_25849',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__25849___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__25849___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_5975',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__5975___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__5975___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27013',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27013___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27013___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_10562',axiom,
! [V_24Y] :
( c_24__type__10562___24t(V_24Y)
<=> t(V_24Y,c_24__type__10562) ) ).
fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21033',axiom,
! [V_24Y] :
( c_24__type__21033___24t(V_24Y)
<=> t(V_24Y,c_24__type__21033) ) ).
fof('$tdef_$_type_10',axiom,
! [V_24Y] :
( c_24__type__10___24t(V_24Y)
<=> t(V_24Y,c_24__type__10) ) ).
fof('$tdef_$_type_23423',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23423___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23423___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_1538',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1538___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1538___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29460',axiom,
! [V_24Y] :
( c_24__type__29460___24t(V_24Y)
<=> t(V_24Y,c_24__type__29460) ) ).
fof('$tdef_$_type_27314',axiom,
! [V_24Y] :
( c_24__type__27314___24t(V_24Y)
<=> t(V_24Y,c_24__type__27314) ) ).
fof('$tdef_$_type_25255',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__25255___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__25255___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_27114',axiom,
! [V_24Y] :
( c_24__type__27114___24t(V_24Y)
<=> t(V_24Y,c_24__type__27114) ) ).
fof('$tdef_$_type_10427',axiom,
! [V_24Y] :
( c_24__type__10427___24t(V_24Y)
<=> t(V_24Y,c_24__type__10427) ) ).
fof('$tdef_$_type_8039',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8039___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8039___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Nat.t',axiom,
! [V_24Y] :
( cCoq_2eInit_2eNat_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eNat_2et) ) ).
fof('$tdef_$_type_30485',axiom,
! [V_24Y] :
( c_24__type__30485___24t(V_24Y)
<=> t(V_24Y,c_24__type__30485) ) ).
fof('$tdef_$_type_1713',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__1713___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__1713___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27384',axiom,
! [V_24Y] :
( c_24__type__27384___24t(V_24Y)
<=> t(V_24Y,c_24__type__27384) ) ).
fof('$tdef_$_type_12490',axiom,
! [V_24Y] :
( c_24__type__12490___24t(V_24Y)
<=> t(V_24Y,c_24__type__12490) ) ).
fof('$tdef_$_type_20862',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20862___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20862___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_909',axiom,
! [V_24Y] :
( c_24__type__909___24t(V_24Y)
<=> t(V_24Y,c_24__type__909) ) ).
fof('$tdef_$_type_1906',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1906___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1906___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23950',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__23950___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__23950___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
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_$_type_989',axiom,
! [V_24Y] :
( c_24__type__989___24t(V_24Y)
<=> t(V_24Y,c_24__type__989) ) ).
fof('$tdef_$_type_17480',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__17480___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__17480___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.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_$_type_29803',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29803___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29803___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_24372',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24372___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__24372___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_17134',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__17134___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__17134___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_13255',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__13255___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__13255___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.InitialRing.hypo',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2ehypo) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).
fof('$tdef_$_type_22782',axiom,
! [V_24Y] :
( c_24__type__22782___24t(V_24Y)
<=> t(V_24Y,c_24__type__22782) ) ).
fof('$tdef_$_type_20963',axiom,
! [V_24Y] :
( c_24__type__20963___24t(V_24Y)
<=> t(V_24Y,c_24__type__20963) ) ).
fof('$tdef_$_type_8234',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8234___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8234___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_6566',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__6566___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__6566___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_5558',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5558___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__5558___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_26982',axiom,
! [V_24Y] :
( c_24__type__26982___24t(V_24Y)
<=> t(V_24Y,c_24__type__26982) ) ).
fof('$tdef_$_type_1445',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1445___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1445___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_29472',axiom,
! [V_24Y] :
( c_24__type__29472___24t(V_24Y)
<=> t(V_24Y,c_24__type__29472) ) ).
