TPTP Problem File: SEV639+1.p
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%------------------------------------------------------------------------------
% File : SEV639+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - InverseImageLemmas inverse image id
% 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 : InverseImageLemmas.inverse.image.id.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2759 ( 947 unt; 0 def)
% Number of atoms : 10030 (2806 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 7511 ( 240 ~; 662 |;1331 &)
% ( 981 <=>;4297 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 513 ( 512 usr; 0 prp; 1-23 aty)
% Number of functors : 1596 (1596 usr;1032 con; 0-22 aty)
% Number of variables : 9153 (8672 !; 481 ?)
% 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.nat$18812',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2418812___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__18813] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18813)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18813)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2418812___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__18813)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$18834',axiom,
! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__18835] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__18835)
& Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__18835)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__18835)) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$225',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24225___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__1 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0) ) )
| ? [Vvar__0___24Anonymous__226] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__226)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__226)
& ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24225___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ? [Vvar__v__CANONICAL__4__227] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vvar__v__CANONICAL__4__227)
& ? [Vvar__v__CANONICAL__5__228] :
( t(Vvar__v__CANONICAL__5__228,Vv__CANONICAL__0)
& Vv__CANONICAL__1 = cCoq_2eSets_2eEnsembles_2eAdd___24a3(Vv__CANONICAL__0,Vvar__v__CANONICAL__4__227,Vvar__v__CANONICAL__5__228)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vvar__v__CANONICAL__4__227,Vvar__v__CANONICAL__5__228)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vv__CANONICAL__0,Vvar__v__CANONICAL__4__227,Vvar__0___24Anonymous__226) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.nat$235',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
& ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24235___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__1 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vv__CANONICAL__0) ) )
| ? [Vvar__0___24Anonymous__236] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__236)
& Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__236)
& ( c_24__case__Coq_2eInit_2eDatatypes_2enat_24235___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) ) ) ) ) ).
fof('$_case_Coq.Init.Datatypes.prod$27660',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__27673___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__27665] :
( t(Vvar__2___24Anonymous__27665,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__27666] :
( t(Vvar__3___24Anonymous__27666,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__27665,Vvar__3___24Anonymous__27666)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2427660___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__27665)),Vvar__3___24Anonymous__27666)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Numbers.BinNums.Z$18829',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2418829___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__18830] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18830)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18830)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2418829___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18830) )
| ? [Vvar__0___24Anonymous__18831] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__18831)
& c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__18831)
& c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2418829___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__18831) ) ) ) ).
fof('$_def_$_let_2_C_1127',axiom,
! [V0__U,V1__D] : c_24__let__2__C__1127___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_1259',axiom,
! [V0__U,V1__D] : c_24__let__2__C__1259___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_1409',axiom,
! [V0__U,V1__D] : c_24__let__2__C__1409___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_1777',axiom,
! [V0__U,V1__D] : c_24__let__2__C__1777___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_1921',axiom,
! [V0__U,V1__D] : c_24__let__2__C__1921___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_2464',axiom,
! [V0__U,V1__D] : c_24__let__2__C__2464___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_2591',axiom,
! [V0__U,V1__D] : c_24__let__2__C__2591___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_2721',axiom,
! [V0__U,V1__D] : c_24__let__2__C__2721___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_2855',axiom,
! [V0__U,V1__D] : c_24__let__2__C__2855___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_413',axiom,
! [V0__U,V1__D] : c_24__let__2__C__413___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_563',axiom,
! [V0__U,V1__D] : c_24__let__2__C__563___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_695',axiom,
! [V0__U,V1__D] : c_24__let__2__C__695___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_845',axiom,
! [V0__U,V1__D] : c_24__let__2__C__845___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_2_C_977',axiom,
! [V0__U,V1__D] : c_24__let__2__C__977___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_1128',axiom,
! [V0__U,V1__D] : c_24__let__3__R__1128___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_1260',axiom,
! [V0__U,V1__D] : c_24__let__3__R__1260___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_1410',axiom,
! [V0__U,V1__D] : c_24__let__3__R__1410___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_1778',axiom,
! [V0__U,V1__D] : c_24__let__3__R__1778___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_1922',axiom,
! [V0__U,V1__D] : c_24__let__3__R__1922___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_2465',axiom,
! [V0__U,V1__D] : c_24__let__3__R__2465___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_2592',axiom,
! [V0__U,V1__D] : c_24__let__3__R__2592___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_2722',axiom,
! [V0__U,V1__D] : c_24__let__3__R__2722___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_2856',axiom,
! [V0__U,V1__D] : c_24__let__3__R__2856___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_414',axiom,
! [V0__U,V1__D] : c_24__let__3__R__414___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_564',axiom,
! [V0__U,V1__D] : c_24__let__3__R__564___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_696',axiom,
! [V0__U,V1__D] : c_24__let__3__R__696___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_846',axiom,
! [V0__U,V1__D] : c_24__let__3__R__846___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_3_R_978',axiom,
! [V0__U,V1__D] : c_24__let__3__R__978___24a2(V0__U,V1__D) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__D) ).
fof('$_def_$_let_var_6_p_24343_24346',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24342] : c_24__let__var__6__p__24343__24346___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24342) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24342) ).
fof('$_def_$_let_var_6_p_24345_24347',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24344] : c_24__let__var__6__p__24345__24347___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24344) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24344) ).
fof('$_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__14944] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14944)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14944)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) ) ) ) )
| ? [Vvar__0___24Anonymous__14945] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14945)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14945)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> p(c_24False) ) )
| ? [Vvar__0___24Anonymous__14948] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__14948)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__14948)
& ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__14945,Vvar__0___24Anonymous__14948) ) ) ) ) ) ) ) ) ).
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('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.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.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__29191] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29191)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29191)
& cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
! [V0__s,V1__s_27] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V0__s,V1__s_27)
<=> ! [V2__a] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__a)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V0__s)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V2__a,V1__s_27) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V0__i,V1__t)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V0__i,V1__t) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__12869] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__12869)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__12869) ) ).
fof('$_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__12917] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__12917)
& ? [Vvar__1___24Anonymous__12918] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__12918)
& ? [Vvar__2___24Anonymous__12919] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__12919)
& ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
=> ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__12917,Vvar__1___24Anonymous__12918,Vvar__2___24Anonymous__12919)
& ( ? [Vvar__0___24Anonymous__12932] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12932)
& V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12932)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__12932,Vvar__2___24Anonymous__12919) )
| ? [Vvar__0___24Anonymous__12933] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12933)
& V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12933)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__12933,Vvar__0___24Anonymous__12917) )
| ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__12918 ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
! [V1__y,V2__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__y)
=> ( ? [Vvar__0___24Anonymous__32784] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32784)
& V1__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32784)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__32784,cCoq_2eNumbers_2eBinNums_2exI___24a1(V2__x)) )
| ? [Vvar__0___24Anonymous__32785] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32785)
& V1__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32785)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(Vvar__0___24Anonymous__32785,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__x)) )
| ( V1__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V1__y,V2__x) = V2__x ) ) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__12895] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__12895)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__12895) ) ).
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.CompSpecT',axiom,
! [V0__A,V1__eq,V2__lt,V3__x,V4__y] : cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V0__A,V1__eq,V2__lt,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(happ(happ(V1__eq,V3__x),V4__y),happ(happ(V2__lt,V3__x),V4__y),happ(happ(V2__lt,V4__y),V3__x)) ).
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('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__3360] :
( t(Vvar__1___24Anonymous__3360,V0__A)
& ? [Vvar__2___24Anonymous__3361] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3361)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3360,Vvar__2___24Anonymous__3361)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3360,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__3361,V3__m)) ) ) ) ) ) ).
fof('$_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__3311] :
( t(Vvar__2___24Anonymous__3311,V0__A)
& ? [Vvar__3___24Anonymous__3312] :
( t(Vvar__3___24Anonymous__3312,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__3311,Vvar__3___24Anonymous__3312)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__3311 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__14495] :
( t(Vvar__1___24Anonymous__14495,V0__A)
& ? [Vvar__2___24Anonymous__14496] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14496)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14495,Vvar__2___24Anonymous__14496)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__14496)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.negb',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2efalse )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).
fof('$_def_Coq.Init.Datatypes.orb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = V1__b2 ) ) ) ).
fof('$_def_Coq.Init.Datatypes.snd',axiom,
! [V0__A,V1__B,V2__p] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
=> ? [Vvar__2___24Anonymous__3323] :
( t(Vvar__2___24Anonymous__3323,V0__A)
& ? [Vvar__3___24Anonymous__3324] :
( t(Vvar__3___24Anonymous__3324,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__3323,Vvar__3___24Anonymous__3324)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__3324 ) ) ) ) ) ).
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.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__5007] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5007)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5007)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__5007,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.compare',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__5030] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5030)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5030)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__5031] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5031)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5031)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__5034] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5034)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5034)
& cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__5031,Vvar__0___24Anonymous__5034) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.div',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__5053] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5053)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5053)
& cCoq_2eInit_2eNat_2ediv___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__5053,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__5053)) ) ) ) ).
fof('$_def_Coq.Init.Nat.div2',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__5058] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5058)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5058)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5058)
& ( ( Vvar__0___24Anonymous__5058 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__5061] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5061)
& Vvar__0___24Anonymous__5058 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5061)
& cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__5061)) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Nat.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__5021] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5021)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5021)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__5022] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5022)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5022)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__5025] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5025)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5025)
& cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__5022,Vvar__0___24Anonymous__5025) ) ) ) ) ) ) ) ).
fof('$_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__17240] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17240)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17240)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17240)
& ( ( Vvar__0___24Anonymous__17240 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__17243] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17243)
& Vvar__0___24Anonymous__17240 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17243)
& cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__17243) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.gcd',axiom,
! [V1__a,V2__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__a)
=> ( ( V1__a = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = V2__b )
| ? [Vvar__0___24Anonymous__30479] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30479)
& V1__a = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30479)
& cCoq_2eInit_2eNat_2egcd___24a2(V1__a,V2__b) = cCoq_2eInit_2eNat_2egcd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V2__b,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30479)),cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30479)) ) ) ) ).
fof('$_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__5039] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5039)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5039)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__5042] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5042)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5042)
& cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__5039,Vvar__0___24Anonymous__5042)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.min',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__5045] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5045)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5045)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__0___24Anonymous__5048] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5048)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5048)
& cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__5045,Vvar__0___24Anonymous__5048)) ) ) ) ) ) ) ) ).
fof('$_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__5012] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5012)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5012)
& cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__5012,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.odd',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eInit_2eNat_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.Init.Nat.pow',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
| ? [Vvar__0___24Anonymous__5051] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5051)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5051)
& 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__5051)) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__3058] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3058)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3058)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__3058 ) ) ) ).
fof('$_def_Coq.Init.Nat.shiftl',axiom,
! [V0__a] : cCoq_2eInit_2eNat_2eshiftl___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(c_24__lam__31939,V0__a,c_24__lam__31940) ).
fof('$_def_Coq.Init.Nat.sqrt',axiom,
! [V0__n] : cCoq_2eInit_2eNat_2esqrt___24a1(V0__n) = cCoq_2eInit_2eNat_2esqrt__iter___24a4(V0__n,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_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__5015] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5015)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5015)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__5018] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5018)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5018)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__5015,Vvar__0___24Anonymous__5018) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.testbit',axiom,
! [V1__a,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
| ? [Vvar__0___24Anonymous__5063] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5063)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5063)
& cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__5063) ) ) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ).
fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
! [V0__A,V1__P,V2__e] :
( cType___24t(V0__A)
=> ( c_24__type__9270___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> ? [Vvar__2__x__9264] :
( t(Vvar__2__x__9264,V0__A)
& p(happ(V1__P,Vvar__2__x__9264))
& V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__9264)
& cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__9264 ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT1',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__9450___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__9444] :
( t(Vvar__2__x__9444,V0__A)
& ? [Vvar__3___24Anonymous__9445] :
( t(Vvar__3___24Anonymous__9445,happ(V1__P,Vvar__2__x__9444))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__9444,Vvar__3___24Anonymous__9445)
& cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__9444 ) ) ) ) ) ).
fof('$_def_Coq.Init.Specif.projT2',axiom,
! [V0__A,V1__P,V2__x] :
( cType___24t(V0__A)
=> ( c_24__type__9473___24t(V0__A,V1__P,V1__P)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
=> ? [Vvar__2__x__9467] :
( t(Vvar__2__x__9467,V0__A)
& ? [Vvar__3___24Anonymous__9468] :
( t(Vvar__3___24Anonymous__9468,happ(V1__P,Vvar__2__x__9467))
& V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__9467,Vvar__3___24Anonymous__9468)
& cCoq_2eInit_2eSpecif_2eprojT2___24a3(V0__A,V1__P,V2__x) = Vvar__3___24Anonymous__9468 ) ) ) ) ) ).
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__17008] :
( t(Vvar__1___24Anonymous__17008,V0__A)
& ? [Vvar__2___24Anonymous__17009] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__17009)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__17008,Vvar__2___24Anonymous__17009)
& ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
<=> ( Vvar__1___24Anonymous__17008 = V2__a
| cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__17009) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_left',axiom,
! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
| ? [Vvar__1___24Anonymous__17045] :
( t(Vvar__1___24Anonymous__17045,V1__B)
& ? [Vvar__2___24Anonymous__17046] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__17046)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__17045,Vvar__2___24Anonymous__17046)
& cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__17046,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__17045)) ) ) ) ) ) ) ).
fof('$_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__17076] :
( t(Vvar__1___24Anonymous__17076,V1__B)
& ? [Vvar__2___24Anonymous__17077] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__17077)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__17076,Vvar__2___24Anonymous__17077)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__17076),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__17077)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.last',axiom,
! [V0__A,V2__l,V3__d] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
| ? [Vvar__1___24Anonymous__56171] :
( t(Vvar__1___24Anonymous__56171,V0__A)
& ? [Vvar__2___24Anonymous__56172] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__56172)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__56172)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__56171,Vvar__2___24Anonymous__56172)
& ( ( Vvar__2___24Anonymous__56172 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__56171 )
| ? [Vvar__1___24Anonymous__56183] :
( t(Vvar__1___24Anonymous__56183,V0__A)
& ? [Vvar__2___24Anonymous__56184] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__56184)
& Vvar__2___24Anonymous__56172 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__56183,Vvar__2___24Anonymous__56184)
& cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__56172,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.map',axiom,
! [V0__A,V1__B,V2__f,V4__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
| ? [Vvar__1___24Anonymous__31897] :
( t(Vvar__1___24Anonymous__31897,V0__A)
& ? [Vvar__2___24Anonymous__31898] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__31898)
& V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__31897,Vvar__2___24Anonymous__31898)
& cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__31897),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__31898)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.nth',axiom,
! [V0__A,V2__n,V3__l,V4__default] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__17020] :
( t(Vvar__1___24Anonymous__17020,V0__A)
& ? [Vvar__2___24Anonymous__17021] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__17021)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__17020,Vvar__2___24Anonymous__17021)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__17020 ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__17023] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__17023)
& ( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__17023)
& ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
| ? [Vvar__1___24Anonymous__17030] :
( t(Vvar__1___24Anonymous__17030,V0__A)
& ? [Vvar__2___24Anonymous__17031] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__17031)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__17030,Vvar__2___24Anonymous__17031)
& cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__17023,Vvar__2___24Anonymous__17031,V4__default) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.compat_bool',axiom,
! [V0__A,V1__eqA,V2__f] :
( cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V0__A,V1__eqA,V2__f)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__30435___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cCoq_2eInit_2eDatatypes_2ebool,V1__eqA,c_3d___24a1(cCoq_2eInit_2eDatatypes_2ebool)),V2__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.Logic.ClassicalFacts.excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> ( p(V0__A)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_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('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V0__U)
<=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__9219___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x) ) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
! [V0__U,V1__p,V2__Q,V3__x] :
( cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on___24a4(V0__U,V1__p,V2__Q,V3__x)
<=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
! [V0__U,V1__x,V2__P] :
( cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V0__U,V1__x,V2__P)
<=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_',axiom,
! [V0__U] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP_____24a1(V0__U)
<=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y) ) ) ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_on_',axiom,
! [V0__U,V1__x,V2__y] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V0__U,V1__x,V2__y)
<=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ).
fof('$_def_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
! [V0__U,V1__x] :
( cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V0__U,V1__x)
<=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.b2n',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V0__b) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('$_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('$_def_Coq.NArith.BinNat.N.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__12398] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12398)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12398)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__12401] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12401)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12401)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__12398,Vvar__0___24Anonymous__12401)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.compare',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq )
| ? [Vvar__0___24Anonymous__12420] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12420)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12420)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
| ? [Vvar__0___24Anonymous__12421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12421)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12421)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__12424] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12424)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12424)
& cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__12421,Vvar__0___24Anonymous__12424) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.double',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12390] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12390)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12390)
& cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12390)) ) ) ) ).
fof('$_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__31474] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31474)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31474)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__31475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31475)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31475)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__31478] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31478)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31478)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__31475,Vvar__0___24Anonymous__31478) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__12429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12429)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12429)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12429)
& ( ? [Vvar__0___24Anonymous__12433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12433)
& Vvar__0___24Anonymous__12429 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12433)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__12434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12434)
& Vvar__0___24Anonymous__12429 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12434)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
| ( Vvar__0___24Anonymous__12429 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V1__b )
| ? [Vvar__0___24Anonymous__12450] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12450)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12450)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = V0__a )
| ? [Vvar__0___24Anonymous__12453] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12453)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12453)
& cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__12450,Vvar__0___24Anonymous__12453)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.log2',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12442] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12442)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12442)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12442)
& ( ? [Vvar__0___24Anonymous__12446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12446)
& Vvar__0___24Anonymous__12442 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12446)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__12446)) )
| ? [Vvar__0___24Anonymous__12447] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12447)
& Vvar__0___24Anonymous__12442 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12447)
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__12447)) )
| ( Vvar__0___24Anonymous__12442 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).
fof('$_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.modulo',axiom,
! [V0__a,V1__b] : cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12415] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12415)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12415)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12418] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12418)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12418)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__12415,Vvar__0___24Anonymous__12418)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.odd',axiom,
! [V0__n] : cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2enegb___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n)) ).
fof('$_def_Coq.NArith.BinNatDef.N.pow',axiom,
! [V0__n,V1__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__p)
=> ( ( V1__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__12437] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12437)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V1__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12437)
& ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12440] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12440)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12440)
& cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__n,V1__p) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(Vvar__0___24Anonymous__12440,Vvar__0___24Anonymous__12437)) ) ) ) ) ) ) ) ).
fof('$_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__12394] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12394)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12394)
& cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__12394) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12455] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12455)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12455)
& cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__12455)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12405)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12405)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__12410] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12410)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12405)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12410)
=> ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12410)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__12405,Vvar__0___24Anonymous__12410) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12413] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12413)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__12405,Vvar__0___24Anonymous__12410) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__12413)
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12413) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__12405,Vvar__0___24Anonymous__12410) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
& cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__12393] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12393)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12393)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12393)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__32768] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32768)
& V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__32768)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32768)) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
! [V0__a,V1__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__12484] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12484)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12484)
& cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__12484,V1__n) ) ) ) ).
fof('$_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__12488] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12488)
& V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12488)
& cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__12488) ) ) ) ).