fof('$tdef_$_type_1030',axiom,
! [V_24Y] :
( c_24__type__1030___24t(V_24Y)
<=> t(V_24Y,c_24__type__1030) ) ).
fof('$tdef_$_type_6779',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__6779___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__6779___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_10875',axiom,
! [V_24Y] :
( c_24__type__10875___24t(V_24Y)
<=> t(V_24Y,c_24__type__10875) ) ).
fof('$tdef_$_type_28916',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28916___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28916___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__27708___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__27708___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_30683',axiom,
! [V_24Y] :
( c_24__type__30683___24t(V_24Y)
<=> t(V_24Y,c_24__type__30683) ) ).
fof('$tdef_$_type_21153',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21153___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21153___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27205',axiom,
! [V_24Y] :
( c_24__type__27205___24t(V_24Y)
<=> t(V_24Y,c_24__type__27205) ) ).
fof('$tdef_$_type_22489',axiom,
! [V_24Y] :
( c_24__type__22489___24t(V_24Y)
<=> t(V_24Y,c_24__type__22489) ) ).
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_5241',axiom,
! [V_24Y] :
( c_24__type__5241___24t(V_24Y)
<=> t(V_24Y,c_24__type__5241) ) ).
fof('$tdef_$_type_18495',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__18495___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__18495___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_933',axiom,
! [V_24Y] :
( c_24__type__933___24t(V_24Y)
<=> t(V_24Y,c_24__type__933) ) ).
fof('$tdef_$_type_11719',axiom,
! [V_24Y] :
( c_24__type__11719___24t(V_24Y)
<=> t(V_24Y,c_24__type__11719) ) ).
fof('$tdef_$_type_12423',axiom,
! [V_24Y] :
( c_24__type__12423___24t(V_24Y)
<=> t(V_24Y,c_24__type__12423) ) ).
fof('$tdef_$_type_3011',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3011___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3011___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13850',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__13850___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__13850___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_20947',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20947___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20947___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_233',axiom,
! [V_24Y] :
( c_24__type__233___24t(V_24Y)
<=> t(V_24Y,c_24__type__233) ) ).
fof('$tdef_$_type_21043',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21043___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21043___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_13457',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__13457___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__13457___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7400',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__7400___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__7400___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_858',axiom,
! [V_24Y] :
( c_24__type__858___24t(V_24Y)
<=> t(V_24Y,c_24__type__858) ) ).
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('$tdef_$_type_20179',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__20179___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__20179___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('$tdef_Coq.micromega.ZMicromega.coneMember',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).
fof('$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_1915',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1915___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1915___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27745',axiom,
! [V_24Y] :
( c_24__type__27745___24t(V_24Y)
<=> t(V_24Y,c_24__type__27745) ) ).
fof('$tdef_$_type_29846',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29846___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29846___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3869',axiom,
! [V_24Y] :
( c_24__type__3869___24t(V_24Y)
<=> t(V_24Y,c_24__type__3869) ) ).
fof('$tdef_$_type_30527',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30527___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30527___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12289',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12289___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__12289___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_10564',axiom,
! [V_24Y] :
( c_24__type__10564___24t(V_24Y)
<=> t(V_24Y,c_24__type__10564) ) ).
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_$_type_14093',axiom,
! [V_24Y] :
( c_24__type__14093___24t(V_24Y)
<=> t(V_24Y,c_24__type__14093) ) ).
fof('$tdef_$_type_1155',axiom,
! [V_24Y] :
( c_24__type__1155___24t(V_24Y)
<=> t(V_24Y,c_24__type__1155) ) ).
fof('$tdef_$_type_1083',axiom,
! [V_24Y] :
( c_24__type__1083___24t(V_24Y)
<=> t(V_24Y,c_24__type__1083) ) ).
fof('$tdef_$_type_976',axiom,
! [V_24Y] :
( c_24__type__976___24t(V_24Y)
<=> t(V_24Y,c_24__type__976) ) ).
fof('$tdef_$_type_25487',axiom,
! [V_24Y] :
( c_24__type__25487___24t(V_24Y)
<=> t(V_24Y,c_24__type__25487) ) ).
fof('$tdef_$_type_27417',axiom,
! [V_24Y] :
( c_24__type__27417___24t(V_24Y)
<=> t(V_24Y,c_24__type__27417) ) ).
fof('$tdef_$_type_27361',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__27361___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__27361___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_9776',axiom,
! [V_24Y] :
( c_24__type__9776___24t(V_24Y)
<=> t(V_24Y,c_24__type__9776) ) ).
fof('$tdef_$_type_25319',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25319___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25319___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_6029',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__6029___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__6029___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_10435',axiom,
! [V_24Y] :
( c_24__type__10435___24t(V_24Y)
<=> t(V_24Y,c_24__type__10435) ) ).
fof('$tdef_$_type_9592',axiom,
! [V_24Y] :
( c_24__type__9592___24t(V_24Y)
<=> t(V_24Y,c_24__type__9592) ) ).
fof('$tdef_$_type_30134',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__30134___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__30134___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27424',axiom,
! [V_24X1,V_24Y] :
( c_24__type__27424___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__27424___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27458',axiom,
! [V_24Y] :
( c_24__type__27458___24t(V_24Y)
<=> t(V_24Y,c_24__type__27458) ) ).
fof('$tdef_$_type_6992',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__6992___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__6992___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_27392',axiom,
! [V_24Y] :
( c_24__type__27392___24t(V_24Y)
<=> t(V_24Y,c_24__type__27392) ) ).
fof('$tdef_$_type_29551',axiom,
! [V_24Y] :
( c_24__type__29551___24t(V_24Y)
<=> t(V_24Y,c_24__type__29551) ) ).
fof('$tdef_$_type_15427',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__15427___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__15427___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_12806',axiom,
! [V_24Y] :
( c_24__type__12806___24t(V_24Y)
<=> t(V_24Y,c_24__type__12806) ) ).
fof('$tdef_$_type_23691',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__23691___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__23691___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_14054',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__14054___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__14054___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_21175',axiom,
! [V_24Y] :
( c_24__type__21175___24t(V_24Y)
<=> t(V_24Y,c_24__type__21175) ) ).
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_26915',axiom,
! [V_24Y] :
( c_24__type__26915___24t(V_24Y)
<=> t(V_24Y,c_24__type__26915) ) ).
fof('$tdef_$_type_99',axiom,
! [V_24Y] :
( c_24__type__99___24t(V_24Y)
<=> t(V_24Y,c_24__type__99) ) ).
fof('$tdef_$_type_24495',axiom,
! [V_24Y] :
( c_24__type__24495___24t(V_24Y)
<=> t(V_24Y,c_24__type__24495) ) ).
fof('$tdef_$_type_23516',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__23516___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__23516___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ) ).
fof('$tdef_$_type_22759',axiom,
! [V_24Y] :
( c_24__type__22759___24t(V_24Y)
<=> t(V_24Y,c_24__type__22759) ) ).
fof('$tdef_$_type_20929',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20929___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20929___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_30044',axiom,
! [V_24Y] :
( c_24__type__30044___24t(V_24Y)
<=> t(V_24Y,c_24__type__30044) ) ).
fof('$tdef_$_type_28725',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28725___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28725___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_22295',axiom,
! [V_24Y] :
( c_24__type__22295___24t(V_24Y)
<=> t(V_24Y,c_24__type__22295) ) ).
fof('$tdef_$_type_11724',axiom,
! [V_24Y] :
( c_24__type__11724___24t(V_24Y)
<=> t(V_24Y,c_24__type__11724) ) ).