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.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__12611] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12611)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12611)
& ( ? [Vvar__0___24Anonymous__12615] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12615)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12615)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__12610__1__add__carry___24a2(Vvar__0___24Anonymous__12611,Vvar__0___24Anonymous__12615)) )
| ? [Vvar__0___24Anonymous__12616] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12616)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12616)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__12611,Vvar__0___24Anonymous__12616)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12611)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12617] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12617)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12617)
& ( ? [Vvar__0___24Anonymous__12621] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12621)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12621)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__12617,Vvar__0___24Anonymous__12621)) )
| ? [Vvar__0___24Anonymous__12622] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12622)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12622)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__12617,Vvar__0___24Anonymous__12622)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12617) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__12623] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12623)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12623)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12623)) )
| ? [Vvar__0___24Anonymous__12624] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12624)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12624)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12624) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.compare',axiom,
cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
! [V0__A,V1__f,V3__x,V4__n] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
=> ( ? [Vvar__0___24Anonymous__12692] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12692)
& V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12692)
& 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__12692),Vvar__0___24Anonymous__12692)) )
| ? [Vvar__0___24Anonymous__12693] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12693)
& V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12693)
& 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__12693),Vvar__0___24Anonymous__12693) )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
! [V0__A,V1__op,V3__p,V4__a] :
( cType___24t(V0__A)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
=> ( ? [Vvar__0___24Anonymous__12809] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12809)
& V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12809)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__12809,happ(happ(V1__op,V4__a),V4__a))) )
| ? [Vvar__0___24Anonymous__12810] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12810)
& V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12810)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__12810,happ(happ(V1__op,V4__a),V4__a)) )
| ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).
fof('$_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__12688] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12688)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12688)
& 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__12688,V2__y))) )
| ? [Vvar__0___24Anonymous__12689] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12689)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12689)
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__12689,V2__y)) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__12828] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12828)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12828)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12828)
& ( ( Vvar__0___24Anonymous__12828 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__12831] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12831)
& Vvar__0___24Anonymous__12828 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__12831)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__12828)) ) ) ) ) ) ) ) ).
fof('$_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__29445] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__29445)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__29445)
& 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__29445)) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.pred',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( ? [Vvar__0___24Anonymous__56475] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56475)
& V0__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__56475)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__56475) )
| ? [Vvar__0___24Anonymous__56476] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56476)
& V0__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__56476)
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(Vvar__0___24Anonymous__56476) )
| ( V0__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
| ? [Vvar__0___24Anonymous__12685] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12685)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__12685)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__12685 )
| ( 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('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
! [V1__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
=> ( ? [Vvar__0___24Anonymous__12608] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12608)
& V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12608)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12608)) )
| ? [Vvar__0___24Anonymous__12609] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12609)
& V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12609)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12609) )
| ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('$_def_Coq.Reals.RIneq.Rsqr',axiom,
! [V0__r] : cCoq_2eReals_2eRIneq_2eRsqr___24a1(V0__r) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r,V0__r) ).
fof('$_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__5106] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5106)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__5106)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__5106) )
| ? [Vvar__0___24Anonymous__5107] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5107)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__5107)
& cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__5107)) ) ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rdiv',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rdefinitions.Rge',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rgt',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V1__r2,V0__r1) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rle',axiom,
! [V0__r1,V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
<=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2 ) ) ).
fof('$_def_Coq.Reals.Rdefinitions.Rminus',axiom,
! [V0__r1,V1__r2] : cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r1,cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V1__r2)) ).
fof('$_def_Coq.Reals.Rpow_def.pow',axiom,
! [V1__r,V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
| ? [Vvar__0___24Anonymous__9094] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__9094)
& V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__9094)
& cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,V2__n) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r,cCoq_2eReals_2eRpow__def_2epow___24a2(V1__r,Vvar__0___24Anonymous__9094)) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__3131___24a1(V0__A) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.Sets.Cpo.Complete_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eComplete__rec___24a2(V0__U,V1__D) = c_24__lam__2595___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Complete_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eComplete__rect___24a2(V0__U,V1__D) = c_24__generic__case__2506 ).
fof('$_def_Coq.Sets.Cpo.Conditionally_complete_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eConditionally__complete__rec___24a2(V0__U,V1__D) = c_24__lam__2859___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Conditionally_complete_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a2(V0__U,V1__D) = c_24__generic__case__2764 ).
fof('$_def_Coq.Sets.Cpo.Glb_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eGlb__rec___24a2(V0__U,V1__D) = c_24__lam__1420___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Glb_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eGlb__rect___24a2(V0__U,V1__D) = c_24__generic__case__1313 ).
fof('$_def_Coq.Sets.Cpo.Lower_Bound_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eLower__Bound__rec___24a2(V0__U,V1__D) = c_24__lam__856___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Lower_Bound_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eLower__Bound__rect___24a2(V0__U,V1__D) = c_24__generic__case__749 ).
fof('$_def_Coq.Sets.Cpo.Lub_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eLub__rec___24a2(V0__U,V1__D) = c_24__lam__1138___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Lub_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eLub__rect___24a2(V0__U,V1__D) = c_24__generic__case__1031 ).
fof('$_def_Coq.Sets.Cpo.Totally_ordered_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eTotally__ordered__rec___24a2(V0__U,V1__D) = c_24__lam__1928___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Totally_ordered_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a2(V0__U,V1__D) = c_24__generic__case__1826 ).
fof('$_def_Coq.Sets.Cpo.Upper_Bound_rec',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eUpper__Bound__rec___24a2(V0__U,V1__D) = c_24__lam__574___24a2(V0__U,V1__D) ).
fof('$_def_Coq.Sets.Cpo.Upper_Bound_rect',axiom,
! [V0__U,V1__D] : cCoq_2eSets_2eCpo_2eUpper__Bound__rect___24a2(V0__U,V1__D) = c_24__generic__case__467 ).
fof('$_def_Coq.Sets.Ensembles.Add',axiom,
! [V0__U,V1__B,V2__x] : cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__B,V2__x) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x)) ).
fof('$_def_Coq.Sets.Ensembles.Complement',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eComplement___24a3(V0__U,V1__A,V2__x)
<=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x) ) ).
fof('$_def_Coq.Sets.Ensembles.Disjoint_rec',axiom,
! [V0__U,V1__B,V2__C,V3__P] : cCoq_2eSets_2eEnsembles_2eDisjoint__rec___24a4(V0__U,V1__B,V2__C,V3__P) = cCoq_2eSets_2eEnsembles_2eDisjoint__rect___24a4(V0__U,V1__B,V2__C,V3__P) ).
fof('$_def_Coq.Sets.Ensembles.Ensemble',axiom,
! [V0__U] : cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U) = c_24__type__5___24a1(V0__U) ).
fof('$_def_Coq.Sets.Ensembles.In',axiom,
! [V0__U,V1__A,V2__x] :
( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V2__x)
<=> p(happ(V1__A,V2__x)) ) ).
fof('$_def_Coq.Sets.Ensembles.Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Same_set',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__B,V2__C)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__C,V1__B) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Setminus',axiom,
! [V0__U,V1__B,V2__C,V3__x] :
( cCoq_2eSets_2eEnsembles_2eSetminus___24a4(V0__U,V1__B,V2__C,V3__x)
<=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ).
fof('$_def_Coq.Sets.Ensembles.Strict_Included',axiom,
! [V0__U,V1__B,V2__C] :
( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__B,V2__C)
<=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__B,V2__C)
& V1__B != V2__C ) ) ).
fof('$_def_Coq.Sets.Ensembles.Subtract',axiom,
! [V0__U,V1__B,V2__x] : cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__B,V2__x) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V1__B,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x)) ).
fof('$_def_Coq.Sets.Partial_Order.Carrier',axiom,
! [V0__U] : cCoq_2eSets_2ePartial__Order_2eCarrier___24a1(V0__U) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U) ).
fof('$_def_Coq.Sets.Partial_Order.Carrier_of',axiom,
! [V0__U,V1__p] :
( cType___24t(V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ? [Vvar__1__Carrier__of__3090] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,Vvar__1__Carrier__of__3090)
& ? [Vvar__2__Rel__of__3091] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,Vvar__2__Rel__of__3091)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,Vvar__1__Carrier__of__3090)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,Vvar__2__Rel__of__3091)
& V1__p = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V0__U,Vvar__1__Carrier__of__3090,Vvar__2__Rel__of__3091)
& cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__p) = Vvar__1__Carrier__of__3090 ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Rel_of',axiom,
! [V0__U,V1__p] :
( cType___24t(V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ? [Vvar__1__Carrier__of__303] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,Vvar__1__Carrier__of__303)
& ? [Vvar__2__Rel__of__304] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,Vvar__2__Rel__of__304)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,Vvar__1__Carrier__of__303)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,Vvar__2__Rel__of__304)
& V1__p = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V0__U,Vvar__1__Carrier__of__303,Vvar__2__Rel__of__304)
& cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__p) = Vvar__2__Rel__of__304 ) ) ) ) ).
fof('$_def_Coq.Sets.Partial_Order.Strict_Rel_of',axiom,
! [V0__U,V1__p,V2__x,V3__y] :
( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V2__x,V3__y)
<=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__p,V2__x,V3__y)
& V2__x != V3__y ) ) ).
fof('$_def_Coq.Sets.Powerset.Power_set_PO',axiom,
! [V0__U,V1__A] : cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a5(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__Inhabited___24a2(V0__U,V1__A),cCoq_2eSets_2ePowerset_2eInclusion__is__an__order___24a1(V0__U)) ).
fof('$_def_Coq.Sets.Relations_1.Antisymmetric',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.Reflexive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__3131___24a1(V0__U) ).
fof('$_def_Coq.Sets.Relations_1.Transitive',axiom,
! [V0__U,V1__R] :
( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.contains',axiom,
! [V0__U,V1__R,V2__R_27] :
( cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V1__R,V2__R_27)
<=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__y] :
( t(V4__y,V0__U)
=> ( p(happ(happ(V2__R_27,V3__x),V4__y))
=> p(happ(happ(V1__R,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Sets.Relations_1.same_relation',axiom,
! [V0__U,V1__R,V2__R_27] :
( cCoq_2eSets_2eRelations__1_2esame__relation___24a3(V0__U,V1__R,V2__R_27)
<=> ( cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V1__R,V2__R_27)
& cCoq_2eSets_2eRelations__1_2econtains___24a3(V0__U,V2__R_27,V1__R) ) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
! [Vvar__29400] :
( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__29400)
<=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__29400) ) ).
fof('$_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__12606] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__12606)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__12606) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__29321] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__29321)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29321) ) ).
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.t',axiom,
! [Vvar__29534] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__29534)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__29534) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq = c_3d___24a1(cCoq_2eStrings_2eString_2estring) ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt = cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts ).
fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
! [Vvar__29536] :
( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__29536)
<=> cCoq_2eStrings_2eString_2estring___24t(Vvar__29536) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__29593] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__29593)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__29593) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.Bezout',axiom,
! [V0__n,V1__m,V2__p] :
( cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V0__n,V1__m,V2__p)
<=> ? [V3__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__a)
& ? [V4__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__b)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__a,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__b,V1__m)) = V2__p ) ) ) ).
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('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
! [V0__f,V1__g] :
( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
<=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.gt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
<=> V0__x != V1__y ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29552] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29552)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29552)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29552) )
| ? [Vvar__0___24Anonymous__29553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29553)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29553)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29553) ) ) ) ).
fof('$_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__13518] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13518)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13518)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__13522] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13522)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13522)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__13518,Vvar__0___24Anonymous__13522)) )
| ? [Vvar__0___24Anonymous__13523] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13523)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13523)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__13518,Vvar__0___24Anonymous__13523) ) ) ) ) )
| ? [Vvar__0___24Anonymous__13524] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13524)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13524)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__13528] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13528)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13528)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__13528,Vvar__0___24Anonymous__13524) )
| ? [Vvar__0___24Anonymous__13529] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13529)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13529)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__13524,Vvar__0___24Anonymous__13529)) ) ) ) ) ) ) ) ).
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__13552] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13552)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13552)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__13553] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13553)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13553)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__13554] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13554)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13554)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__13558] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13558)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13558)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__13554,Vvar__0___24Anonymous__13558) )
| ? [Vvar__0___24Anonymous__13559] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13559)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13559)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__13560] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13560)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13560)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__13564] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13564)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13564)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__13565] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13565)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13565)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__13560,Vvar__0___24Anonymous__13565)) ) ) ) ) ) ) ) ).
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__13601] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__13601)
& ? [Vvar__3___24Anonymous__13602] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__13602)
& 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__13601,Vvar__3___24Anonymous__13602)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__13601 ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.eqb',axiom,
! [V1__x,V2__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
=> ( ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZ0
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__13572] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13572)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13572)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__13573] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13573)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13573)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__13574] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13574)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13574)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__13578] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13578)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13578)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__13574,Vvar__0___24Anonymous__13578) )
| ? [Vvar__0___24Anonymous__13579] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13579)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13579)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
| ? [Vvar__0___24Anonymous__13580] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13580)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
=> ( V1__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13580)
& ( ( V2__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__13584] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13584)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13584)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__13585] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13585)
& V2__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13585)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V1__x,V2__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__13580,Vvar__0___24Anonymous__13585) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.gcd',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b) )
| ? [Vvar__0___24Anonymous__31828] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31828)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31828)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__31832] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31832)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31832)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__31828,Vvar__0___24Anonymous__31832)) )
| ? [Vvar__0___24Anonymous__31833] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31833)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31833)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__31828,Vvar__0___24Anonymous__31833)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__31834] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31834)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31834)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
| ? [Vvar__0___24Anonymous__31838] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31838)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31838)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__31834,Vvar__0___24Anonymous__31838)) )
| ? [Vvar__0___24Anonymous__31839] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31839)
& V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31839)
& cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__31834,Vvar__0___24Anonymous__31839)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.leb',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eBinIntDef_2eZ_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.log2',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__31821] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31821)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31821)
=> ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31821)
& ( ? [Vvar__0___24Anonymous__31825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31825)
& Vvar__0___24Anonymous__31821 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__31825)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__31825)) )
| ? [Vvar__0___24Anonymous__31826] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31826)
& Vvar__0___24Anonymous__31821 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__31826)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(Vvar__0___24Anonymous__31826)) )
| ( Vvar__0___24Anonymous__31821 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) )
| ? [Vvar__0___24Anonymous__31827] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31827)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31827)
& cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
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('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ? [Vvar__2___24Anonymous__13609] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__13609)
& ? [Vvar__3___24Anonymous__13610] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__13610)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__13609,Vvar__3___24Anonymous__13610)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__13610 ) ) ) ) ).
fof('$_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__13536] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13536)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13536)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__13540] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13540)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13540)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__13536,Vvar__0___24Anonymous__13540)) )
| ? [Vvar__0___24Anonymous__13541] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13541)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13541)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__13536,Vvar__0___24Anonymous__13541)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__13542] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13542)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13542)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__13546] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13546)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13546)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__13542,Vvar__0___24Anonymous__13546)) )
| ? [Vvar__0___24Anonymous__13547] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13547)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13547)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__13542,Vvar__0___24Anonymous__13547)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__29556] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29556)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29556)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29556) ) ) ) ).
fof('$_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__31811] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31811)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31811)
& 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__31811)) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.opp',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__13533] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13533)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13533)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13533) )
| ? [Vvar__0___24Anonymous__13534] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13534)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13534)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13534) ) ) ) ).
fof('$_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__13549] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13549)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__13549)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__13549) )
| ? [Vvar__0___24Anonymous__13550] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__13550)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__13550)
& cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.pred',axiom,
! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.quot',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2efst___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.rem',axiom,
! [V0__a,V1__b] : cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b)) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
! [V0__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
=> ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__31809] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31809)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__31809)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__31810] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31810)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__31810)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__32813] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32813)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32813)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(Vvar__0___24Anonymous__32813)) )
| ? [Vvar__0___24Anonymous__32814] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32814)
& V0__n = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32814)
& cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('$_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.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__29559] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29559)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__29559)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__29559 )
| ? [Vvar__0___24Anonymous__29560] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29560)
& V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__29560)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).
fof('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.ZArith.Zdiv.Remainder',axiom,
! [V0__r,V1__b] :
( cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V0__r,V1__b)
<=> ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__r))
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__r,V1__b) )
| ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__b,V0__r)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__r,cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ) ).
fof('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__3544___24a1(V0__D) ).
fof('$_def_Coq.micromega.Env.jump',axiom,
! [V0__D,V1__j,V2__e,V3__x] : cCoq_2emicromega_2eEnv_2ejump___24a4(V0__D,V1__j,V2__e,V3__x) = happ(V2__e,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V3__x,V1__j)) ).
fof('$_def_Coq.micromega.Env.nth',axiom,
! [V0__D,V1__n,V2__e] : cCoq_2emicromega_2eEnv_2enth___24a3(V0__D,V1__n,V2__e) = happ(V2__e,V1__n) ).
fof('$_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__18753] :
( t(Vvar__1___24Anonymous__18753,V1__A)
& ? [Vvar__2___24Anonymous__18754] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__18754)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__18754)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__18753,Vvar__2___24Anonymous__18754)
& ( ( Vvar__2___24Anonymous__18754 = 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__18753)) ) )
| ? [Vvar__1___24Anonymous__18765] :
( t(Vvar__1___24Anonymous__18765,V1__A)
& ? [Vvar__2___24Anonymous__18766] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__18766)
& Vvar__2___24Anonymous__18754 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__18765,Vvar__2___24Anonymous__18766)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__18753))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__18754) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__4750] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__4750)
& ? [Vvar__2___24Anonymous__4751] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__4751)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__4750,Vvar__2___24Anonymous__4751)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__4750),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__4751,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.condition',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__4275] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__4275)
& ? [Vvar__2__denum__4276] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__4276)
& ? [Vvar__3__condition__4277] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__4277)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__4275,Vvar__2__denum__4276,Vvar__3__condition__4277)
& cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V0__C,V1__l) = Vvar__3__condition__4277 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.denum',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__4266] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__4266)
& ? [Vvar__2__denum__4267] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__4267)
& ? [Vvar__3__condition__4268] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__4268)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__4266,Vvar__2__denum__4267,Vvar__3__condition__4268)
& cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V0__C,V1__l) = Vvar__2__denum__4267 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.num',axiom,
! [V0__C,V1__l] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(V0__C,V1__l)
=> ? [Vvar__1__num__4255] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__num__4255)
& ? [Vvar__2__denum__4256] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__denum__4256)
& ? [Vvar__3__condition__4257] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__3__condition__4257)
& V1__l = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(V0__C,Vvar__1__num__4255,Vvar__2__denum__4256,Vvar__3__condition__4257)
& cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V0__C,V1__l) = Vvar__1__num__4255 ) ) ) ) ) ).
fof('$_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__56097] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__56097)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__56097)
& 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__56097) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__4947] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4947)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__4947)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__4947) )
| ? [Vvar__0___24Anonymous__4948] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__4948)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__4948)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = happ(V5__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__4948)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.triv_div',axiom,
! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
( cType___24t(V0__C)
=> ( c_24__type__4744___24t(V0__C,V3__ceqb)
=> ( t(V4__x,V0__C)
=> ( t(V5__y,V0__C)
=> ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
| ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).
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__5165] :
( t(Vvar__1___24Anonymous__5165,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__5165)
& ( ? [Vvar__1___24Anonymous__5175] :
( t(Vvar__1___24Anonymous__5175,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__5175)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__5165),Vvar__1___24Anonymous__5175) )
| ? [Vvar__1___24Anonymous__5177] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5177)
& ? [Vvar__2___24Anonymous__5178] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5178)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__5177,Vvar__2___24Anonymous__5178)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__5181] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5181)
& ? [Vvar__2___24Anonymous__5182] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5182)
& ? [Vvar__3___24Anonymous__5183] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5183)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__5181,Vvar__2___24Anonymous__5182,Vvar__3___24Anonymous__5183)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__5188] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5188)
& ? [Vvar__2___24Anonymous__5189] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5189)
& ( 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__5188,Vvar__2___24Anonymous__5189)
& ( ? [Vvar__1___24Anonymous__5209] :
( t(Vvar__1___24Anonymous__5209,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__5209)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__5211] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5211)
& ? [Vvar__2___24Anonymous__5212] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5212)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5188)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5211)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__5211,Vvar__2___24Anonymous__5212)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__5188,Vvar__1___24Anonymous__5211) = 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__5189,Vvar__2___24Anonymous__5212) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__5188,Vvar__1___24Anonymous__5211) = 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__5188,Vvar__1___24Anonymous__5211) = 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__5217] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5217)
& ? [Vvar__2___24Anonymous__5218] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5218)
& ? [Vvar__3___24Anonymous__5219] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5219)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__5217,Vvar__2___24Anonymous__5218,Vvar__3___24Anonymous__5219)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__5224] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5224)
& ? [Vvar__2___24Anonymous__5225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5225)
& ? [Vvar__3___24Anonymous__5226] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5226)
& ( 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__5224,Vvar__2___24Anonymous__5225,Vvar__3___24Anonymous__5226)
& ( ? [Vvar__1___24Anonymous__5259] :
( t(Vvar__1___24Anonymous__5259,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__5259)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__5261] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5261)
& ? [Vvar__2___24Anonymous__5262] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__5262)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__5261,Vvar__2___24Anonymous__5262)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__5265] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5265)
& ? [Vvar__2___24Anonymous__5266] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5266)
& ? [Vvar__3___24Anonymous__5267] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__5267)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5225)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5266)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__5265,Vvar__2___24Anonymous__5266,Vvar__3___24Anonymous__5267)
& ( ( cType___24t(V0__C)
=> ( c_24__type__4744___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5224)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__5265)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__5225,Vvar__2___24Anonymous__5266) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__5224,Vvar__1___24Anonymous__5265) = 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__5226,Vvar__3___24Anonymous__5267) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__5224,Vvar__1___24Anonymous__5265) = 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__5225,Vvar__2___24Anonymous__5266) = 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__5225,Vvar__2___24Anonymous__5266) = 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('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).
fof('$_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__24362] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24362)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__24362)
& 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__24362) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
! [V0__R,V1__rmul,V3__x,V4__i] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__i)
=> ( ? [Vvar__0___24Anonymous__24342] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24342)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__24342)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,V3__x),happ(happ(V1__rmul,c_24__let__var__6__p__24343__24346___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24342)),c_24__let__var__6__p__24343__24346___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24342))) )
| ? [Vvar__0___24Anonymous__24344] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__24344)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__24344)
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = happ(happ(V1__rmul,c_24__let__var__6__p__24345__24347___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24344)),c_24__let__var__6__p__24345__24347___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__24344)) )
| ( V4__i = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,V4__i) = V3__x ) ) ) ) ).
fof('$_def_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
! [V0__X,V1__P] : cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,V1__P) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P) ).
fof('$_def_ZornsLemma.Families.Family',axiom,
! [V0__T] : cZornsLemma_2eFamilies_2eFamily___24a1(V0__T) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T)) ).
fof('$_def_ZornsLemma.InverseImage.inverse_image',axiom,
! [V0__X,V1__Y,V2__f,V3__T] : cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__95___24a4(V0__X,V1__Y,V2__f,V3__T)) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__14236,Vvar__1___24Anonymous__14237,Vvar__0__P__14238,Vvar__1___24Anonymous__14239] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__14236) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__14238) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__12874,Vvar__1___24Anonymous__12875,Vvar__2___24Anonymous__12876] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__12874,Vvar__1___24Anonymous__12875,Vvar__2___24Anonymous__12876) ).
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__3410,Vvar__1__Plt__3411,Vvar__2__Pgt__3412,Vvar__3___24Anonymous__3413,Vvar__0__Peq__3414,Vvar__1__Plt__3415,Vvar__2__Pgt__3416,Vvar__3___24Anonymous__3417] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__3410,Vvar__1__Plt__3411,Vvar__2__Pgt__3412) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__3414,Vvar__1__Plt__3415,Vvar__2__Pgt__3416) ).
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__144] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__144) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3267,Vvar__1___24Anonymous__3268,Vvar__0__A__3269] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3267,Vvar__1___24Anonymous__3268) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3269) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__14463,Vvar__1__B__14464,Vvar__2___24Anonymous__14465,Vvar__0__A__14466,Vvar__1__B__14467,Vvar__2___24Anonymous__14468] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__14463,Vvar__1__B__14464,Vvar__2___24Anonymous__14465) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__14466,Vvar__1__B__14467,Vvar__2___24Anonymous__14468) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3337,Vvar__0__A__3338,Vvar__1___24Anonymous__3339,Vvar__2___24Anonymous__3340] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3337) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3338,Vvar__1___24Anonymous__3339,Vvar__2___24Anonymous__3340) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__28557,Vvar__1__B__28558,Vvar__2___24Anonymous__28559,Vvar__0__A__28560,Vvar__1__B__28561,Vvar__2___24Anonymous__28562] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28557,Vvar__1__B__28558,Vvar__2___24Anonymous__28559) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28560,Vvar__1__B__28561) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__11499,Vvar__1__B__11500,Vvar__2___24Anonymous__11501,Vvar__0__A__11502,Vvar__1__B__11503,Vvar__2___24Anonymous__11504] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11499,Vvar__1__B__11500) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11502,Vvar__1__B__11503) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3206] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3206) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__3217] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3217) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__3190,Vvar__0___24Anonymous__3191] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3190) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3191) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__12647] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__12647) ).
fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__18854,Vvar__1___24Anonymous__18855,Vvar__0__x__18856,Vvar__1__n__18857,Vvar__2___24Anonymous__18858] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__18854) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__18856,Vvar__1__n__18857) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__11520,Vvar__1___24Anonymous__11521] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__11520,Vvar__1___24Anonymous__11521) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__18471,Vvar__1__lt__18472,Vvar__2__eq__18473,Vvar__3__x__18474,Vvar__4__y__18475,Vvar__5___24Anonymous__18476,Vvar__0__X__18477,Vvar__1__lt__18478,Vvar__2__eq__18479,Vvar__3__x__18480,Vvar__4__y__18481,Vvar__5___24Anonymous__18482] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__18471,Vvar__1__lt__18472,Vvar__2__eq__18473,Vvar__3__x__18474,Vvar__4__y__18475) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__18477,Vvar__1__lt__18478,Vvar__2__eq__18479,Vvar__3__x__18480,Vvar__4__y__18481) ).
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__16916,Vvar__0__n__16917,Vvar__1___24Anonymous__16918] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__16916) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__16917,Vvar__1___24Anonymous__16918) ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__11577,Vvar__0__A__11578,Vvar__1__h__11579,Vvar__2__n__11580,Vvar__3___24Anonymous__11581] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__11577) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__11578,Vvar__1__h__11579,Vvar__2__n__11580,Vvar__3___24Anonymous__11581) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__14821,Vvar__1___24Anonymous__14822,Vvar__0__C__14823,Vvar__1___24Anonymous__14824] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14821,Vvar__1___24Anonymous__14822) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14823,Vvar__1___24Anonymous__14824) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__14888,Vvar__1___24Anonymous__14889,Vvar__0__C__14890,Vvar__1___24Anonymous__14891,Vvar__2___24Anonymous__14892] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14888,Vvar__1___24Anonymous__14889) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14890,Vvar__1___24Anonymous__14891,Vvar__2___24Anonymous__14892) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__14933,Vvar__1___24Anonymous__14934] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__14933,Vvar__1___24Anonymous__14934) ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__28924,Vvar__1__TX__28925,Vvar__2__AA__28926,Vvar__3__AF__28927,Vvar__0__TA__28928,Vvar__1__TX__28929,Vvar__2__AA__28930,Vvar__3__AF__28931] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28924,Vvar__1__TX__28925,Vvar__2__AA__28926,Vvar__3__AF__28927) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28928,Vvar__1__TX__28929,Vvar__2__AA__28930,Vvar__3__AF__28931) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__3870,Vvar__0__C__3871] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3870) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3871) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__5495,Vvar__0__C__5496] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5495) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5496) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__5139,Vvar__1___24Anonymous__5140,Vvar__0__C__5141,Vvar__1___24Anonymous__5142,Vvar__2___24Anonymous__5143] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5139,Vvar__1___24Anonymous__5140) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5141,Vvar__1___24Anonymous__5142,Vvar__2___24Anonymous__5143) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__5305,Vvar__1___24Anonymous__5306] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5305,Vvar__1___24Anonymous__5306) ).
fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__28071,Vvar__1__req__28072,Vvar__2__reqb__28073,Vvar__3___24Anonymous__28074] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28071,Vvar__1__req__28072,Vvar__2__reqb__28073) ).
fof('$_fix_12610_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__12625] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12625)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12625)
& ( ? [Vvar__0___24Anonymous__12629] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12629)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12629)
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__12610__1__add__carry___24a2(Vvar__0___24Anonymous__12625,Vvar__0___24Anonymous__12629)) )
| ? [Vvar__0___24Anonymous__12630] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12630)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12630)
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__12610__1__add__carry___24a2(Vvar__0___24Anonymous__12625,Vvar__0___24Anonymous__12630)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12625)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__12631] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12631)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12631)
& ( ? [Vvar__0___24Anonymous__12635] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12635)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12635)
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__12610__1__add__carry___24a2(Vvar__0___24Anonymous__12631,Vvar__0___24Anonymous__12635)) )
| ? [Vvar__0___24Anonymous__12636] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12636)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12636)
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__12631,Vvar__0___24Anonymous__12636)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12631)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__12637] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12637)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__12637)
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12637)) )
| ? [Vvar__0___24Anonymous__12638] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12638)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__12638)
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__12638)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__12610__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__14244,Vvar__0__P__14245,Vvar__1___24Anonymous__14246,Vvar__1___24Anonymous__14247] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__14244) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__14245)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__14244 = Vvar__0__P__14245 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__14240,Vvar__0__P__14241,Vvar__1___24Anonymous__14242,Vvar__1___24Anonymous__14243] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__14240) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__14241)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__14240 = Vvar__0__P__14241 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__12877,Vvar__0___24Anonymous__12878,Vvar__1___24Anonymous__12879,Vvar__1___24Anonymous__12880,Vvar__2___24Anonymous__12881,Vvar__2___24Anonymous__12882] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__12877,Vvar__1___24Anonymous__12879,Vvar__2___24Anonymous__12881) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__12878,Vvar__1___24Anonymous__12880,Vvar__2___24Anonymous__12882)
=> ( Vvar__2___24Anonymous__12881 = Vvar__2___24Anonymous__12882
& Vvar__1___24Anonymous__12879 = Vvar__1___24Anonymous__12880
& Vvar__0___24Anonymous__12877 = Vvar__0___24Anonymous__12878 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
! [Vvar__0__Peq__3418,Vvar__0__Peq__3419,Vvar__1__Plt__3420,Vvar__1__Plt__3421,Vvar__2__Pgt__3422,Vvar__2__Pgt__3423,Vvar__3___24Anonymous__3424,Vvar__3___24Anonymous__3425] :
( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__3418,Vvar__1__Plt__3420,Vvar__2__Pgt__3422) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__3419,Vvar__1__Plt__3421,Vvar__2__Pgt__3423)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__3422 = Vvar__2__Pgt__3423
& Vvar__1__Plt__3420 = Vvar__1__Plt__3421
& Vvar__0__Peq__3418 = Vvar__0__Peq__3419 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
! [Vvar__0__Peq__3434,Vvar__0__Peq__3435,Vvar__1__Plt__3436,Vvar__1__Plt__3437,Vvar__2__Pgt__3438,Vvar__2__Pgt__3439,Vvar__3___24Anonymous__3440,Vvar__3___24Anonymous__3441] :
( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__3434,Vvar__1__Plt__3436,Vvar__2__Pgt__3438) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__3435,Vvar__1__Plt__3437,Vvar__2__Pgt__3439)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__3438 = Vvar__2__Pgt__3439
& Vvar__1__Plt__3436 = Vvar__1__Plt__3437
& Vvar__0__Peq__3434 = Vvar__0__Peq__3435 ) ) ).
fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
! [Vvar__0__Peq__3426,Vvar__0__Peq__3427,Vvar__1__Plt__3428,Vvar__1__Plt__3429,Vvar__2__Pgt__3430,Vvar__2__Pgt__3431,Vvar__3___24Anonymous__3432,Vvar__3___24Anonymous__3433] :
( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__3426,Vvar__1__Plt__3428,Vvar__2__Pgt__3430) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__3427,Vvar__1__Plt__3429,Vvar__2__Pgt__3431)
=> ( c_24Proof = c_24Proof
& Vvar__2__Pgt__3430 = Vvar__2__Pgt__3431
& Vvar__1__Plt__3428 = Vvar__1__Plt__3429
& Vvar__0__Peq__3426 = Vvar__0__Peq__3427 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3274,Vvar__0__A__3275] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3274) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3275)
=> Vvar__0__A__3274 = Vvar__0__A__3275 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__145,Vvar__0___24Anonymous__146] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__145) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__146)
=> Vvar__0___24Anonymous__145 = Vvar__0___24Anonymous__146 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__3270,Vvar__0__A__3271,Vvar__1___24Anonymous__3272,Vvar__1___24Anonymous__3273] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3270,Vvar__1___24Anonymous__3272) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3271,Vvar__1___24Anonymous__3273)
=> ( Vvar__1___24Anonymous__3272 = Vvar__1___24Anonymous__3273
& Vvar__0__A__3270 = Vvar__0__A__3271 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3343,Vvar__0__A__3344,Vvar__1___24Anonymous__3345,Vvar__1___24Anonymous__3346,Vvar__2___24Anonymous__3347,Vvar__2___24Anonymous__3348] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3343,Vvar__1___24Anonymous__3345,Vvar__2___24Anonymous__3347) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3344,Vvar__1___24Anonymous__3346,Vvar__2___24Anonymous__3348)
=> ( Vvar__2___24Anonymous__3347 = Vvar__2___24Anonymous__3348
& Vvar__1___24Anonymous__3345 = Vvar__1___24Anonymous__3346
& Vvar__0__A__3343 = Vvar__0__A__3344 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__14469,Vvar__0__A__14470,Vvar__1__B__14471,Vvar__1__B__14472,Vvar__2___24Anonymous__14473,Vvar__2___24Anonymous__14474] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__14469,Vvar__1__B__14471,Vvar__2___24Anonymous__14473) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__14470,Vvar__1__B__14472,Vvar__2___24Anonymous__14474)
=> ( Vvar__2___24Anonymous__14473 = Vvar__2___24Anonymous__14474
& Vvar__1__B__14471 = Vvar__1__B__14472
& Vvar__0__A__14469 = Vvar__0__A__14470 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__14475,Vvar__0__A__14476,Vvar__1__B__14477,Vvar__1__B__14478,Vvar__2___24Anonymous__14479,Vvar__2___24Anonymous__14480] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__14475,Vvar__1__B__14477,Vvar__2___24Anonymous__14479) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__14476,Vvar__1__B__14478,Vvar__2___24Anonymous__14480)
=> ( Vvar__2___24Anonymous__14479 = Vvar__2___24Anonymous__14480
& Vvar__1__B__14477 = Vvar__1__B__14478
& Vvar__0__A__14475 = Vvar__0__A__14476 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__3341,Vvar__0__A__3342] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3341) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3342)
=> Vvar__0__A__3341 = Vvar__0__A__3342 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__3291,Vvar__0__A__3292,Vvar__1__B__3293,Vvar__1__B__3294,Vvar__2___24Anonymous__3295,Vvar__2___24Anonymous__3296,Vvar__3___24Anonymous__3297,Vvar__3___24Anonymous__3298] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__3291,Vvar__1__B__3293,Vvar__2___24Anonymous__3295,Vvar__3___24Anonymous__3297) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__3292,Vvar__1__B__3294,Vvar__2___24Anonymous__3296,Vvar__3___24Anonymous__3298)
=> ( Vvar__3___24Anonymous__3297 = Vvar__3___24Anonymous__3298
& Vvar__2___24Anonymous__3295 = Vvar__2___24Anonymous__3296
& Vvar__1__B__3293 = Vvar__1__B__3294
& Vvar__0__A__3291 = Vvar__0__A__3292 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__28478,Vvar__0__A__28479,Vvar__1__P__28480,Vvar__1__P__28481,Vvar__2__x__28482,Vvar__2__x__28483,Vvar__3___24Anonymous__28484,Vvar__3___24Anonymous__28485] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__28478,Vvar__1__P__28480,Vvar__2__x__28482) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__28479,Vvar__1__P__28481,Vvar__2__x__28483)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__28482 = Vvar__2__x__28483
& Vvar__1__P__28480 = Vvar__1__P__28481
& Vvar__0__A__28478 = Vvar__0__A__28479 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__9142,Vvar__0__A__9143,Vvar__1__P__9144,Vvar__1__P__9145,Vvar__2__Q__9146,Vvar__2__Q__9147,Vvar__3__x__9148,Vvar__3__x__9149,Vvar__4___24Anonymous__9150,Vvar__4___24Anonymous__9151,Vvar__5___24Anonymous__9152,Vvar__5___24Anonymous__9153] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__9142,Vvar__1__P__9144,Vvar__2__Q__9146,Vvar__3__x__9148) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__9143,Vvar__1__P__9145,Vvar__2__Q__9147,Vvar__3__x__9149)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__9148 = Vvar__3__x__9149
& Vvar__2__Q__9146 = Vvar__2__Q__9147
& Vvar__1__P__9144 = Vvar__1__P__9145
& Vvar__0__A__9142 = Vvar__0__A__9143 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__28517,Vvar__0__A__28518,Vvar__1__P__28519,Vvar__1__P__28520,Vvar__2__x__28521,Vvar__2__x__28522,Vvar__3___24Anonymous__28523,Vvar__3___24Anonymous__28524] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__28517,Vvar__1__P__28519,Vvar__2__x__28521,Vvar__3___24Anonymous__28523) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__28518,Vvar__1__P__28520,Vvar__2__x__28522,Vvar__3___24Anonymous__28524)
=> ( Vvar__3___24Anonymous__28523 = Vvar__3___24Anonymous__28524
& Vvar__2__x__28521 = Vvar__2__x__28522
& Vvar__1__P__28519 = Vvar__1__P__28520
& Vvar__0__A__28517 = Vvar__0__A__28518 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__9222,Vvar__0__A__9223,Vvar__1__P__9224,Vvar__1__P__9225,Vvar__2__Q__9226,Vvar__2__Q__9227,Vvar__3__x__9228,Vvar__3__x__9229,Vvar__4___24Anonymous__9230,Vvar__4___24Anonymous__9231,Vvar__5___24Anonymous__9232,Vvar__5___24Anonymous__9233] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__9222,Vvar__1__P__9224,Vvar__2__Q__9226,Vvar__3__x__9228,Vvar__4___24Anonymous__9230,Vvar__5___24Anonymous__9232) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__9223,Vvar__1__P__9225,Vvar__2__Q__9227,Vvar__3__x__9229,Vvar__4___24Anonymous__9231,Vvar__5___24Anonymous__9233)
=> ( Vvar__5___24Anonymous__9232 = Vvar__5___24Anonymous__9233
& Vvar__4___24Anonymous__9230 = Vvar__4___24Anonymous__9231
& Vvar__3__x__9228 = Vvar__3__x__9229
& Vvar__2__Q__9226 = Vvar__2__Q__9227
& Vvar__1__P__9224 = Vvar__1__P__9225
& Vvar__0__A__9222 = Vvar__0__A__9223 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__28563,Vvar__0__A__28564,Vvar__1__B__28565,Vvar__1__B__28566,Vvar__2___24Anonymous__28567,Vvar__2___24Anonymous__28568] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28563,Vvar__1__B__28565,Vvar__2___24Anonymous__28567) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28564,Vvar__1__B__28566,Vvar__2___24Anonymous__28568)
=> ( Vvar__2___24Anonymous__28567 = Vvar__2___24Anonymous__28568
& Vvar__1__B__28565 = Vvar__1__B__28566
& Vvar__0__A__28563 = Vvar__0__A__28564 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__28569,Vvar__0__A__28570,Vvar__1__B__28571,Vvar__1__B__28572,Vvar__2___24Anonymous__28573,Vvar__2___24Anonymous__28574] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28569,Vvar__1__B__28571) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28570,Vvar__1__B__28572)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__28571 = Vvar__1__B__28572
& Vvar__0__A__28569 = Vvar__0__A__28570 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__11505,Vvar__0__A__11506,Vvar__1__B__11507,Vvar__1__B__11508,Vvar__2___24Anonymous__11509,Vvar__2___24Anonymous__11510] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11505,Vvar__1__B__11507) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11506,Vvar__1__B__11508)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__11507 = Vvar__1__B__11508
& Vvar__0__A__11505 = Vvar__0__A__11506 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__11511,Vvar__0__A__11512,Vvar__1__B__11513,Vvar__1__B__11514,Vvar__2___24Anonymous__11515,Vvar__2___24Anonymous__11516] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11511,Vvar__1__B__11513) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11512,Vvar__1__B__11514)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__11513 = Vvar__1__B__11514
& Vvar__0__A__11511 = Vvar__0__A__11512 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3207,Vvar__0___24Anonymous__3208] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3207) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3208)
=> Vvar__0___24Anonymous__3207 = Vvar__0___24Anonymous__3208 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__3220,Vvar__0___24Anonymous__3221] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3220) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3221)
=> Vvar__0___24Anonymous__3220 = Vvar__0___24Anonymous__3221 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__3218,Vvar__0___24Anonymous__3219] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3218) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3219)
=> Vvar__0___24Anonymous__3218 = Vvar__0___24Anonymous__3219 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__3192,Vvar__0___24Anonymous__3193] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3192) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3193)
=> Vvar__0___24Anonymous__3192 = Vvar__0___24Anonymous__3193 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__3194,Vvar__0___24Anonymous__3195] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3194) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3195)
=> Vvar__0___24Anonymous__3194 = Vvar__0___24Anonymous__3195 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__12648,Vvar__0___24Anonymous__12649] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__12648) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__12649)
=> Vvar__0___24Anonymous__12648 = Vvar__0___24Anonymous__12649 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__18542,Vvar__0__Qnum__18543,Vvar__1__Qden__18544,Vvar__1__Qden__18545] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__18542,Vvar__1__Qden__18544) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__18543,Vvar__1__Qden__18545)
=> ( Vvar__1__Qden__18544 = Vvar__1__Qden__18545
& Vvar__0__Qnum__18542 = Vvar__0__Qnum__18543 ) ) ).
fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
! [Vvar__0__nonzero__18576,Vvar__0__nonzero__18577,Vvar__1__cond__nonzero__18578,Vvar__1__cond__nonzero__18579] :
( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__18576) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__18577)
=> ( c_24Proof = c_24Proof
& Vvar__0__nonzero__18576 = Vvar__0__nonzero__18577 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
! [Vvar__0__x__18869,Vvar__0__x__18870,Vvar__1__n__18871,Vvar__1__n__18872,Vvar__2___24Anonymous__18873,Vvar__2___24Anonymous__18874] :
( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__18869,Vvar__1__n__18871) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__18870,Vvar__1__n__18872)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__18871 = Vvar__1__n__18872
& Vvar__0__x__18869 = Vvar__0__x__18870 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
! [Vvar__0__x__18859,Vvar__0__x__18860,Vvar__1___24Anonymous__18861,Vvar__1___24Anonymous__18862] :
( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__18859) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__18860)
=> ( c_24Proof = c_24Proof
& Vvar__0__x__18859 = Vvar__0__x__18860 ) ) ).
fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
! [Vvar__0__x__18863,Vvar__0__x__18864,Vvar__1__n__18865,Vvar__1__n__18866,Vvar__2___24Anonymous__18867,Vvar__2___24Anonymous__18868] :
( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__18863,Vvar__1__n__18865) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__18864,Vvar__1__n__18866)
=> ( c_24Proof = c_24Proof
& Vvar__1__n__18865 = Vvar__1__n__18866
& Vvar__0__x__18863 = Vvar__0__x__18864 ) ) ).
fof('$_inj_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
! [Vvar__0__U__3066,Vvar__0__U__3067,Vvar__1__Carrier__of__3068,Vvar__1__Carrier__of__3069,Vvar__2__Rel__of__3070,Vvar__2__Rel__of__3071,Vvar__3__PO__cond1__3072,Vvar__3__PO__cond1__3073,Vvar__4__PO__cond2__3074,Vvar__4__PO__cond2__3075] :
( cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__3066,Vvar__1__Carrier__of__3068,Vvar__2__Rel__of__3070) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__3067,Vvar__1__Carrier__of__3069,Vvar__2__Rel__of__3071)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__2__Rel__of__3070 = Vvar__2__Rel__of__3071
& Vvar__1__Carrier__of__3068 = Vvar__1__Carrier__of__3069
& Vvar__0__U__3066 = Vvar__0__U__3067 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__3166,Vvar__0___24Anonymous__3167,Vvar__1___24Anonymous__3168,Vvar__1___24Anonymous__3169,Vvar__2___24Anonymous__3170,Vvar__2___24Anonymous__3171,Vvar__3___24Anonymous__3172,Vvar__3___24Anonymous__3173,Vvar__4___24Anonymous__3174,Vvar__4___24Anonymous__3175,Vvar__5___24Anonymous__3176,Vvar__5___24Anonymous__3177,Vvar__6___24Anonymous__3178,Vvar__6___24Anonymous__3179,Vvar__7___24Anonymous__3180,Vvar__7___24Anonymous__3181] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__3166,Vvar__1___24Anonymous__3168,Vvar__2___24Anonymous__3170,Vvar__3___24Anonymous__3172,Vvar__4___24Anonymous__3174,Vvar__5___24Anonymous__3176,Vvar__6___24Anonymous__3178,Vvar__7___24Anonymous__3180) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__3167,Vvar__1___24Anonymous__3169,Vvar__2___24Anonymous__3171,Vvar__3___24Anonymous__3173,Vvar__4___24Anonymous__3175,Vvar__5___24Anonymous__3177,Vvar__6___24Anonymous__3179,Vvar__7___24Anonymous__3181)
=> ( Vvar__7___24Anonymous__3180 = Vvar__7___24Anonymous__3181
& Vvar__6___24Anonymous__3178 = Vvar__6___24Anonymous__3179
& Vvar__5___24Anonymous__3176 = Vvar__5___24Anonymous__3177
& Vvar__4___24Anonymous__3174 = Vvar__4___24Anonymous__3175
& Vvar__3___24Anonymous__3172 = Vvar__3___24Anonymous__3173
& Vvar__2___24Anonymous__3170 = Vvar__2___24Anonymous__3171
& Vvar__1___24Anonymous__3168 = Vvar__1___24Anonymous__3169
& Vvar__0___24Anonymous__3166 = Vvar__0___24Anonymous__3167 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__11522,Vvar__0___24Anonymous__11523,Vvar__1___24Anonymous__11524,Vvar__1___24Anonymous__11525] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__11522,Vvar__1___24Anonymous__11524) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__11523,Vvar__1___24Anonymous__11525)
=> ( Vvar__1___24Anonymous__11524 = Vvar__1___24Anonymous__11525
& Vvar__0___24Anonymous__11522 = Vvar__0___24Anonymous__11523 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__18495,Vvar__0__X__18496,Vvar__1__lt__18497,Vvar__1__lt__18498,Vvar__2__eq__18499,Vvar__2__eq__18500,Vvar__3__x__18501,Vvar__3__x__18502,Vvar__4__y__18503,Vvar__4__y__18504,Vvar__5___24Anonymous__18505,Vvar__5___24Anonymous__18506] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__18495,Vvar__1__lt__18497,Vvar__2__eq__18499,Vvar__3__x__18501,Vvar__4__y__18503) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__18496,Vvar__1__lt__18498,Vvar__2__eq__18500,Vvar__3__x__18502,Vvar__4__y__18504)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__18503 = Vvar__4__y__18504
& Vvar__3__x__18501 = Vvar__3__x__18502
& Vvar__2__eq__18499 = Vvar__2__eq__18500
& Vvar__1__lt__18497 = Vvar__1__lt__18498
& Vvar__0__X__18495 = Vvar__0__X__18496 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__18507,Vvar__0__X__18508,Vvar__1__lt__18509,Vvar__1__lt__18510,Vvar__2__eq__18511,Vvar__2__eq__18512,Vvar__3__x__18513,Vvar__3__x__18514,Vvar__4__y__18515,Vvar__4__y__18516,Vvar__5___24Anonymous__18517,Vvar__5___24Anonymous__18518] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__18507,Vvar__1__lt__18509,Vvar__2__eq__18511,Vvar__3__x__18513,Vvar__4__y__18515) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__18508,Vvar__1__lt__18510,Vvar__2__eq__18512,Vvar__3__x__18514,Vvar__4__y__18516)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__18515 = Vvar__4__y__18516
& Vvar__3__x__18513 = Vvar__3__x__18514
& Vvar__2__eq__18511 = Vvar__2__eq__18512
& Vvar__1__lt__18509 = Vvar__1__lt__18510
& Vvar__0__X__18507 = Vvar__0__X__18508 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__18483,Vvar__0__X__18484,Vvar__1__lt__18485,Vvar__1__lt__18486,Vvar__2__eq__18487,Vvar__2__eq__18488,Vvar__3__x__18489,Vvar__3__x__18490,Vvar__4__y__18491,Vvar__4__y__18492,Vvar__5___24Anonymous__18493,Vvar__5___24Anonymous__18494] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__18483,Vvar__1__lt__18485,Vvar__2__eq__18487,Vvar__3__x__18489,Vvar__4__y__18491) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__18484,Vvar__1__lt__18486,Vvar__2__eq__18488,Vvar__3__x__18490,Vvar__4__y__18492)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__18491 = Vvar__4__y__18492
& Vvar__3__x__18489 = Vvar__3__x__18490
& Vvar__2__eq__18487 = Vvar__2__eq__18488
& Vvar__1__lt__18485 = Vvar__1__lt__18486
& Vvar__0__X__18483 = Vvar__0__X__18484 ) ) ).
fof('$_inj_Coq.Vectors.Fin.F1',axiom,
! [Vvar__0__n__16919,Vvar__0__n__16920] :
( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__16919) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__16920)
=> Vvar__0__n__16919 = Vvar__0__n__16920 ) ).
fof('$_inj_Coq.Vectors.Fin.FS',axiom,
! [Vvar__0__n__16921,Vvar__0__n__16922,Vvar__1___24Anonymous__16923,Vvar__1___24Anonymous__16924] :
( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__16921,Vvar__1___24Anonymous__16923) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__16922,Vvar__1___24Anonymous__16924)
=> ( Vvar__1___24Anonymous__16923 = Vvar__1___24Anonymous__16924
& Vvar__0__n__16921 = Vvar__0__n__16922 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__11584,Vvar__0__A__11585,Vvar__1__h__11586,Vvar__1__h__11587,Vvar__2__n__11588,Vvar__2__n__11589,Vvar__3___24Anonymous__11590,Vvar__3___24Anonymous__11591] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__11584,Vvar__1__h__11586,Vvar__2__n__11588,Vvar__3___24Anonymous__11590) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__11585,Vvar__1__h__11587,Vvar__2__n__11589,Vvar__3___24Anonymous__11591)
=> ( Vvar__3___24Anonymous__11590 = Vvar__3___24Anonymous__11591
& Vvar__2__n__11588 = Vvar__2__n__11589
& Vvar__1__h__11586 = Vvar__1__h__11587
& Vvar__0__A__11584 = Vvar__0__A__11585 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__11582,Vvar__0__A__11583] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__11582) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__11583)
=> Vvar__0__A__11582 = Vvar__0__A__11583 ) ).
fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
! [Vvar__0__a__29256,Vvar__0__a__29257,Vvar__1__b__29258,Vvar__1__b__29259,Vvar__2__u__29260,Vvar__2__u__29261,Vvar__3__v__29262,Vvar__3__v__29263,Vvar__4__d__29264,Vvar__4__d__29265,Vvar__5___24Anonymous__29266,Vvar__5___24Anonymous__29267,Vvar__6___24Anonymous__29268,Vvar__6___24Anonymous__29269] :
( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__29256,Vvar__1__b__29258,Vvar__2__u__29260,Vvar__3__v__29262,Vvar__4__d__29264) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__29257,Vvar__1__b__29259,Vvar__2__u__29261,Vvar__3__v__29263,Vvar__4__d__29265)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__4__d__29264 = Vvar__4__d__29265
& Vvar__3__v__29262 = Vvar__3__v__29263
& Vvar__2__u__29260 = Vvar__2__u__29261
& Vvar__1__b__29258 = Vvar__1__b__29259
& Vvar__0__a__29256 = Vvar__0__a__29257 ) ) ).
fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
! [Vvar__0__x__29307,Vvar__0__x__29308,Vvar__1__p__29309,Vvar__1__p__29310,Vvar__2__q__29311,Vvar__2__q__29312,Vvar__3__r__29313,Vvar__3__r__29314,Vvar__4___24Anonymous__29315,Vvar__4___24Anonymous__29316,Vvar__5___24Anonymous__29317,Vvar__5___24Anonymous__29318,Vvar__6___24Anonymous__29319,Vvar__6___24Anonymous__29320] :
( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__29307,Vvar__1__p__29309,Vvar__2__q__29311,Vvar__3__r__29313) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__29308,Vvar__1__p__29310,Vvar__2__q__29312,Vvar__3__r__29314)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__r__29313 = Vvar__3__r__29314
& Vvar__2__q__29311 = Vvar__2__q__29312
& Vvar__1__p__29309 = Vvar__1__p__29310
& Vvar__0__x__29307 = Vvar__0__x__29308 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__14829,Vvar__0__C__14830,Vvar__1___24Anonymous__14831,Vvar__1___24Anonymous__14832] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14829,Vvar__1___24Anonymous__14831) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14830,Vvar__1___24Anonymous__14832)
=> ( Vvar__1___24Anonymous__14831 = Vvar__1___24Anonymous__14832
& Vvar__0__C__14829 = Vvar__0__C__14830 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__14833,Vvar__0__C__14834,Vvar__1___24Anonymous__14835,Vvar__1___24Anonymous__14836,Vvar__2___24Anonymous__14837,Vvar__2___24Anonymous__14838] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__14833,Vvar__1___24Anonymous__14835,Vvar__2___24Anonymous__14837) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__14834,Vvar__1___24Anonymous__14836,Vvar__2___24Anonymous__14838)
=> ( Vvar__2___24Anonymous__14837 = Vvar__2___24Anonymous__14838
& Vvar__1___24Anonymous__14835 = Vvar__1___24Anonymous__14836
& Vvar__0__C__14833 = Vvar__0__C__14834 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__14825,Vvar__0__C__14826,Vvar__1___24Anonymous__14827,Vvar__1___24Anonymous__14828] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14825,Vvar__1___24Anonymous__14827) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14826,Vvar__1___24Anonymous__14828)
=> ( Vvar__1___24Anonymous__14827 = Vvar__1___24Anonymous__14828
& Vvar__0__C__14825 = Vvar__0__C__14826 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__14845,Vvar__0__C__14846,Vvar__1___24Anonymous__14847,Vvar__1___24Anonymous__14848,Vvar__2___24Anonymous__14849,Vvar__2___24Anonymous__14850] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__14845,Vvar__1___24Anonymous__14847,Vvar__2___24Anonymous__14849) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__14846,Vvar__1___24Anonymous__14848,Vvar__2___24Anonymous__14850)
=> ( Vvar__2___24Anonymous__14849 = Vvar__2___24Anonymous__14850
& Vvar__1___24Anonymous__14847 = Vvar__1___24Anonymous__14848
& Vvar__0__C__14845 = Vvar__0__C__14846 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__14851,Vvar__0__C__14852,Vvar__1___24Anonymous__14853,Vvar__1___24Anonymous__14854] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__14851,Vvar__1___24Anonymous__14853) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__14852,Vvar__1___24Anonymous__14854)
=> ( Vvar__1___24Anonymous__14853 = Vvar__1___24Anonymous__14854
& Vvar__0__C__14851 = Vvar__0__C__14852 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__14855,Vvar__0__C__14856,Vvar__1___24Anonymous__14857,Vvar__1___24Anonymous__14858,Vvar__2___24Anonymous__14859,Vvar__2___24Anonymous__14860] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__14855,Vvar__1___24Anonymous__14857,Vvar__2___24Anonymous__14859) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__14856,Vvar__1___24Anonymous__14858,Vvar__2___24Anonymous__14860)
=> ( Vvar__2___24Anonymous__14859 = Vvar__2___24Anonymous__14860
& Vvar__1___24Anonymous__14857 = Vvar__1___24Anonymous__14858
& Vvar__0__C__14855 = Vvar__0__C__14856 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__14839,Vvar__0__C__14840,Vvar__1___24Anonymous__14841,Vvar__1___24Anonymous__14842,Vvar__2___24Anonymous__14843,Vvar__2___24Anonymous__14844] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__14839,Vvar__1___24Anonymous__14841,Vvar__2___24Anonymous__14843) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__14840,Vvar__1___24Anonymous__14842,Vvar__2___24Anonymous__14844)
=> ( Vvar__2___24Anonymous__14843 = Vvar__2___24Anonymous__14844
& Vvar__1___24Anonymous__14841 = Vvar__1___24Anonymous__14842
& Vvar__0__C__14839 = Vvar__0__C__14840 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__14903,Vvar__0__C__14904,Vvar__1___24Anonymous__14905,Vvar__1___24Anonymous__14906,Vvar__2___24Anonymous__14907,Vvar__2___24Anonymous__14908,Vvar__3___24Anonymous__14909,Vvar__3___24Anonymous__14910] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__14903,Vvar__1___24Anonymous__14905,Vvar__2___24Anonymous__14907,Vvar__3___24Anonymous__14909) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__14904,Vvar__1___24Anonymous__14906,Vvar__2___24Anonymous__14908,Vvar__3___24Anonymous__14910)
=> ( Vvar__3___24Anonymous__14909 = Vvar__3___24Anonymous__14910
& Vvar__2___24Anonymous__14907 = Vvar__2___24Anonymous__14908
& Vvar__1___24Anonymous__14905 = Vvar__1___24Anonymous__14906
& Vvar__0__C__14903 = Vvar__0__C__14904 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__14893,Vvar__0__C__14894,Vvar__1___24Anonymous__14895,Vvar__1___24Anonymous__14896] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14893,Vvar__1___24Anonymous__14895) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14894,Vvar__1___24Anonymous__14896)
=> ( Vvar__1___24Anonymous__14895 = Vvar__1___24Anonymous__14896
& Vvar__0__C__14893 = Vvar__0__C__14894 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__14897,Vvar__0__C__14898,Vvar__1___24Anonymous__14899,Vvar__1___24Anonymous__14900,Vvar__2___24Anonymous__14901,Vvar__2___24Anonymous__14902] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14897,Vvar__1___24Anonymous__14899,Vvar__2___24Anonymous__14901) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14898,Vvar__1___24Anonymous__14900,Vvar__2___24Anonymous__14902)
=> ( Vvar__2___24Anonymous__14901 = Vvar__2___24Anonymous__14902
& Vvar__1___24Anonymous__14899 = Vvar__1___24Anonymous__14900
& Vvar__0__C__14897 = Vvar__0__C__14898 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__14939,Vvar__0___24Anonymous__14940,Vvar__1___24Anonymous__14941,Vvar__1___24Anonymous__14942] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__14939,Vvar__1___24Anonymous__14941) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__14940,Vvar__1___24Anonymous__14942)
=> ( Vvar__1___24Anonymous__14941 = Vvar__1___24Anonymous__14942
& Vvar__0___24Anonymous__14939 = Vvar__0___24Anonymous__14940 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__14935,Vvar__0___24Anonymous__14936,Vvar__1___24Anonymous__14937,Vvar__1___24Anonymous__14938] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__14935,Vvar__1___24Anonymous__14937) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__14936,Vvar__1___24Anonymous__14938)
=> ( Vvar__1___24Anonymous__14937 = Vvar__1___24Anonymous__14938
& Vvar__0___24Anonymous__14935 = Vvar__0___24Anonymous__14936 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__24322,Vvar__0__T__24323,Vvar__1__Flhs__24324,Vvar__1__Flhs__24325,Vvar__2__Fop__24326,Vvar__2__Fop__24327,Vvar__3__Frhs__24328,Vvar__3__Frhs__24329] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__24322,Vvar__1__Flhs__24324,Vvar__2__Fop__24326,Vvar__3__Frhs__24328) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__24323,Vvar__1__Flhs__24325,Vvar__2__Fop__24327,Vvar__3__Frhs__24329)
=> ( Vvar__3__Frhs__24328 = Vvar__3__Frhs__24329
& Vvar__2__Fop__24326 = Vvar__2__Fop__24327
& Vvar__1__Flhs__24324 = Vvar__1__Flhs__24325
& Vvar__0__T__24322 = Vvar__0__T__24323 ) ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__28958,Vvar__0__TA__28959,Vvar__1__TX__28960,Vvar__1__TX__28961,Vvar__2__AA__28962,Vvar__2__AA__28963,Vvar__3__AF__28964,Vvar__3__AF__28965,Vvar__4___24Anonymous__28966,Vvar__4___24Anonymous__28967,Vvar__5___24Anonymous__28968,Vvar__5___24Anonymous__28969] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__28958,Vvar__1__TX__28960,Vvar__2__AA__28962,Vvar__3__AF__28964,Vvar__4___24Anonymous__28966,Vvar__5___24Anonymous__28968) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__28959,Vvar__1__TX__28961,Vvar__2__AA__28963,Vvar__3__AF__28965,Vvar__4___24Anonymous__28967,Vvar__5___24Anonymous__28969)
=> ( Vvar__5___24Anonymous__28968 = Vvar__5___24Anonymous__28969