fof('$tdef_$_type_25591',axiom,
! [V_24Y] :
( c_24__type__25591___24t(V_24Y)
<=> t(V_24Y,c_24__type__25591) ) ).
fof('$tdef_$_type_1888',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__1888___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__1888___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_94',axiom,
! [V_24Y] :
( c_24__type__94___24t(V_24Y)
<=> t(V_24Y,c_24__type__94) ) ).
fof('$tdef_$_type_12814',axiom,
! [V_24Y] :
( c_24__type__12814___24t(V_24Y)
<=> t(V_24Y,c_24__type__12814) ) ).
fof('$tdef_$_type_22839',axiom,
! [V_24Y] :
( c_24__type__22839___24t(V_24Y)
<=> t(V_24Y,c_24__type__22839) ) ).
fof('$tdef_$_type_22275',axiom,
! [V_24Y] :
( c_24__type__22275___24t(V_24Y)
<=> t(V_24Y,c_24__type__22275) ) ).
fof('$tdef_$_type_9463',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9463___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9463___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_13356',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__13356___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__13356___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2987',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2987___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2987___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29568',axiom,
! [V_24Y] :
( c_24__type__29568___24t(V_24Y)
<=> t(V_24Y,c_24__type__29568) ) ).
fof('$tdef_$_type_21577',axiom,
! [V_24Y] :
( c_24__type__21577___24t(V_24Y)
<=> t(V_24Y,c_24__type__21577) ) ).
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_$_type_6',axiom,
! [V_24Y] :
( c_24__type__6___24t(V_24Y)
<=> t(V_24Y,c_24__type__6) ) ).
fof('$tdef_$_type_26805',axiom,
! [V_24Y] :
( c_24__type__26805___24t(V_24Y)
<=> t(V_24Y,c_24__type__26805) ) ).
fof('$tdef_$_type_21093',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21093___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21093___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_21118',axiom,
! [V_24Y] :
( c_24__type__21118___24t(V_24Y)
<=> t(V_24Y,c_24__type__21118) ) ).
fof('$tdef_$_type_21114',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__21114___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__21114___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11716',axiom,
! [V_24Y] :
( c_24__type__11716___24t(V_24Y)
<=> t(V_24Y,c_24__type__11716) ) ).
fof('$tdef_$_type_18172',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__18172___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__18172___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_27469',axiom,
! [V_24Y] :
( c_24__type__27469___24t(V_24Y)
<=> t(V_24Y,c_24__type__27469) ) ).
fof('$tdef_$_type_26925',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__26925___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__26925___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12646',axiom,
! [V_24Y] :
( c_24__type__12646___24t(V_24Y)
<=> t(V_24Y,c_24__type__12646) ) ).
fof('$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_30600',axiom,
! [V_24Y] :
( c_24__type__30600___24t(V_24Y)
<=> t(V_24Y,c_24__type__30600) ) ).
fof('$tdef_$_type_27768',axiom,
! [V_24Y] :
( c_24__type__27768___24t(V_24Y)
<=> t(V_24Y,c_24__type__27768) ) ).
fof('$tdef_$_type_5495',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5495___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__5495___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_25311',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__25311___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__25311___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_25569',axiom,
! [V_24Y] :
( c_24__type__25569___24t(V_24Y)
<=> t(V_24Y,c_24__type__25569) ) ).
fof('$tdef_$_type_26224',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__26224___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__26224___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('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_$_type_14539',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14539___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14539___24a1(V_24X1)) ) ).
fof('$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_$_type_295',axiom,
! [V_24Y] :
( c_24__type__295___24t(V_24Y)
<=> t(V_24Y,c_24__type__295) ) ).
fof('$tdef_$_type_28818',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28818___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28818___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_14511',axiom,
! [V_24Y] :
( c_24__type__14511___24t(V_24Y)
<=> t(V_24Y,c_24__type__14511) ) ).