& Vvar__4___24Anonymous__28966 = Vvar__4___24Anonymous__28967
& Vvar__3__AF__28964 = Vvar__3__AF__28965
& Vvar__2__AA__28962 = Vvar__2__AA__28963
& Vvar__1__TX__28960 = Vvar__1__TX__28961
& Vvar__0__TA__28958 = Vvar__0__TA__28959 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__28970,Vvar__0__TA__28971,Vvar__1__TX__28972,Vvar__1__TX__28973,Vvar__2__AA__28974,Vvar__2__AA__28975,Vvar__3__AF__28976,Vvar__3__AF__28977,Vvar__4___24Anonymous__28978,Vvar__4___24Anonymous__28979,Vvar__5___24Anonymous__28980,Vvar__5___24Anonymous__28981] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__28970,Vvar__1__TX__28972,Vvar__2__AA__28974,Vvar__3__AF__28976,Vvar__4___24Anonymous__28978,Vvar__5___24Anonymous__28980) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__28971,Vvar__1__TX__28973,Vvar__2__AA__28975,Vvar__3__AF__28977,Vvar__4___24Anonymous__28979,Vvar__5___24Anonymous__28981)
=> ( Vvar__5___24Anonymous__28980 = Vvar__5___24Anonymous__28981
& Vvar__4___24Anonymous__28978 = Vvar__4___24Anonymous__28979
& Vvar__3__AF__28976 = Vvar__3__AF__28977
& Vvar__2__AA__28974 = Vvar__2__AA__28975
& Vvar__1__TX__28972 = Vvar__1__TX__28973
& Vvar__0__TA__28970 = Vvar__0__TA__28971 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__28982,Vvar__0__TA__28983,Vvar__1__TX__28984,Vvar__1__TX__28985,Vvar__2__AA__28986,Vvar__2__AA__28987,Vvar__3__AF__28988,Vvar__3__AF__28989,Vvar__4___24Anonymous__28990,Vvar__4___24Anonymous__28991,Vvar__5___24Anonymous__28992,Vvar__5___24Anonymous__28993] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__28982,Vvar__1__TX__28984,Vvar__2__AA__28986,Vvar__3__AF__28988,Vvar__4___24Anonymous__28990,Vvar__5___24Anonymous__28992) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__28983,Vvar__1__TX__28985,Vvar__2__AA__28987,Vvar__3__AF__28989,Vvar__4___24Anonymous__28991,Vvar__5___24Anonymous__28993)
=> ( Vvar__5___24Anonymous__28992 = Vvar__5___24Anonymous__28993
& Vvar__4___24Anonymous__28990 = Vvar__4___24Anonymous__28991
& Vvar__3__AF__28988 = Vvar__3__AF__28989
& Vvar__2__AA__28986 = Vvar__2__AA__28987
& Vvar__1__TX__28984 = Vvar__1__TX__28985
& Vvar__0__TA__28982 = Vvar__0__TA__28983 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__28940,Vvar__0__TA__28941,Vvar__1__TX__28942,Vvar__1__TX__28943,Vvar__2__AA__28944,Vvar__2__AA__28945,Vvar__3__AF__28946,Vvar__3__AF__28947] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28940,Vvar__1__TX__28942,Vvar__2__AA__28944,Vvar__3__AF__28946) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28941,Vvar__1__TX__28943,Vvar__2__AA__28945,Vvar__3__AF__28947)
=> ( Vvar__3__AF__28946 = Vvar__3__AF__28947
& Vvar__2__AA__28944 = Vvar__2__AA__28945
& Vvar__1__TX__28942 = Vvar__1__TX__28943
& Vvar__0__TA__28940 = Vvar__0__TA__28941 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__29004,Vvar__0__TA__29005,Vvar__1__TX__29006,Vvar__1__TX__29007,Vvar__2__AA__29008,Vvar__2__AA__29009,Vvar__3__AF__29010,Vvar__3__AF__29011,Vvar__4___24Anonymous__29012,Vvar__4___24Anonymous__29013,Vvar__5___24Anonymous__29014,Vvar__5___24Anonymous__29015,Vvar__6___24Anonymous__29016,Vvar__6___24Anonymous__29017] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__29004,Vvar__1__TX__29006,Vvar__2__AA__29008,Vvar__3__AF__29010,Vvar__4___24Anonymous__29012,Vvar__5___24Anonymous__29014,Vvar__6___24Anonymous__29016) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__29005,Vvar__1__TX__29007,Vvar__2__AA__29009,Vvar__3__AF__29011,Vvar__4___24Anonymous__29013,Vvar__5___24Anonymous__29015,Vvar__6___24Anonymous__29017)
=> ( Vvar__6___24Anonymous__29016 = Vvar__6___24Anonymous__29017
& Vvar__5___24Anonymous__29014 = Vvar__5___24Anonymous__29015
& Vvar__4___24Anonymous__29012 = Vvar__4___24Anonymous__29013
& Vvar__3__AF__29010 = Vvar__3__AF__29011
& Vvar__2__AA__29008 = Vvar__2__AA__29009
& Vvar__1__TX__29006 = Vvar__1__TX__29007
& Vvar__0__TA__29004 = Vvar__0__TA__29005 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__28994,Vvar__0__TA__28995,Vvar__1__TX__28996,Vvar__1__TX__28997,Vvar__2__AA__28998,Vvar__2__AA__28999,Vvar__3__AF__29000,Vvar__3__AF__29001,Vvar__4___24Anonymous__29002,Vvar__4___24Anonymous__29003] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__28994,Vvar__1__TX__28996,Vvar__2__AA__28998,Vvar__3__AF__29000,Vvar__4___24Anonymous__29002) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__28995,Vvar__1__TX__28997,Vvar__2__AA__28999,Vvar__3__AF__29001,Vvar__4___24Anonymous__29003)
=> ( Vvar__4___24Anonymous__29002 = Vvar__4___24Anonymous__29003
& Vvar__3__AF__29000 = Vvar__3__AF__29001
& Vvar__2__AA__28998 = Vvar__2__AA__28999
& Vvar__1__TX__28996 = Vvar__1__TX__28997
& Vvar__0__TA__28994 = Vvar__0__TA__28995 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__28932,Vvar__0__TA__28933,Vvar__1__TX__28934,Vvar__1__TX__28935,Vvar__2__AA__28936,Vvar__2__AA__28937,Vvar__3__AF__28938,Vvar__3__AF__28939] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28932,Vvar__1__TX__28934,Vvar__2__AA__28936,Vvar__3__AF__28938) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28933,Vvar__1__TX__28935,Vvar__2__AA__28937,Vvar__3__AF__28939)
=> ( Vvar__3__AF__28938 = Vvar__3__AF__28939
& Vvar__2__AA__28936 = Vvar__2__AA__28937
& Vvar__1__TX__28934 = Vvar__1__TX__28935
& Vvar__0__TA__28932 = Vvar__0__TA__28933 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__28948,Vvar__0__TA__28949,Vvar__1__TX__28950,Vvar__1__TX__28951,Vvar__2__AA__28952,Vvar__2__AA__28953,Vvar__3__AF__28954,Vvar__3__AF__28955,Vvar__4___24Anonymous__28956,Vvar__4___24Anonymous__28957] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__28948,Vvar__1__TX__28950,Vvar__2__AA__28952,Vvar__3__AF__28954,Vvar__4___24Anonymous__28956) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__28949,Vvar__1__TX__28951,Vvar__2__AA__28953,Vvar__3__AF__28955,Vvar__4___24Anonymous__28957)
=> ( Vvar__4___24Anonymous__28956 = Vvar__4___24Anonymous__28957
& Vvar__3__AF__28954 = Vvar__3__AF__28955
& Vvar__2__AA__28952 = Vvar__2__AA__28953
& Vvar__1__TX__28950 = Vvar__1__TX__28951
& Vvar__0__TA__28948 = Vvar__0__TA__28949 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__3874,Vvar__0__C__3875] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3874) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3875)
=> Vvar__0__C__3874 = Vvar__0__C__3875 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__3872,Vvar__0__C__3873] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3872) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3873)
=> Vvar__0__C__3872 = Vvar__0__C__3873 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__3880,Vvar__0__C__3881,Vvar__1___24Anonymous__3882,Vvar__1___24Anonymous__3883] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3880,Vvar__1___24Anonymous__3882) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3881,Vvar__1___24Anonymous__3883)
=> ( Vvar__1___24Anonymous__3882 = Vvar__1___24Anonymous__3883
& Vvar__0__C__3880 = Vvar__0__C__3881 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__3884,Vvar__0__C__3885,Vvar__1___24Anonymous__3886,Vvar__1___24Anonymous__3887,Vvar__2___24Anonymous__3888,Vvar__2___24Anonymous__3889] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3884,Vvar__1___24Anonymous__3886,Vvar__2___24Anonymous__3888) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3885,Vvar__1___24Anonymous__3887,Vvar__2___24Anonymous__3889)
=> ( Vvar__2___24Anonymous__3888 = Vvar__2___24Anonymous__3889
& Vvar__1___24Anonymous__3886 = Vvar__1___24Anonymous__3887
& Vvar__0__C__3884 = Vvar__0__C__3885 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__3876,Vvar__0__C__3877,Vvar__1___24Anonymous__3878,Vvar__1___24Anonymous__3879] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3876,Vvar__1___24Anonymous__3878) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3877,Vvar__1___24Anonymous__3879)
=> ( Vvar__1___24Anonymous__3878 = Vvar__1___24Anonymous__3879
& Vvar__0__C__3876 = Vvar__0__C__3877 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__3910,Vvar__0__C__3911,Vvar__1___24Anonymous__3912,Vvar__1___24Anonymous__3913,Vvar__2___24Anonymous__3914,Vvar__2___24Anonymous__3915] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3910,Vvar__1___24Anonymous__3912,Vvar__2___24Anonymous__3914) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3911,Vvar__1___24Anonymous__3913,Vvar__2___24Anonymous__3915)
=> ( Vvar__2___24Anonymous__3914 = Vvar__2___24Anonymous__3915
& Vvar__1___24Anonymous__3912 = Vvar__1___24Anonymous__3913
& Vvar__0__C__3910 = Vvar__0__C__3911 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__3906,Vvar__0__C__3907,Vvar__1___24Anonymous__3908,Vvar__1___24Anonymous__3909] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3906,Vvar__1___24Anonymous__3908) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3907,Vvar__1___24Anonymous__3909)
=> ( Vvar__1___24Anonymous__3908 = Vvar__1___24Anonymous__3909
& Vvar__0__C__3906 = Vvar__0__C__3907 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__3896,Vvar__0__C__3897,Vvar__1___24Anonymous__3898,Vvar__1___24Anonymous__3899,Vvar__2___24Anonymous__3900,Vvar__2___24Anonymous__3901] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3896,Vvar__1___24Anonymous__3898,Vvar__2___24Anonymous__3900) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3897,Vvar__1___24Anonymous__3899,Vvar__2___24Anonymous__3901)
=> ( Vvar__2___24Anonymous__3900 = Vvar__2___24Anonymous__3901
& Vvar__1___24Anonymous__3898 = Vvar__1___24Anonymous__3899
& Vvar__0__C__3896 = Vvar__0__C__3897 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__3902,Vvar__0__C__3903,Vvar__1___24Anonymous__3904,Vvar__1___24Anonymous__3905] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3902,Vvar__1___24Anonymous__3904) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3903,Vvar__1___24Anonymous__3905)
=> ( Vvar__1___24Anonymous__3904 = Vvar__1___24Anonymous__3905
& Vvar__0__C__3902 = Vvar__0__C__3903 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__3916,Vvar__0__C__3917,Vvar__1___24Anonymous__3918,Vvar__1___24Anonymous__3919,Vvar__2___24Anonymous__3920,Vvar__2___24Anonymous__3921] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3916,Vvar__1___24Anonymous__3918,Vvar__2___24Anonymous__3920) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3917,Vvar__1___24Anonymous__3919,Vvar__2___24Anonymous__3921)
=> ( Vvar__2___24Anonymous__3920 = Vvar__2___24Anonymous__3921
& Vvar__1___24Anonymous__3918 = Vvar__1___24Anonymous__3919
& Vvar__0__C__3916 = Vvar__0__C__3917 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__3890,Vvar__0__C__3891,Vvar__1___24Anonymous__3892,Vvar__1___24Anonymous__3893,Vvar__2___24Anonymous__3894,Vvar__2___24Anonymous__3895] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3890,Vvar__1___24Anonymous__3892,Vvar__2___24Anonymous__3894) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3891,Vvar__1___24Anonymous__3893,Vvar__2___24Anonymous__3895)
=> ( Vvar__2___24Anonymous__3894 = Vvar__2___24Anonymous__3895
& Vvar__1___24Anonymous__3892 = Vvar__1___24Anonymous__3893
& Vvar__0__C__3890 = Vvar__0__C__3891 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
! [Vvar__0__C__4237,Vvar__0__C__4238,Vvar__1__num__4239,Vvar__1__num__4240,Vvar__2__denum__4241,Vvar__2__denum__4242,Vvar__3__condition__4243,Vvar__3__condition__4244] :
( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__4237,Vvar__1__num__4239,Vvar__2__denum__4241,Vvar__3__condition__4243) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__4238,Vvar__1__num__4240,Vvar__2__denum__4242,Vvar__3__condition__4244)
=> ( Vvar__3__condition__4243 = Vvar__3__condition__4244
& Vvar__2__denum__4241 = Vvar__2__denum__4242
& Vvar__1__num__4239 = Vvar__1__num__4240
& Vvar__0__C__4237 = Vvar__0__C__4238 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
! [Vvar__0__C__15770,Vvar__0__C__15771,Vvar__1__rsplit__left__15772,Vvar__1__rsplit__left__15773,Vvar__2__rsplit__common__15774,Vvar__2__rsplit__common__15775,Vvar__3__rsplit__right__15776,Vvar__3__rsplit__right__15777] :
( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__15770,Vvar__1__rsplit__left__15772,Vvar__2__rsplit__common__15774,Vvar__3__rsplit__right__15776) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__15771,Vvar__1__rsplit__left__15773,Vvar__2__rsplit__common__15775,Vvar__3__rsplit__right__15777)
=> ( Vvar__3__rsplit__right__15776 = Vvar__3__rsplit__right__15777
& Vvar__2__rsplit__common__15774 = Vvar__2__rsplit__common__15775
& Vvar__1__rsplit__left__15772 = Vvar__1__rsplit__left__15773
& Vvar__0__C__15770 = Vvar__0__C__15771 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__5499,Vvar__0__C__5500] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5499) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5500)
=> Vvar__0__C__5499 = Vvar__0__C__5500 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__5497,Vvar__0__C__5498] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5497) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5498)
=> Vvar__0__C__5497 = Vvar__0__C__5498 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__5505,Vvar__0__C__5506,Vvar__1___24Anonymous__5507,Vvar__1___24Anonymous__5508] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5505,Vvar__1___24Anonymous__5507) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5506,Vvar__1___24Anonymous__5508)
=> ( Vvar__1___24Anonymous__5507 = Vvar__1___24Anonymous__5508
& Vvar__0__C__5505 = Vvar__0__C__5506 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__5509,Vvar__0__C__5510,Vvar__1___24Anonymous__5511,Vvar__1___24Anonymous__5512,Vvar__2___24Anonymous__5513,Vvar__2___24Anonymous__5514] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5509,Vvar__1___24Anonymous__5511,Vvar__2___24Anonymous__5513) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5510,Vvar__1___24Anonymous__5512,Vvar__2___24Anonymous__5514)
=> ( Vvar__2___24Anonymous__5513 = Vvar__2___24Anonymous__5514
& Vvar__1___24Anonymous__5511 = Vvar__1___24Anonymous__5512
& Vvar__0__C__5509 = Vvar__0__C__5510 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__5501,Vvar__0__C__5502,Vvar__1___24Anonymous__5503,Vvar__1___24Anonymous__5504] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5501,Vvar__1___24Anonymous__5503) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5502,Vvar__1___24Anonymous__5504)
=> ( Vvar__1___24Anonymous__5503 = Vvar__1___24Anonymous__5504
& Vvar__0__C__5501 = Vvar__0__C__5502 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__5521,Vvar__0__C__5522,Vvar__1___24Anonymous__5523,Vvar__1___24Anonymous__5524,Vvar__2___24Anonymous__5525,Vvar__2___24Anonymous__5526] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5521,Vvar__1___24Anonymous__5523,Vvar__2___24Anonymous__5525) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5522,Vvar__1___24Anonymous__5524,Vvar__2___24Anonymous__5526)
=> ( Vvar__2___24Anonymous__5525 = Vvar__2___24Anonymous__5526
& Vvar__1___24Anonymous__5523 = Vvar__1___24Anonymous__5524
& Vvar__0__C__5521 = Vvar__0__C__5522 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__5527,Vvar__0__C__5528,Vvar__1___24Anonymous__5529,Vvar__1___24Anonymous__5530] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5527,Vvar__1___24Anonymous__5529) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5528,Vvar__1___24Anonymous__5530)
=> ( Vvar__1___24Anonymous__5529 = Vvar__1___24Anonymous__5530
& Vvar__0__C__5527 = Vvar__0__C__5528 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__5531,Vvar__0__C__5532,Vvar__1___24Anonymous__5533,Vvar__1___24Anonymous__5534,Vvar__2___24Anonymous__5535,Vvar__2___24Anonymous__5536] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5531,Vvar__1___24Anonymous__5533,Vvar__2___24Anonymous__5535) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5532,Vvar__1___24Anonymous__5534,Vvar__2___24Anonymous__5536)
=> ( Vvar__2___24Anonymous__5535 = Vvar__2___24Anonymous__5536
& Vvar__1___24Anonymous__5533 = Vvar__1___24Anonymous__5534
& Vvar__0__C__5531 = Vvar__0__C__5532 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__5515,Vvar__0__C__5516,Vvar__1___24Anonymous__5517,Vvar__1___24Anonymous__5518,Vvar__2___24Anonymous__5519,Vvar__2___24Anonymous__5520] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5515,Vvar__1___24Anonymous__5517,Vvar__2___24Anonymous__5519) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5516,Vvar__1___24Anonymous__5518,Vvar__2___24Anonymous__5520)
=> ( Vvar__2___24Anonymous__5519 = Vvar__2___24Anonymous__5520
& Vvar__1___24Anonymous__5517 = Vvar__1___24Anonymous__5518
& Vvar__0__C__5515 = Vvar__0__C__5516 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__5154,Vvar__0__C__5155,Vvar__1___24Anonymous__5156,Vvar__1___24Anonymous__5157,Vvar__2___24Anonymous__5158,Vvar__2___24Anonymous__5159,Vvar__3___24Anonymous__5160,Vvar__3___24Anonymous__5161] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__5154,Vvar__1___24Anonymous__5156,Vvar__2___24Anonymous__5158,Vvar__3___24Anonymous__5160) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__5155,Vvar__1___24Anonymous__5157,Vvar__2___24Anonymous__5159,Vvar__3___24Anonymous__5161)
=> ( Vvar__3___24Anonymous__5160 = Vvar__3___24Anonymous__5161
& Vvar__2___24Anonymous__5158 = Vvar__2___24Anonymous__5159
& Vvar__1___24Anonymous__5156 = Vvar__1___24Anonymous__5157
& Vvar__0__C__5154 = Vvar__0__C__5155 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__5144,Vvar__0__C__5145,Vvar__1___24Anonymous__5146,Vvar__1___24Anonymous__5147] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5144,Vvar__1___24Anonymous__5146) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5145,Vvar__1___24Anonymous__5147)
=> ( Vvar__1___24Anonymous__5146 = Vvar__1___24Anonymous__5147
& Vvar__0__C__5144 = Vvar__0__C__5145 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__5148,Vvar__0__C__5149,Vvar__1___24Anonymous__5150,Vvar__1___24Anonymous__5151,Vvar__2___24Anonymous__5152,Vvar__2___24Anonymous__5153] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5148,Vvar__1___24Anonymous__5150,Vvar__2___24Anonymous__5152) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5149,Vvar__1___24Anonymous__5151,Vvar__2___24Anonymous__5153)
=> ( Vvar__2___24Anonymous__5152 = Vvar__2___24Anonymous__5153
& Vvar__1___24Anonymous__5150 = Vvar__1___24Anonymous__5151
& Vvar__0__C__5148 = Vvar__0__C__5149 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__5311,Vvar__0___24Anonymous__5312,Vvar__1___24Anonymous__5313,Vvar__1___24Anonymous__5314] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__5311,Vvar__1___24Anonymous__5313) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__5312,Vvar__1___24Anonymous__5314)
=> ( Vvar__1___24Anonymous__5313 = Vvar__1___24Anonymous__5314
& Vvar__0___24Anonymous__5311 = Vvar__0___24Anonymous__5312 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__5307,Vvar__0___24Anonymous__5308,Vvar__1___24Anonymous__5309,Vvar__1___24Anonymous__5310] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5307,Vvar__1___24Anonymous__5309) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5308,Vvar__1___24Anonymous__5310)
=> ( Vvar__1___24Anonymous__5309 = Vvar__1___24Anonymous__5310
& Vvar__0___24Anonymous__5307 = Vvar__0___24Anonymous__5308 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
! [Vvar__0__R__28075,Vvar__0__R__28076,Vvar__1__req__28077,Vvar__1__req__28078,Vvar__2__reqb__28079,Vvar__2__reqb__28080,Vvar__3___24Anonymous__28081,Vvar__3___24Anonymous__28082] :
( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28075,Vvar__1__req__28077,Vvar__2__reqb__28079) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__28076,Vvar__1__req__28078,Vvar__2__reqb__28080)
=> ( c_24Proof = c_24Proof
& Vvar__2__reqb__28079 = Vvar__2__reqb__28080
& Vvar__1__req__28077 = Vvar__1__req__28078
& Vvar__0__R__28075 = Vvar__0__R__28076 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
! [Vvar__0__R__28083,Vvar__0__R__28084,Vvar__1__rO__28085,Vvar__1__rO__28086,Vvar__2__rI__28087,Vvar__2__rI__28088,Vvar__3__radd__28089,Vvar__3__radd__28090,Vvar__4__rmul__28091,Vvar__4__rmul__28092,Vvar__5__rsub__28093,Vvar__5__rsub__28094,Vvar__6__ropp__28095,Vvar__6__ropp__28096,Vvar__7__req__28097,Vvar__7__req__28098,Vvar__8__C__28099,Vvar__8__C__28100,Vvar__9__cO__28101,Vvar__9__cO__28102,Vvar__10__cI__28103,Vvar__10__cI__28104,Vvar__11__cadd__28105,Vvar__11__cadd__28106,Vvar__12__cmul__28107,Vvar__12__cmul__28108,Vvar__13__csub__28109,Vvar__13__csub__28110,Vvar__14__copp__28111,Vvar__14__copp__28112,Vvar__15__ceqb__28113,Vvar__15__ceqb__28114,Vvar__16__phi__28115,Vvar__16__phi__28116,Vvar__17___24Anonymous__28117,Vvar__17___24Anonymous__28118] :
( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__28083,Vvar__1__rO__28085,Vvar__2__rI__28087,Vvar__3__radd__28089,Vvar__4__rmul__28091,Vvar__5__rsub__28093,Vvar__6__ropp__28095,Vvar__7__req__28097,Vvar__8__C__28099,Vvar__9__cO__28101,Vvar__10__cI__28103,Vvar__11__cadd__28105,Vvar__12__cmul__28107,Vvar__13__csub__28109,Vvar__14__copp__28111,Vvar__15__ceqb__28113,Vvar__16__phi__28115) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__28084,Vvar__1__rO__28086,Vvar__2__rI__28088,Vvar__3__radd__28090,Vvar__4__rmul__28092,Vvar__5__rsub__28094,Vvar__6__ropp__28096,Vvar__7__req__28098,Vvar__8__C__28100,Vvar__9__cO__28102,Vvar__10__cI__28104,Vvar__11__cadd__28106,Vvar__12__cmul__28108,Vvar__13__csub__28110,Vvar__14__copp__28112,Vvar__15__ceqb__28114,Vvar__16__phi__28116)
=> ( c_24Proof = c_24Proof
& Vvar__16__phi__28115 = Vvar__16__phi__28116
& Vvar__15__ceqb__28113 = Vvar__15__ceqb__28114
& Vvar__14__copp__28111 = Vvar__14__copp__28112
& Vvar__13__csub__28109 = Vvar__13__csub__28110
& Vvar__12__cmul__28107 = Vvar__12__cmul__28108
& Vvar__11__cadd__28105 = Vvar__11__cadd__28106
& Vvar__10__cI__28103 = Vvar__10__cI__28104
& Vvar__9__cO__28101 = Vvar__9__cO__28102
& Vvar__8__C__28099 = Vvar__8__C__28100
& Vvar__7__req__28097 = Vvar__7__req__28098
& Vvar__6__ropp__28095 = Vvar__6__ropp__28096
& Vvar__5__rsub__28093 = Vvar__5__rsub__28094
& Vvar__4__rmul__28091 = Vvar__4__rmul__28092
& Vvar__3__radd__28089 = Vvar__3__radd__28090
& Vvar__2__rI__28087 = Vvar__2__rI__28088
& Vvar__1__rO__28085 = Vvar__1__rO__28086
& Vvar__0__R__28083 = Vvar__0__R__28084 ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__15020] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15020)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__15020)
=> ( Vvar__0___24Anonymous__15020 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__15022] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__15022)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__15022)
& Vvar__0___24Anonymous__15020 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__15022) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Even.odd',axiom,
! [Vvar__0___24Anonymous__15024] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__15024)
=> ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__15024)
=> ? [Vvar__0__n__15026] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__15026)
& cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__15026)
& Vvar__0___24Anonymous__15024 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__15026) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__14226,Vvar__1___24Anonymous__14227,VX14228] :
( cProp___24t(Vvar__0__P__14226)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__14227)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__14226,Vvar__1___24Anonymous__14227,VX14228)
=> ( ( p(Vvar__0__P__14226)
& Vvar__1___24Anonymous__14227 = cCoq_2eInit_2eDatatypes_2etrue
& VX14228 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__14226) )
| ( ~ p(Vvar__0__P__14226)
& Vvar__1___24Anonymous__14227 = cCoq_2eInit_2eDatatypes_2efalse
& VX14228 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__14226) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX12870] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX12870)
=> ( VX12870 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__12871] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__12871)
& ? [Vvar__1___24Anonymous__12872] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__12872)
& ? [Vvar__2___24Anonymous__12873] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__12873)
& VX12870 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__12871,Vvar__1___24Anonymous__12872,Vvar__2___24Anonymous__12873) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX14250] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX14250)
=> ( VX14250 = cCoq_2eInit_2eByte_2ex00
| VX14250 = cCoq_2eInit_2eByte_2ex01
| VX14250 = cCoq_2eInit_2eByte_2ex02
| VX14250 = cCoq_2eInit_2eByte_2ex03
| VX14250 = cCoq_2eInit_2eByte_2ex04
| VX14250 = cCoq_2eInit_2eByte_2ex05
| VX14250 = cCoq_2eInit_2eByte_2ex06
| VX14250 = cCoq_2eInit_2eByte_2ex07
| VX14250 = cCoq_2eInit_2eByte_2ex08
| VX14250 = cCoq_2eInit_2eByte_2ex09
| VX14250 = cCoq_2eInit_2eByte_2ex0a
| VX14250 = cCoq_2eInit_2eByte_2ex0b
| VX14250 = cCoq_2eInit_2eByte_2ex0c
| VX14250 = cCoq_2eInit_2eByte_2ex0d
| VX14250 = cCoq_2eInit_2eByte_2ex0e
| VX14250 = cCoq_2eInit_2eByte_2ex0f
| VX14250 = cCoq_2eInit_2eByte_2ex10
| VX14250 = cCoq_2eInit_2eByte_2ex11
| VX14250 = cCoq_2eInit_2eByte_2ex12
| VX14250 = cCoq_2eInit_2eByte_2ex13
| VX14250 = cCoq_2eInit_2eByte_2ex14
| VX14250 = cCoq_2eInit_2eByte_2ex15
| VX14250 = cCoq_2eInit_2eByte_2ex16
| VX14250 = cCoq_2eInit_2eByte_2ex17
| VX14250 = cCoq_2eInit_2eByte_2ex18
| VX14250 = cCoq_2eInit_2eByte_2ex19
| VX14250 = cCoq_2eInit_2eByte_2ex1a
| VX14250 = cCoq_2eInit_2eByte_2ex1b
| VX14250 = cCoq_2eInit_2eByte_2ex1c
| VX14250 = cCoq_2eInit_2eByte_2ex1d
| VX14250 = cCoq_2eInit_2eByte_2ex1e
| VX14250 = cCoq_2eInit_2eByte_2ex1f
| VX14250 = cCoq_2eInit_2eByte_2ex20
| VX14250 = cCoq_2eInit_2eByte_2ex21
| VX14250 = cCoq_2eInit_2eByte_2ex22
| VX14250 = cCoq_2eInit_2eByte_2ex23
| VX14250 = cCoq_2eInit_2eByte_2ex24
| VX14250 = cCoq_2eInit_2eByte_2ex25
| VX14250 = cCoq_2eInit_2eByte_2ex26
| VX14250 = cCoq_2eInit_2eByte_2ex27
| VX14250 = cCoq_2eInit_2eByte_2ex28
| VX14250 = cCoq_2eInit_2eByte_2ex29
| VX14250 = cCoq_2eInit_2eByte_2ex2a
| VX14250 = cCoq_2eInit_2eByte_2ex2b
| VX14250 = cCoq_2eInit_2eByte_2ex2c
| VX14250 = cCoq_2eInit_2eByte_2ex2d
| VX14250 = cCoq_2eInit_2eByte_2ex2e
| VX14250 = cCoq_2eInit_2eByte_2ex2f
| VX14250 = cCoq_2eInit_2eByte_2ex30
| VX14250 = cCoq_2eInit_2eByte_2ex31
| VX14250 = cCoq_2eInit_2eByte_2ex32
| VX14250 = cCoq_2eInit_2eByte_2ex33
| VX14250 = cCoq_2eInit_2eByte_2ex34
| VX14250 = cCoq_2eInit_2eByte_2ex35
| VX14250 = cCoq_2eInit_2eByte_2ex36
| VX14250 = cCoq_2eInit_2eByte_2ex37
| VX14250 = cCoq_2eInit_2eByte_2ex38
| VX14250 = cCoq_2eInit_2eByte_2ex39
| VX14250 = cCoq_2eInit_2eByte_2ex3a
| VX14250 = cCoq_2eInit_2eByte_2ex3b
| VX14250 = cCoq_2eInit_2eByte_2ex3c
| VX14250 = cCoq_2eInit_2eByte_2ex3d
| VX14250 = cCoq_2eInit_2eByte_2ex3e
| VX14250 = cCoq_2eInit_2eByte_2ex3f
| VX14250 = cCoq_2eInit_2eByte_2ex40
| VX14250 = cCoq_2eInit_2eByte_2ex41
| VX14250 = cCoq_2eInit_2eByte_2ex42
| VX14250 = cCoq_2eInit_2eByte_2ex43
| VX14250 = cCoq_2eInit_2eByte_2ex44
| VX14250 = cCoq_2eInit_2eByte_2ex45
| VX14250 = cCoq_2eInit_2eByte_2ex46
| VX14250 = cCoq_2eInit_2eByte_2ex47
| VX14250 = cCoq_2eInit_2eByte_2ex48
| VX14250 = cCoq_2eInit_2eByte_2ex49
| VX14250 = cCoq_2eInit_2eByte_2ex4a
| VX14250 = cCoq_2eInit_2eByte_2ex4b
| VX14250 = cCoq_2eInit_2eByte_2ex4c
| VX14250 = cCoq_2eInit_2eByte_2ex4d
| VX14250 = cCoq_2eInit_2eByte_2ex4e
| VX14250 = cCoq_2eInit_2eByte_2ex4f
| VX14250 = cCoq_2eInit_2eByte_2ex50
| VX14250 = cCoq_2eInit_2eByte_2ex51
| VX14250 = cCoq_2eInit_2eByte_2ex52
| VX14250 = cCoq_2eInit_2eByte_2ex53
| VX14250 = cCoq_2eInit_2eByte_2ex54
| VX14250 = cCoq_2eInit_2eByte_2ex55
| VX14250 = cCoq_2eInit_2eByte_2ex56
| VX14250 = cCoq_2eInit_2eByte_2ex57
| VX14250 = cCoq_2eInit_2eByte_2ex58
| VX14250 = cCoq_2eInit_2eByte_2ex59
| VX14250 = cCoq_2eInit_2eByte_2ex5a
| VX14250 = cCoq_2eInit_2eByte_2ex5b
| VX14250 = cCoq_2eInit_2eByte_2ex5c
| VX14250 = cCoq_2eInit_2eByte_2ex5d
| VX14250 = cCoq_2eInit_2eByte_2ex5e
| VX14250 = cCoq_2eInit_2eByte_2ex5f
| VX14250 = cCoq_2eInit_2eByte_2ex60
| VX14250 = cCoq_2eInit_2eByte_2ex61
| VX14250 = cCoq_2eInit_2eByte_2ex62
| VX14250 = cCoq_2eInit_2eByte_2ex63
| VX14250 = cCoq_2eInit_2eByte_2ex64
| VX14250 = cCoq_2eInit_2eByte_2ex65
| VX14250 = cCoq_2eInit_2eByte_2ex66
| VX14250 = cCoq_2eInit_2eByte_2ex67
| VX14250 = cCoq_2eInit_2eByte_2ex68
| VX14250 = cCoq_2eInit_2eByte_2ex69
| VX14250 = cCoq_2eInit_2eByte_2ex6a
| VX14250 = cCoq_2eInit_2eByte_2ex6b
| VX14250 = cCoq_2eInit_2eByte_2ex6c
| VX14250 = cCoq_2eInit_2eByte_2ex6d
| VX14250 = cCoq_2eInit_2eByte_2ex6e
| VX14250 = cCoq_2eInit_2eByte_2ex6f
| VX14250 = cCoq_2eInit_2eByte_2ex70
| VX14250 = cCoq_2eInit_2eByte_2ex71
| VX14250 = cCoq_2eInit_2eByte_2ex72
| VX14250 = cCoq_2eInit_2eByte_2ex73
| VX14250 = cCoq_2eInit_2eByte_2ex74
| VX14250 = cCoq_2eInit_2eByte_2ex75
| VX14250 = cCoq_2eInit_2eByte_2ex76
| VX14250 = cCoq_2eInit_2eByte_2ex77
| VX14250 = cCoq_2eInit_2eByte_2ex78
| VX14250 = cCoq_2eInit_2eByte_2ex79
| VX14250 = cCoq_2eInit_2eByte_2ex7a
| VX14250 = cCoq_2eInit_2eByte_2ex7b
| VX14250 = cCoq_2eInit_2eByte_2ex7c
| VX14250 = cCoq_2eInit_2eByte_2ex7d
| VX14250 = cCoq_2eInit_2eByte_2ex7e
| VX14250 = cCoq_2eInit_2eByte_2ex7f
| VX14250 = cCoq_2eInit_2eByte_2ex80
| VX14250 = cCoq_2eInit_2eByte_2ex81
| VX14250 = cCoq_2eInit_2eByte_2ex82
| VX14250 = cCoq_2eInit_2eByte_2ex83
| VX14250 = cCoq_2eInit_2eByte_2ex84
| VX14250 = cCoq_2eInit_2eByte_2ex85
| VX14250 = cCoq_2eInit_2eByte_2ex86
| VX14250 = cCoq_2eInit_2eByte_2ex87
| VX14250 = cCoq_2eInit_2eByte_2ex88
| VX14250 = cCoq_2eInit_2eByte_2ex89
| VX14250 = cCoq_2eInit_2eByte_2ex8a
| VX14250 = cCoq_2eInit_2eByte_2ex8b
| VX14250 = cCoq_2eInit_2eByte_2ex8c
| VX14250 = cCoq_2eInit_2eByte_2ex8d
| VX14250 = cCoq_2eInit_2eByte_2ex8e
| VX14250 = cCoq_2eInit_2eByte_2ex8f
| VX14250 = cCoq_2eInit_2eByte_2ex90
| VX14250 = cCoq_2eInit_2eByte_2ex91
| VX14250 = cCoq_2eInit_2eByte_2ex92
| VX14250 = cCoq_2eInit_2eByte_2ex93
| VX14250 = cCoq_2eInit_2eByte_2ex94
| VX14250 = cCoq_2eInit_2eByte_2ex95
| VX14250 = cCoq_2eInit_2eByte_2ex96
| VX14250 = cCoq_2eInit_2eByte_2ex97
| VX14250 = cCoq_2eInit_2eByte_2ex98
| VX14250 = cCoq_2eInit_2eByte_2ex99
| VX14250 = cCoq_2eInit_2eByte_2ex9a
| VX14250 = cCoq_2eInit_2eByte_2ex9b
| VX14250 = cCoq_2eInit_2eByte_2ex9c
| VX14250 = cCoq_2eInit_2eByte_2ex9d
| VX14250 = cCoq_2eInit_2eByte_2ex9e
| VX14250 = cCoq_2eInit_2eByte_2ex9f
| VX14250 = cCoq_2eInit_2eByte_2exa0
| VX14250 = cCoq_2eInit_2eByte_2exa1
| VX14250 = cCoq_2eInit_2eByte_2exa2
| VX14250 = cCoq_2eInit_2eByte_2exa3
| VX14250 = cCoq_2eInit_2eByte_2exa4
| VX14250 = cCoq_2eInit_2eByte_2exa5
| VX14250 = cCoq_2eInit_2eByte_2exa6
| VX14250 = cCoq_2eInit_2eByte_2exa7
| VX14250 = cCoq_2eInit_2eByte_2exa8
| VX14250 = cCoq_2eInit_2eByte_2exa9
| VX14250 = cCoq_2eInit_2eByte_2exaa
| VX14250 = cCoq_2eInit_2eByte_2exab
| VX14250 = cCoq_2eInit_2eByte_2exac
| VX14250 = cCoq_2eInit_2eByte_2exad
| VX14250 = cCoq_2eInit_2eByte_2exae
| VX14250 = cCoq_2eInit_2eByte_2exaf
| VX14250 = cCoq_2eInit_2eByte_2exb0
| VX14250 = cCoq_2eInit_2eByte_2exb1
| VX14250 = cCoq_2eInit_2eByte_2exb2
| VX14250 = cCoq_2eInit_2eByte_2exb3
| VX14250 = cCoq_2eInit_2eByte_2exb4
| VX14250 = cCoq_2eInit_2eByte_2exb5
| VX14250 = cCoq_2eInit_2eByte_2exb6
| VX14250 = cCoq_2eInit_2eByte_2exb7
| VX14250 = cCoq_2eInit_2eByte_2exb8
| VX14250 = cCoq_2eInit_2eByte_2exb9
| VX14250 = cCoq_2eInit_2eByte_2exba
| VX14250 = cCoq_2eInit_2eByte_2exbb
| VX14250 = cCoq_2eInit_2eByte_2exbc
| VX14250 = cCoq_2eInit_2eByte_2exbd
| VX14250 = cCoq_2eInit_2eByte_2exbe
| VX14250 = cCoq_2eInit_2eByte_2exbf
| VX14250 = cCoq_2eInit_2eByte_2exc0
| VX14250 = cCoq_2eInit_2eByte_2exc1
| VX14250 = cCoq_2eInit_2eByte_2exc2
| VX14250 = cCoq_2eInit_2eByte_2exc3
| VX14250 = cCoq_2eInit_2eByte_2exc4
| VX14250 = cCoq_2eInit_2eByte_2exc5
| VX14250 = cCoq_2eInit_2eByte_2exc6
| VX14250 = cCoq_2eInit_2eByte_2exc7
| VX14250 = cCoq_2eInit_2eByte_2exc8
| VX14250 = cCoq_2eInit_2eByte_2exc9
| VX14250 = cCoq_2eInit_2eByte_2exca
| VX14250 = cCoq_2eInit_2eByte_2excb
| VX14250 = cCoq_2eInit_2eByte_2excc
| VX14250 = cCoq_2eInit_2eByte_2excd
| VX14250 = cCoq_2eInit_2eByte_2exce
| VX14250 = cCoq_2eInit_2eByte_2excf
| VX14250 = cCoq_2eInit_2eByte_2exd0
| VX14250 = cCoq_2eInit_2eByte_2exd1
| VX14250 = cCoq_2eInit_2eByte_2exd2
| VX14250 = cCoq_2eInit_2eByte_2exd3
| VX14250 = cCoq_2eInit_2eByte_2exd4
| VX14250 = cCoq_2eInit_2eByte_2exd5
| VX14250 = cCoq_2eInit_2eByte_2exd6
| VX14250 = cCoq_2eInit_2eByte_2exd7
| VX14250 = cCoq_2eInit_2eByte_2exd8
| VX14250 = cCoq_2eInit_2eByte_2exd9
| VX14250 = cCoq_2eInit_2eByte_2exda
| VX14250 = cCoq_2eInit_2eByte_2exdb
| VX14250 = cCoq_2eInit_2eByte_2exdc
| VX14250 = cCoq_2eInit_2eByte_2exdd
| VX14250 = cCoq_2eInit_2eByte_2exde
| VX14250 = cCoq_2eInit_2eByte_2exdf
| VX14250 = cCoq_2eInit_2eByte_2exe0
| VX14250 = cCoq_2eInit_2eByte_2exe1
| VX14250 = cCoq_2eInit_2eByte_2exe2
| VX14250 = cCoq_2eInit_2eByte_2exe3
| VX14250 = cCoq_2eInit_2eByte_2exe4
| VX14250 = cCoq_2eInit_2eByte_2exe5
| VX14250 = cCoq_2eInit_2eByte_2exe6
| VX14250 = cCoq_2eInit_2eByte_2exe7
| VX14250 = cCoq_2eInit_2eByte_2exe8
| VX14250 = cCoq_2eInit_2eByte_2exe9
| VX14250 = cCoq_2eInit_2eByte_2exea
| VX14250 = cCoq_2eInit_2eByte_2exeb
| VX14250 = cCoq_2eInit_2eByte_2exec
| VX14250 = cCoq_2eInit_2eByte_2exed
| VX14250 = cCoq_2eInit_2eByte_2exee
| VX14250 = cCoq_2eInit_2eByte_2exef
| VX14250 = cCoq_2eInit_2eByte_2exf0
| VX14250 = cCoq_2eInit_2eByte_2exf1
| VX14250 = cCoq_2eInit_2eByte_2exf2
| VX14250 = cCoq_2eInit_2eByte_2exf3
| VX14250 = cCoq_2eInit_2eByte_2exf4
| VX14250 = cCoq_2eInit_2eByte_2exf5
| VX14250 = cCoq_2eInit_2eByte_2exf6
| VX14250 = cCoq_2eInit_2eByte_2exf7
| VX14250 = cCoq_2eInit_2eByte_2exf8
| VX14250 = cCoq_2eInit_2eByte_2exf9
| VX14250 = cCoq_2eInit_2eByte_2exfa
| VX14250 = cCoq_2eInit_2eByte_2exfb
| VX14250 = cCoq_2eInit_2eByte_2exfc
| VX14250 = cCoq_2eInit_2eByte_2exfd
| VX14250 = cCoq_2eInit_2eByte_2exfe
| VX14250 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__3248,Vvar__1__Q__3249,Vvar__2___24Anonymous__3250] :
( cProp___24t(Vvar__0__P__3248)
=> ( cProp___24t(Vvar__1__Q__3249)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__3250)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__3248,Vvar__1__Q__3249,Vvar__2___24Anonymous__3250)
=> ( ( p(Vvar__0__P__3248)
& Vvar__2___24Anonymous__3250 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__3249)
& Vvar__2___24Anonymous__3250 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__14503,Vvar__1__Plt__14504,Vvar__2__Pgt__14505,Vvar__3___24Anonymous__14506] :
( cProp___24t(Vvar__0__Peq__14503)
=> ( cProp___24t(Vvar__1__Plt__14504)
=> ( cProp___24t(Vvar__2__Pgt__14505)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__14506)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__14503,Vvar__1__Plt__14504,Vvar__2__Pgt__14505,Vvar__3___24Anonymous__14506)
=> ( ( p(Vvar__0__Peq__14503)
& Vvar__3___24Anonymous__14506 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__14504)
& Vvar__3___24Anonymous__14506 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__14505)
& Vvar__3___24Anonymous__14506 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
! [Vvar__0__Peq__3369,Vvar__1__Plt__3370,Vvar__2__Pgt__3371,Vvar__3___24Anonymous__3372,VX3373] :
( cProp___24t(Vvar__0__Peq__3369)
=> ( cProp___24t(Vvar__1__Plt__3370)
=> ( cProp___24t(Vvar__2__Pgt__3371)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__3372)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__3369,Vvar__1__Plt__3370,Vvar__2__Pgt__3371,Vvar__3___24Anonymous__3372,VX3373)