fof('$tdef_$_type_27022',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__27022___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__27022___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_20885',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__20885___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__20885___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_10431',axiom,
! [V_24Y] :
( c_24__type__10431___24t(V_24Y)
<=> t(V_24Y,c_24__type__10431) ) ).
fof('$tdef_$_type_7187',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__7187___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__7187___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('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_6167',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__6167___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__6167___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3438',axiom,
! [V_24Y] :
( c_24__type__3438___24t(V_24Y)
<=> t(V_24Y,c_24__type__3438) ) ).
fof('$tdef_$_type_10703',axiom,
! [V_24Y] :
( c_24__type__10703___24t(V_24Y)
<=> t(V_24Y,c_24__type__10703) ) ).
fof('$tdef_$_type_6116',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__6116___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__6116___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3864',axiom,
! [V_24Y] :
( c_24__type__3864___24t(V_24Y)
<=> t(V_24Y,c_24__type__3864) ) ).
fof('$tdef_$_type_30562',axiom,
! [V_24Y] :
( c_24__type__30562___24t(V_24Y)
<=> t(V_24Y,c_24__type__30562) ) ).
fof('$tdef_$_type_25350',axiom,
! [V_24Y] :
( c_24__type__25350___24t(V_24Y)
<=> t(V_24Y,c_24__type__25350) ) ).
fof('$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_30657',axiom,
! [V_24Y] :
( c_24__type__30657___24t(V_24Y)
<=> t(V_24Y,c_24__type__30657) ) ).
fof('$tdef_$_type_14073',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__14073___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__14073___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9012',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9012___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9012___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__14684___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__14684___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_27231',axiom,
! [V_24Y] :
( c_24__type__27231___24t(V_24Y)
<=> t(V_24Y,c_24__type__27231) ) ).
fof('$tdef_$_type_27273',axiom,
! [V_24Y] :
( c_24__type__27273___24t(V_24Y)
<=> t(V_24Y,c_24__type__27273) ) ).
fof('$tdef_$_type_12621',axiom,
! [V_24Y] :
( c_24__type__12621___24t(V_24Y)
<=> t(V_24Y,c_24__type__12621) ) ).
fof('$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_$_type_144',axiom,
! [V_24Y] :
( c_24__type__144___24t(V_24Y)
<=> t(V_24Y,c_24__type__144) ) ).
fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
! [V_24Y] :
( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).
fof('$tdef_Coq.Init.Datatypes.ID',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).
fof('$tdef_Hammer.Tactics.Reconstr.ReconstrT',axiom,
! [V_24Y] :
( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(V_24Y)
<=> t(V_24Y,cHammer_2eTactics_2eReconstr_2eReconstrT) ) ).
fof('$tdef_$_type_10549',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10549___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10549___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1352',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__1352___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__1352___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_21157',axiom,
! [V_24Y] :
( c_24__type__21157___24t(V_24Y)
<=> t(V_24Y,c_24__type__21157) ) ).
fof('$tdef_$_type_24435',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24435___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__24435___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_15773',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__15773___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__15773___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_26847',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__26847___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__26847___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27626',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__27626___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__27626___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29381',axiom,
! [V_24Y] :
( c_24__type__29381___24t(V_24Y)
<=> t(V_24Y,c_24__type__29381) ) ).
fof('$tdef_$_type_25324',axiom,
! [V_24Y] :
( c_24__type__25324___24t(V_24Y)
<=> t(V_24Y,c_24__type__25324) ) ).
fof('$tdef_$_type_20725',axiom,
! [V_24Y] :
( c_24__type__20725___24t(V_24Y)
<=> t(V_24Y,c_24__type__20725) ) ).
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_$_type_28628',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28628___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28628___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_14536',axiom,
! [V_24Y] :
( c_24__type__14536___24t(V_24Y)
<=> t(V_24Y,c_24__type__14536) ) ).
fof('$tdef_$_type_16119',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__16119___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__16119___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_30101',axiom,
! [V_24Y] :
( c_24__type__30101___24t(V_24Y)
<=> t(V_24Y,c_24__type__30101) ) ).
fof('$tdef_$_type_29474',axiom,
! [V_24Y] :
( c_24__type__29474___24t(V_24Y)
<=> t(V_24Y,c_24__type__29474) ) ).
fof('$tdef_$_type_96',axiom,
! [V_24Y] :
( c_24__type__96___24t(V_24Y)
<=> t(V_24Y,c_24__type__96) ) ).
fof('$tdef_$_type_275',axiom,
! [V_24Y] :
( c_24__type__275___24t(V_24Y)
<=> t(V_24Y,c_24__type__275) ) ).
fof('$tdef_$_type_14218',axiom,
! [V_24Y] :
( c_24__type__14218___24t(V_24Y)
<=> t(V_24Y,c_24__type__14218) ) ).
fof('$tdef_$_type_1897',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1897___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1897___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1102',axiom,
! [V_24Y] :
( c_24__type__1102___24t(V_24Y)
<=> t(V_24Y,c_24__type__1102) ) ).
fof('$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_27673',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__27673___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__27673___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_30522',axiom,
! [V_24Y] :
( c_24__type__30522___24t(V_24Y)
<=> t(V_24Y,c_24__type__30522) ) ).
fof('$tdef_$_type_21560',axiom,
! [V_24Y] :
( c_24__type__21560___24t(V_24Y)
<=> t(V_24Y,c_24__type__21560) ) ).
fof('$tdef_$_type_1075',axiom,
! [V_24Y] :
( c_24__type__1075___24t(V_24Y)
<=> t(V_24Y,c_24__type__1075) ) ).
fof('$tdef_$_type_30292',axiom,
! [V_24Y] :
( c_24__type__30292___24t(V_24Y)
<=> t(V_24Y,c_24__type__30292) ) ).
fof('$tdef_$_type_22394',axiom,
! [V_24Y] :
( c_24__type__22394___24t(V_24Y)
<=> t(V_24Y,c_24__type__22394) ) ).
fof('$tdef_$_type_146',axiom,
! [V_24Y] :
( c_24__type__146___24t(V_24Y)
<=> t(V_24Y,c_24__type__146) ) ).
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_$_type_14750',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__14750___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__14750___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_30544',axiom,
! [V_24Y] :
( c_24__type__30544___24t(V_24Y)
<=> t(V_24Y,c_24__type__30544) ) ).
fof('$tdef_$_type_14713',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__14713___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__14713___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_855',axiom,
! [V_24Y] :
( c_24__type__855___24t(V_24Y)
<=> t(V_24Y,c_24__type__855) ) ).
fof('$tdef_$_type_24551',axiom,
! [V_24Y] :
( c_24__type__24551___24t(V_24Y)
<=> t(V_24Y,c_24__type__24551) ) ).
fof('$tdef_$_type_12226',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12226___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12226___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_14494',axiom,
! [V_24Y] :
( c_24__type__14494___24t(V_24Y)
<=> t(V_24Y,c_24__type__14494) ) ).
fof('$tdef_$_type_12109',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__12109___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__12109___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23341',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23341___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23341___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9339',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__9339___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__9339___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_945',axiom,
! [V_24Y] :
( c_24__type__945___24t(V_24Y)
<=> t(V_24Y,c_24__type__945) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_12797',axiom,
! [V_24Y] :
( c_24__type__12797___24t(V_24Y)
<=> t(V_24Y,c_24__type__12797) ) ).
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_$_type_27278',axiom,
! [V_24Y] :
( c_24__type__27278___24t(V_24Y)
<=> t(V_24Y,c_24__type__27278) ) ).
fof('$tdef_$_type_26474',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26474___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26474___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_25974',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__25974___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__25974___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_890',axiom,
! [V_24Y] :
( c_24__type__890___24t(V_24Y)
<=> t(V_24Y,c_24__type__890) ) ).
fof('$tdef_$_type_30164',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__30164___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__30164___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27286',axiom,
! [V_24X1,V_24Y] :
( c_24__type__27286___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__27286___24a1(V_24X1)) ) ).
fof('$tdef_$_type_14439',axiom,
! [V_24Y] :
( c_24__type__14439___24t(V_24Y)
<=> t(V_24Y,c_24__type__14439) ) ).
fof('$tdef_$_type_17826',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__17826___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__17826___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_30230',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__30230___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__30230___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_27419',axiom,
! [V_24Y] :
( c_24__type__27419___24t(V_24Y)
<=> t(V_24Y,c_24__type__27419) ) ).
fof('$tdef_$_type_27309',axiom,
! [V_24Y] :
( c_24__type__27309___24t(V_24Y)
<=> t(V_24Y,c_24__type__27309) ) ).
fof('$tdef_$_type_28700',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__28700___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__28700___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.Vectors.Fin.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).
fof('$tdef_$_type_13648',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__13648___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__13648___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27502',axiom,
! [V_24Y] :
( c_24__type__27502___24t(V_24Y)
<=> t(V_24Y,c_24__type__27502) ) ).
fof('$tdef_$_type_23155',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__23155___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__23155___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_27379',axiom,
! [V_24Y] :
( c_24__type__27379___24t(V_24Y)
<=> t(V_24Y,c_24__type__27379) ) ).
fof('$tdef_$_type_30038',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__30038___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__30038___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7613',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__7613___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__7613___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_27478',axiom,
! [V_24Y] :
( c_24__type__27478___24t(V_24Y)
<=> t(V_24Y,c_24__type__27478) ) ).
fof('$tdef_$_type_23911',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__23911___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__23911___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$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_27555',axiom,
! [V_24Y] :
( c_24__type__27555___24t(V_24Y)
<=> t(V_24Y,c_24__type__27555) ) ).
fof('$tdef_$_type_14228',axiom,
! [V_24Y] :
( c_24__type__14228___24t(V_24Y)
<=> t(V_24Y,c_24__type__14228) ) ).
fof('$tdef_$_type_7826',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__7826___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__7826___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('$tdef_Coq.Reals.RIneq.negreal',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRIneq_2enegreal___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRIneq_2enegreal) ) ).
fof('$tdef_$_type_950',axiom,
! [V_24Y] :
( c_24__type__950___24t(V_24Y)
<=> t(V_24Y,c_24__type__950) ) ).
fof('$tdef_$_type_20698',axiom,
! [V_24Y] :
( c_24__type__20698___24t(V_24Y)
<=> t(V_24Y,c_24__type__20698) ) ).
fof('$tdef_$_type_29563',axiom,
! [V_24Y] :
( c_24__type__29563___24t(V_24Y)
<=> t(V_24Y,c_24__type__29563) ) ).
fof('$tdef_$_type_9482',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9482___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9482___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.Empty_set',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eEmpty__set___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eEmpty__set) ) ).
fof('$tdef_$_type_14434',axiom,
! [V_24Y] :
( c_24__type__14434___24t(V_24Y)
<=> t(V_24Y,c_24__type__14434) ) ).
fof('$tdef_$_type_19833',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__19833___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__19833___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_29584',axiom,
! [V_24Y] :
( c_24__type__29584___24t(V_24Y)
<=> t(V_24Y,c_24__type__29584) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__M] :
( cLambda_2eTerms_2elambda___24t(V0__M)
=> ! [V1__N] :
( cLambda_2eTerms_2elambda___24t(V1__N)
=> ( cReduction_2ered___24a2(V0__M,V1__N)
=> cReduction_2epar__red___24a2(V0__M,V1__N) ) ) ) ).
%------------------------------------------------------------------------------