=> ( ( p(Vvar__0__Peq__3369)
& Vvar__3___24Anonymous__3372 = cCoq_2eInit_2eDatatypes_2eEq
& VX3373 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__3369,Vvar__1__Plt__3370,Vvar__2__Pgt__3371) )
| ( p(Vvar__1__Plt__3370)
& Vvar__3___24Anonymous__3372 = cCoq_2eInit_2eDatatypes_2eLt
& VX3373 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__3369,Vvar__1__Plt__3370,Vvar__2__Pgt__3371) )
| ( p(Vvar__2__Pgt__3371)
& Vvar__3___24Anonymous__3372 = cCoq_2eInit_2eDatatypes_2eGt
& VX3373 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__3369,Vvar__1__Plt__3370,Vvar__2__Pgt__3371) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX3242] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX3242)
=> ( VX3242 = cCoq_2eInit_2eDatatypes_2etrue
| VX3242 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX3368] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX3368)
=> ( VX3368 = cCoq_2eInit_2eDatatypes_2eEq
| VX3368 = cCoq_2eInit_2eDatatypes_2eLt
| VX3368 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__3331,VX3332] :
( cType___24t(Vvar__0__A__3331)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3331,VX3332)
=> ( VX3332 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3331)
| ? [Vvar__1___24Anonymous__3335] :
( t(Vvar__1___24Anonymous__3335,Vvar__0__A__3331)
& ? [Vvar__2___24Anonymous__3336] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3331,Vvar__2___24Anonymous__3336)
& VX3332 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3331,Vvar__1___24Anonymous__3335,Vvar__2___24Anonymous__3336) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX142] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX142)
=> ( VX142 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__143] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__143)
& VX142 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__143) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__3262,VX3263] :
( cType___24t(Vvar__0__A__3262)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__3262,VX3263)
=> ( ? [Vvar__1___24Anonymous__3265] :
( t(Vvar__1___24Anonymous__3265,Vvar__0__A__3262)
& VX3263 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3262,Vvar__1___24Anonymous__3265) )
| VX3263 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3262) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__3281,Vvar__1__B__3282,VX3283] :
( cType___24t(Vvar__0__A__3281)
=> ( cType___24t(Vvar__1__B__3282)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__3281,Vvar__1__B__3282,VX3283)
=> ? [Vvar__2___24Anonymous__3286] :
( t(Vvar__2___24Anonymous__3286,Vvar__0__A__3281)
& ? [Vvar__3___24Anonymous__3287] :
( t(Vvar__3___24Anonymous__3287,Vvar__1__B__3282)
& VX3283 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__3281,Vvar__1__B__3282,Vvar__2___24Anonymous__3286,Vvar__3___24Anonymous__3287) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__14453,Vvar__1__B__14454,VX14455] :
( cType___24t(Vvar__0__A__14453)
=> ( cType___24t(Vvar__1__B__14454)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__14453,Vvar__1__B__14454,VX14455)
=> ( ? [Vvar__2___24Anonymous__14458] :
( t(Vvar__2___24Anonymous__14458,Vvar__0__A__14453)
& VX14455 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__14453,Vvar__1__B__14454,Vvar__2___24Anonymous__14458) )
| ? [Vvar__2___24Anonymous__14461] :
( t(Vvar__2___24Anonymous__14461,Vvar__1__B__14454)
& VX14455 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__14453,Vvar__1__B__14454,Vvar__2___24Anonymous__14461) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX3241] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX3241)
=> VX3241 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__5069,Vvar__1___24Anonymous__5070] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__5069)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__5070)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__5069,Vvar__1___24Anonymous__5070)
=> ( Vvar__1___24Anonymous__5070 = Vvar__0__n__5069
| ? [Vvar__1__m__5074] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__5074)
& cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__5069,Vvar__1__m__5074)
& Vvar__1___24Anonymous__5070 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__5074) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__28457,Vvar__1__P__28458,VX28461] :
( cType___24t(Vvar__0__A__28457)
=> ( c_24__type__28471___24t(Vvar__0__A__28457,Vvar__1__P__28458,Vvar__1__P__28458)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__28457,Vvar__1__P__28458,VX28461)
=> ? [Vvar__2__x__28466] :
( t(Vvar__2__x__28466,Vvar__0__A__28457)
& p(happ(Vvar__1__P__28458,Vvar__2__x__28466))
& VX28461 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__28457,Vvar__1__P__28458,Vvar__2__x__28466) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__9098,Vvar__1__P__9099,Vvar__2__Q__9102,VX9105] :
( cType___24t(Vvar__0__A__9098)
=> ( c_24__type__9122___24t(Vvar__0__A__9098,Vvar__1__P__9099,Vvar__2__Q__9102,Vvar__1__P__9099)
=> ( c_24__type__9130___24t(Vvar__0__A__9098,Vvar__1__P__9099,Vvar__2__Q__9102,Vvar__2__Q__9102)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__9098,Vvar__1__P__9099,Vvar__2__Q__9102,VX9105)
=> ? [Vvar__3__x__9113] :
( t(Vvar__3__x__9113,Vvar__0__A__9098)
& p(happ(Vvar__1__P__9099,Vvar__3__x__9113))
& p(happ(Vvar__2__Q__9102,Vvar__3__x__9113))
& VX9105 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__9098,Vvar__1__P__9099,Vvar__2__Q__9102,Vvar__3__x__9113) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__28496,Vvar__1__P__28497,VX28500] :
( cType___24t(Vvar__0__A__28496)
=> ( c_24__type__28510___24t(Vvar__0__A__28496,Vvar__1__P__28497,Vvar__1__P__28497)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__28496,Vvar__1__P__28497,VX28500)
=> ? [Vvar__2__x__28505] :
( t(Vvar__2__x__28505,Vvar__0__A__28496)
& ? [Vvar__3___24Anonymous__28506] :
( t(Vvar__3___24Anonymous__28506,happ(Vvar__1__P__28497,Vvar__2__x__28505))
& VX28500 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__28496,Vvar__1__P__28497,Vvar__2__x__28505,Vvar__3___24Anonymous__28506) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__9176,Vvar__1__P__9177,Vvar__2__Q__9180,VX9183] :
( cType___24t(Vvar__0__A__9176)
=> ( c_24__type__9200___24t(Vvar__0__A__9176,Vvar__1__P__9177,Vvar__2__Q__9180,Vvar__1__P__9177)
=> ( c_24__type__9208___24t(Vvar__0__A__9176,Vvar__1__P__9177,Vvar__2__Q__9180,Vvar__2__Q__9180)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__9176,Vvar__1__P__9177,Vvar__2__Q__9180,VX9183)
=> ? [Vvar__3__x__9191] :
( t(Vvar__3__x__9191,Vvar__0__A__9176)
& ? [Vvar__4___24Anonymous__9192] :
( t(Vvar__4___24Anonymous__9192,happ(Vvar__1__P__9177,Vvar__3__x__9191))
& ? [Vvar__5___24Anonymous__9193] :
( t(Vvar__5___24Anonymous__9193,happ(Vvar__2__Q__9180,Vvar__3__x__9191))
& VX9183 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__9176,Vvar__1__P__9177,Vvar__2__Q__9180,Vvar__3__x__9191,Vvar__4___24Anonymous__9192,Vvar__5___24Anonymous__9193) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__11487,Vvar__1__B__11488,VX11489] :
( cProp___24t(Vvar__0__A__11487)
=> ( cProp___24t(Vvar__1__B__11488)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__11487,Vvar__1__B__11488,VX11489)
=> ( ( p(Vvar__0__A__11487)
& VX11489 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__11487,Vvar__1__B__11488) )
| ( p(Vvar__1__B__11488)
& VX11489 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__11487,Vvar__1__B__11488) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__28545,Vvar__1__B__28546,VX28547] :
( cType___24t(Vvar__0__A__28545)
=> ( cProp___24t(Vvar__1__B__28546)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__28545,Vvar__1__B__28546,VX28547)
=> ( ? [Vvar__2___24Anonymous__28550] :
( t(Vvar__2___24Anonymous__28550,Vvar__0__A__28545)
& VX28547 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__28545,Vvar__1__B__28546,Vvar__2___24Anonymous__28550) )
| ( p(Vvar__1__B__28546)
& VX28547 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__28545,Vvar__1__B__28546) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__29056,Vvar__1__R__29057,Vvar__2__x__29062] :
( cType___24t(Vvar__0__A__29056)
=> ( c_24__type__29091___24t(Vvar__0__A__29056,Vvar__1__R__29057,Vvar__2__x__29062,Vvar__1__R__29057)
=> ( t(Vvar__2__x__29062,Vvar__0__A__29056)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__29056,Vvar__1__R__29057,Vvar__2__x__29062)
=> ( ! [Vvar__var__var__var__var__3__y__29072__29074__29076__29078__29080] :
( t(Vvar__var__var__var__var__3__y__29072__29074__29076__29078__29080,Vvar__0__A__29056)
=> ( p(happ(happ(Vvar__1__R__29057,Vvar__var__var__var__var__3__y__29072__29074__29076__29078__29080),Vvar__2__x__29062))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__29056,Vvar__1__R__29057,Vvar__var__var__var__var__3__y__29072__29074__29076__29078__29080) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__17126,Vvar__1__P__17127,Vvar__2___24Anonymous__17130] :
( cType___24t(Vvar__0__A__17126)
=> ( c_24__type__17148___24t(Vvar__0__A__17126,Vvar__1__P__17127,Vvar__2___24Anonymous__17130,Vvar__1__P__17127)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__17126,Vvar__2___24Anonymous__17130)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__17126,Vvar__1__P__17127,Vvar__2___24Anonymous__17130)
=> ( Vvar__2___24Anonymous__17130 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__17126)
| ? [Vvar__2__x__17140] :
( t(Vvar__2__x__17140,Vvar__0__A__17126)
& ? [Vvar__3__l__17141] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__17126,Vvar__3__l__17141)
& p(happ(Vvar__1__P__17127,Vvar__2__x__17140))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__17126,Vvar__1__P__17127,Vvar__3__l__17141)
& Vvar__2___24Anonymous__17130 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__17126,Vvar__2__x__17140,Vvar__3__l__17141) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__17117,Vvar__1___24Anonymous__17118] :
( cType___24t(Vvar__0__A__17117)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__17117,Vvar__1___24Anonymous__17118)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__17117,Vvar__1___24Anonymous__17118)
=> ( Vvar__1___24Anonymous__17118 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__17117)
| ? [Vvar__1__x__17122] :
( t(Vvar__1__x__17122,Vvar__0__A__17117)
& ? [Vvar__2__l__17123] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__17117,Vvar__2__l__17123)
& ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__17117,Vvar__1__x__17122,Vvar__2__l__17123)
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__17117,Vvar__2__l__17123)
& Vvar__1___24Anonymous__17118 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__17117,Vvar__1__x__17122,Vvar__2__l__17123) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__28122,Vvar__1__eqA__28123,Vvar__2__x__28128,Vvar__3___24Anonymous__28129] :
( cType___24t(Vvar__0__A__28122)
=> ( c_24__type__28162___24t(Vvar__0__A__28122,Vvar__1__eqA__28123,Vvar__2__x__28128,Vvar__3___24Anonymous__28129,Vvar__1__eqA__28123)
=> ( t(Vvar__2__x__28128,Vvar__0__A__28122)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28122,Vvar__3___24Anonymous__28129)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28122,Vvar__1__eqA__28123,Vvar__2__x__28128,Vvar__3___24Anonymous__28129)
=> ( ? [Vvar__3__y__28138] :
( t(Vvar__3__y__28138,Vvar__0__A__28122)
& ? [Vvar__4__l__28139] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28122,Vvar__4__l__28139)
& p(happ(happ(Vvar__1__eqA__28123,Vvar__2__x__28128),Vvar__3__y__28138))
& Vvar__3___24Anonymous__28129 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28122,Vvar__3__y__28138,Vvar__4__l__28139) ) )
| ? [Vvar__3__y__28148] :
( t(Vvar__3__y__28148,Vvar__0__A__28122)
& ? [Vvar__4__l__28149] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28122,Vvar__4__l__28149)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__28122,Vvar__1__eqA__28123,Vvar__2__x__28128,Vvar__4__l__28149)
& Vvar__3___24Anonymous__28129 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28122,Vvar__3__y__28148,Vvar__4__l__28149) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.has_fixpoint',axiom,
! [Vvar__0__A__14276] :
( cProp___24t(Vvar__0__A__14276)
=> ( cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(Vvar__0__A__14276)
=> ( ( ( p(Vvar__0__A__14276)
=> p(Vvar__0__A__14276) )
=> p(Vvar__0__A__14276) )
& ( ( p(Vvar__0__A__14276)
=> p(Vvar__0__A__14276) )
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.Logic.ClassicalFacts.retract',axiom,
! [Vvar__0__A__14252,Vvar__1__B__14253] :
( cProp___24t(Vvar__0__A__14252)
=> ( cProp___24t(Vvar__1__B__14253)
=> ( cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(Vvar__0__A__14252,Vvar__1__B__14253)
=> ( ( p(Vvar__0__A__14252)
=> p(Vvar__1__B__14253) )
& ( p(Vvar__1__B__14253)
=> p(Vvar__0__A__14252) )
& ( p(Vvar__1__B__14253)
=> c_24Proof = c_24Proof )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__14950,Vvar__1__P__14951,Vvar__2__p__14954,Vvar__3__x__14955,Vvar__4__q__14956,Vvar__5___24Anonymous__14957] :
( cType___24t(Vvar__0__U__14950)
=> ( c_24__type__14972___24t(Vvar__0__U__14950,Vvar__1__P__14951,Vvar__2__p__14954,Vvar__3__x__14955,Vvar__4__q__14956,Vvar__5___24Anonymous__14957,Vvar__1__P__14951)
=> ( t(Vvar__2__p__14954,Vvar__0__U__14950)
=> ( t(Vvar__3__x__14955,happ(Vvar__1__P__14951,Vvar__2__p__14954))
=> ( t(Vvar__4__q__14956,Vvar__0__U__14950)
=> ( t(Vvar__5___24Anonymous__14957,happ(Vvar__1__P__14951,Vvar__4__q__14956))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__14950,Vvar__1__P__14951,Vvar__2__p__14954,Vvar__3__x__14955,Vvar__4__q__14956,Vvar__5___24Anonymous__14957)
=> ( Vvar__5___24Anonymous__14957 = Vvar__3__x__14955
& Vvar__4__q__14956 = Vvar__2__p__14954 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
! [Vvar__0__U__14974,Vvar__1__P__14975,Vvar__2__p__14978,Vvar__3__x__14979,Vvar__4__q__14980,Vvar__5__y__14981] :
( cType___24t(Vvar__0__U__14974)
=> ( c_24__type__15000___24t(Vvar__0__U__14974,Vvar__1__P__14975,Vvar__2__p__14978,Vvar__3__x__14979,Vvar__4__q__14980,Vvar__5__y__14981,Vvar__1__P__14975)
=> ( t(Vvar__2__p__14978,Vvar__0__U__14974)
=> ( t(Vvar__3__x__14979,happ(Vvar__1__P__14975,Vvar__2__p__14978))
=> ( t(Vvar__4__q__14980,Vvar__0__U__14974)
=> ( t(Vvar__5__y__14981,happ(Vvar__1__P__14975,Vvar__4__q__14980))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__14974,Vvar__1__P__14975,Vvar__2__p__14978,Vvar__3__x__14979,Vvar__4__q__14980,Vvar__5__y__14981)
=> ( Vvar__4__q__14980 = Vvar__2__p__14978
& Vvar__3__x__14979 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__14974,Vvar__4__q__14980,Vvar__1__P__14975,Vvar__5__y__14981,Vvar__2__p__14978)
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX3204] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX3204)
=> ( VX3204 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__3205] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3205)
& VX3204 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3205) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX3211] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX3211)
=> ( VX3211 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__3212] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3212)
& VX3211 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3212) )
| ? [Vvar__0___24Anonymous__3213] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3213)
& VX3211 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3213) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX3185] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX3185)
=> ( ? [Vvar__0___24Anonymous__3186] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3186)
& VX3185 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__3186) )
| ? [Vvar__0___24Anonymous__3187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3187)
& VX3185 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__3187) )
| VX3185 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
! [Vvar__0__p__29512,Vvar__1__q__29513,Vvar__2___24Anonymous__29514] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__29512)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__29513)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__29514)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__29512,Vvar__1__q__29513,Vvar__2___24Anonymous__29514)
=> ( ( Vvar__0__p__29512 = Vvar__1__q__29513
& Vvar__2___24Anonymous__29514 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
| ? [Vvar__2__r__29521] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__29521)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__29513,Vvar__2__r__29521) = Vvar__0__p__29512
& Vvar__2___24Anonymous__29514 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__29521) )
| ? [Vvar__2__r__29525] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__29525)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__29512,Vvar__2__r__29525) = Vvar__1__q__29513
& Vvar__2___24Anonymous__29514 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX12644] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX12644)
=> ( VX12644 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__12645] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12645)
& VX12644 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__12645) )
| VX12644 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX18539] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX18539)
=> ? [Vvar__0__Qnum__18540] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__18540)
& ? [Vvar__1__Qden__18541] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__18541)
& VX18539 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__18540,Vvar__1__Qden__18541) ) ) ) ).
fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
! [VX18573] :
( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX18573)
=> ? [Vvar__0__nonzero__18574] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__18574)
& Vvar__0__nonzero__18574 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
& VX18573 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__18574) ) ) ).
fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
! [Vvar__0__x__18786,Vvar__1___24Anonymous__18787,VX18788] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__18786)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__18787)
=> ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__18786,Vvar__1___24Anonymous__18787,VX18788)
=> ( ( Vvar__0__x__18786 = cCoq_2eNumbers_2eBinNums_2eZ0
& Vvar__1___24Anonymous__18787 = cCoq_2eNumbers_2eBinNums_2eZ0
& VX18788 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__18786) )
| ? [Vvar__1__n__18792] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__18792)
& Vvar__0__x__18786 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__18792)
& Vvar__1___24Anonymous__18787 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2418812___24a3(Vvar__0__x__18786,Vvar__1___24Anonymous__18787,Vvar__1__n__18792)
& VX18788 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__18786,Vvar__1__n__18792) )
| ? [Vvar__1__n__18797] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__18797)
& Vvar__0__x__18786 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__18797))
& Vvar__1___24Anonymous__18787 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2418829___24a3(Vvar__0__x__18786,Vvar__1___24Anonymous__18787,Vvar__1__n__18797)
& VX18788 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__18786,Vvar__1__n__18797) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Bottom',axiom,
! [Vvar__0__U__1472,Vvar__1__D__1473,Vvar__2__bot__1474] :
( cType___24t(Vvar__0__U__1472)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1472,Vvar__1__D__1473)
=> ( t(Vvar__2__bot__1474,Vvar__0__U__1472)
=> ( cCoq_2eSets_2eCpo_2eBottom___24a3(Vvar__0__U__1472,Vvar__1__D__1473,Vvar__2__bot__1474)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1472,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1472,Vvar__1__D__1473),Vvar__2__bot__1474)
& ! [Vvar__var__var__var__var__4__y__1481__1483__1485__1487__1489] :
( t(Vvar__var__var__var__var__4__y__1481__1483__1485__1487__1489,Vvar__0__U__1472)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__1472,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1472,Vvar__1__D__1473),Vvar__var__var__var__var__4__y__1481__1483__1485__1487__1489)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1472,Vvar__1__D__1473,Vvar__2__bot__1474,Vvar__var__var__var__var__4__y__1481__1483__1485__1487__1489) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Complete',axiom,
! [Vvar__0__U__2391,Vvar__1__D__2392] :
( cType___24t(Vvar__0__U__2391)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__2391,Vvar__1__D__2392)
=> ( cCoq_2eSets_2eCpo_2eComplete___24a2(Vvar__0__U__2391,Vvar__1__D__2392)
=> ( ? [Vvar__var__var__var__2__bot__2397__2398__2406__2407] :
( t(Vvar__var__var__var__2__bot__2397__2398__2406__2407,Vvar__0__U__2391)
& cCoq_2eSets_2eCpo_2eBottom___24a3(Vvar__0__U__2391,Vvar__1__D__2392,Vvar__var__var__var__2__bot__2397__2398__2406__2407) )
& ! [Vvar__var__var__var__3__X__2400__2403__2408__2411] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2391,Vvar__var__var__var__3__X__2400__2403__2408__2411)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vvar__0__U__2391,Vvar__1__D__2392,Vvar__var__var__var__3__X__2400__2403__2408__2411)
=> ? [Vvar__var__var__var__5__bsup__2401__2404__2409__2412] :
( t(Vvar__var__var__var__5__bsup__2401__2404__2409__2412,Vvar__0__U__2391)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__2391,Vvar__1__D__2392,Vvar__var__var__var__3__X__2400__2403__2408__2411,Vvar__var__var__var__5__bsup__2401__2404__2409__2412) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Conditionally_complete',axiom,
! [Vvar__0__U__2641,Vvar__1__D__2642] :
( cType___24t(Vvar__0__U__2641)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__2641,Vvar__1__D__2642)
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(Vvar__0__U__2641,Vvar__1__D__2642)
=> ( ! [Vvar__var__var__var__2__X__2647__2652__2657__2662] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2641,Vvar__var__var__var__2__X__2647__2652__2657__2662)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__2641,Vvar__var__var__var__2__X__2647__2652__2657__2662,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__2641,Vvar__1__D__2642))
=> ( ? [Vvar__var__var__var__4__maj__2648__2653__2658__2663] :
( t(Vvar__var__var__var__4__maj__2648__2653__2658__2663,Vvar__0__U__2641)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__2641,Vvar__1__D__2642,Vvar__var__var__var__2__X__2647__2652__2657__2662,Vvar__var__var__var__4__maj__2648__2653__2658__2663) )
=> ? [Vvar__var__var__var__5__bsup__2649__2654__2659__2664] :
( t(Vvar__var__var__var__5__bsup__2649__2654__2659__2664,Vvar__0__U__2641)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__2641,Vvar__1__D__2642,Vvar__var__var__var__2__X__2647__2652__2657__2662,Vvar__var__var__var__5__bsup__2649__2654__2659__2664) ) ) ) )
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Directed',axiom,
! [Vvar__0__U__2025,Vvar__1__D__2026,Vvar__2__X__2027] :
( cType___24t(Vvar__0__U__2025)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__2025,Vvar__1__D__2026)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__2025,Vvar__2__X__2027)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vvar__0__U__2025,Vvar__1__D__2026,Vvar__2__X__2027)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__2025,Vvar__2__X__2027,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__2025,Vvar__1__D__2026))
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__2025,Vvar__2__X__2027)
& ! [Vvar__var__var__var__var__5__x1__2035__2039__2043__2047__2051] :
( t(Vvar__var__var__var__var__5__x1__2035__2039__2043__2047__2051,Vvar__0__U__2025)
=> ! [Vvar__var__var__var__var__6__x2__2036__2040__2044__2048__2052] :
( t(Vvar__var__var__var__var__6__x2__2036__2040__2044__2048__2052,Vvar__0__U__2025)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__2025,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__2025,Vvar__var__var__var__var__5__x1__2035__2039__2043__2047__2051,Vvar__var__var__var__var__6__x2__2036__2040__2044__2048__2052),Vvar__2__X__2027)
=> ? [Vvar__var__var__var__var__8__x3__2037__2041__2045__2049__2053] :
( t(Vvar__var__var__var__var__8__x3__2037__2041__2045__2049__2053,Vvar__0__U__2025)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__2025,Vvar__2__X__2027,Vvar__var__var__var__var__8__x3__2037__2041__2045__2049__2053)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__2025,Vvar__1__D__2026,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__2025,Vvar__var__var__var__var__5__x1__2035__2039__2043__2047__2051,Vvar__var__var__var__var__6__x2__2036__2040__2044__2048__2052),Vvar__var__var__var__var__8__x3__2037__2041__2045__2049__2053) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Glb',axiom,
! [Vvar__0__U__1190,Vvar__1__D__1191,Vvar__2__B__1192,Vvar__3__x__1193] :
( cType___24t(Vvar__0__U__1190)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1190,Vvar__1__D__1191)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1190,Vvar__2__B__1192)
=> ( t(Vvar__3__x__1193,Vvar__0__U__1190)
=> ( cCoq_2eSets_2eCpo_2eGlb___24a4(Vvar__0__U__1190,Vvar__1__D__1191,Vvar__2__B__1192,Vvar__3__x__1193)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__1190,Vvar__1__D__1191,Vvar__2__B__1192,Vvar__3__x__1193)
& ! [Vvar__var__var__var__var__var__5__y__1201__1203__1205__1207__1209__1211] :
( t(Vvar__var__var__var__var__var__5__y__1201__1203__1205__1207__1209__1211,Vvar__0__U__1190)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__1190,Vvar__1__D__1191,Vvar__2__B__1192,Vvar__var__var__var__var__var__5__y__1201__1203__1205__1207__1209__1211)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1190,Vvar__1__D__1191,Vvar__var__var__var__var__var__5__y__1201__1203__1205__1207__1209__1211,Vvar__3__x__1193) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Lower_Bound',axiom,
! [Vvar__0__U__626,Vvar__1__D__627,Vvar__2__B__628,Vvar__3__x__629] :
( cType___24t(Vvar__0__U__626)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__626,Vvar__1__D__627)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__626,Vvar__2__B__628)
=> ( t(Vvar__3__x__629,Vvar__0__U__626)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vvar__0__U__626,Vvar__1__D__627,Vvar__2__B__628,Vvar__3__x__629)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__626,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__626,Vvar__1__D__627),Vvar__3__x__629)
& ! [Vvar__var__var__var__var__var__5__y__637__639__641__643__645__647] :
( t(Vvar__var__var__var__var__var__5__y__637__639__641__643__645__647,Vvar__0__U__626)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__626,Vvar__2__B__628,Vvar__var__var__var__var__var__5__y__637__639__641__643__645__647)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__626,Vvar__1__D__627,Vvar__3__x__629,Vvar__var__var__var__var__var__5__y__637__639__641__643__645__647) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Lub',axiom,
! [Vvar__0__U__908,Vvar__1__D__909,Vvar__2__B__910,Vvar__3__x__911] :
( cType___24t(Vvar__0__U__908)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__908,Vvar__1__D__909)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__908,Vvar__2__B__910)
=> ( t(Vvar__3__x__911,Vvar__0__U__908)
=> ( cCoq_2eSets_2eCpo_2eLub___24a4(Vvar__0__U__908,Vvar__1__D__909,Vvar__2__B__910,Vvar__3__x__911)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__908,Vvar__1__D__909,Vvar__2__B__910,Vvar__3__x__911)
& ! [Vvar__var__var__var__var__var__5__y__919__921__923__925__927__929] :
( t(Vvar__var__var__var__var__var__5__y__919__921__923__925__927__929,Vvar__0__U__908)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__908,Vvar__1__D__909,Vvar__2__B__910,Vvar__var__var__var__var__var__5__y__919__921__923__925__927__929)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__908,Vvar__1__D__909,Vvar__3__x__911,Vvar__var__var__var__var__var__5__y__919__921__923__925__927__929) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Totally_ordered',axiom,
! [Vvar__0__U__1703,Vvar__1__D__1704,Vvar__2__B__1705] :
( cType___24t(Vvar__0__U__1703)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__1703,Vvar__1__D__1704)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__1703,Vvar__2__B__1705)
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vvar__0__U__1703,Vvar__1__D__1704,Vvar__2__B__1705)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__1703,Vvar__2__B__1705,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__1703,Vvar__1__D__1704))
=> ! [Vvar__var__var__var__var__4__x__1711__1715__1719__1723__1727] :
( t(Vvar__var__var__var__var__4__x__1711__1715__1719__1723__1727,Vvar__0__U__1703)
=> ! [Vvar__var__var__var__var__5__y__1712__1716__1720__1724__1728] :
( t(Vvar__var__var__var__var__5__y__1712__1716__1720__1724__1728,Vvar__0__U__1703)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__1703,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vvar__0__U__1703,Vvar__var__var__var__var__4__x__1711__1715__1719__1723__1727,Vvar__var__var__var__var__5__y__1712__1716__1720__1724__1728),Vvar__2__B__1705)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1703,Vvar__1__D__1704,Vvar__var__var__var__var__4__x__1711__1715__1719__1723__1727,Vvar__var__var__var__var__5__y__1712__1716__1720__1724__1728)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__1703,Vvar__1__D__1704,Vvar__var__var__var__var__5__y__1712__1716__1720__1724__1728,Vvar__var__var__var__var__4__x__1711__1715__1719__1723__1727) ) ) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Cpo.Upper_Bound',axiom,
! [Vvar__0__U__344,Vvar__1__D__345,Vvar__2__B__346,Vvar__3__x__347] :
( cType___24t(Vvar__0__U__344)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__344,Vvar__1__D__345)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__344,Vvar__2__B__346)
=> ( t(Vvar__3__x__347,Vvar__0__U__344)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vvar__0__U__344,Vvar__1__D__345,Vvar__2__B__346,Vvar__3__x__347)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__344,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vvar__0__U__344,Vvar__1__D__345),Vvar__3__x__347)
& ! [Vvar__var__var__var__var__var__5__y__355__357__359__361__363__365] :
( t(Vvar__var__var__var__var__var__5__y__355__357__359__361__363__365,Vvar__0__U__344)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__344,Vvar__2__B__346,Vvar__var__var__var__var__var__5__y__355__357__359__361__363__365)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vvar__0__U__344,Vvar__1__D__345,Vvar__var__var__var__var__var__5__y__355__357__359__361__363__365,Vvar__3__x__347) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Couple',axiom,
! [Vvar__0__U__239,Vvar__1__x__240,Vvar__2__y__241,Vvar__1___24Anonymous__242] :
( cType___24t(Vvar__0__U__239)
=> ( t(Vvar__1__x__240,Vvar__0__U__239)
=> ( t(Vvar__2__y__241,Vvar__0__U__239)
=> ( t(Vvar__1___24Anonymous__242,Vvar__0__U__239)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(Vvar__0__U__239,Vvar__1__x__240,Vvar__2__y__241,Vvar__1___24Anonymous__242)
=> ( Vvar__1___24Anonymous__242 = Vvar__1__x__240
| Vvar__1___24Anonymous__242 = Vvar__2__y__241 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Disjoint',axiom,
! [Vvar__0__U__164,Vvar__1__B__165,Vvar__2__C__166] :
( cType___24t(Vvar__0__U__164)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__164,Vvar__1__B__165)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__164,Vvar__2__C__166)
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(Vvar__0__U__164,Vvar__1__B__165,Vvar__2__C__166)
=> ( ! [Vvar__var__var__var__var__3__x__172__173__174__175__176] :
( t(Vvar__var__var__var__var__3__x__172__173__174__175__176,Vvar__0__U__164)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__164,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vvar__0__U__164,Vvar__1__B__165,Vvar__2__C__166),Vvar__var__var__var__var__3__x__172__173__174__175__176) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Full_set',axiom,
! [Vvar__0__U__22,Vvar__1___24Anonymous__23] :
( cType___24t(Vvar__0__U__22)
=> ( t(Vvar__1___24Anonymous__23,Vvar__0__U__22)
=> ( cCoq_2eSets_2eEnsembles_2eFull__set___24a2(Vvar__0__U__22,Vvar__1___24Anonymous__23)
=> ? [Vvar__1__x__26] :
( t(Vvar__1__x__26,Vvar__0__U__22)
& Vvar__1___24Anonymous__23 = Vvar__1__x__26 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Inhabited',axiom,
! [Vvar__0__U__178,Vvar__1__B__179] :
( cType___24t(Vvar__0__U__178)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__178,Vvar__1__B__179)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__178,Vvar__1__B__179)
=> ? [Vvar__2__x__183] :
( t(Vvar__2__x__183,Vvar__0__U__178)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__178,Vvar__1__B__179,Vvar__2__x__183)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Intersection',axiom,
! [Vvar__0__U__53,Vvar__1__B__54,Vvar__2__C__55,Vvar__1___24Anonymous__56] :
( cType___24t(Vvar__0__U__53)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__53,Vvar__1__B__54)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__53,Vvar__2__C__55)
=> ( t(Vvar__1___24Anonymous__56,Vvar__0__U__53)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(Vvar__0__U__53,Vvar__1__B__54,Vvar__2__C__55,Vvar__1___24Anonymous__56)
=> ? [Vvar__3__x__61] :
( t(Vvar__3__x__61,Vvar__0__U__53)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__53,Vvar__1__B__54,Vvar__3__x__61)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__53,Vvar__2__C__55,Vvar__3__x__61)
& Vvar__1___24Anonymous__56 = Vvar__3__x__61 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Singleton',axiom,
! [Vvar__0__U__27,Vvar__1__x__28,Vvar__1___24Anonymous__29] :
( cType___24t(Vvar__0__U__27)
=> ( t(Vvar__1__x__28,Vvar__0__U__27)
=> ( t(Vvar__1___24Anonymous__29,Vvar__0__U__27)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(Vvar__0__U__27,Vvar__1__x__28,Vvar__1___24Anonymous__29)
=> Vvar__1___24Anonymous__29 = Vvar__1__x__28 ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Triple',axiom,
! [Vvar__0__U__250,Vvar__1__x__251,Vvar__2__y__252,Vvar__3__z__253,Vvar__1___24Anonymous__254] :
( cType___24t(Vvar__0__U__250)
=> ( t(Vvar__1__x__251,Vvar__0__U__250)
=> ( t(Vvar__2__y__252,Vvar__0__U__250)
=> ( t(Vvar__3__z__253,Vvar__0__U__250)
=> ( t(Vvar__1___24Anonymous__254,Vvar__0__U__250)
=> ( cCoq_2eSets_2eEnsembles_2eTriple___24a5(Vvar__0__U__250,Vvar__1__x__251,Vvar__2__y__252,Vvar__3__z__253,Vvar__1___24Anonymous__254)
=> ( Vvar__1___24Anonymous__254 = Vvar__1__x__251
| Vvar__1___24Anonymous__254 = Vvar__2__y__252
| Vvar__1___24Anonymous__254 = Vvar__3__z__253 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Ensembles.Union',axiom,
! [Vvar__0__U__33,Vvar__1__B__34,Vvar__2__C__35,Vvar__1___24Anonymous__36] :
( cType___24t(Vvar__0__U__33)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__33,Vvar__1__B__34)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__33,Vvar__2__C__35)
=> ( t(Vvar__1___24Anonymous__36,Vvar__0__U__33)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(Vvar__0__U__33,Vvar__1__B__34,Vvar__2__C__35,Vvar__1___24Anonymous__36)
=> ( ? [Vvar__3__x__41] :
( t(Vvar__3__x__41,Vvar__0__U__33)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__33,Vvar__1__B__34,Vvar__3__x__41)
& Vvar__1___24Anonymous__36 = Vvar__3__x__41 )
| ? [Vvar__3__x__46] :
( t(Vvar__3__x__46,Vvar__0__U__33)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__33,Vvar__2__C__35,Vvar__3__x__46)
& Vvar__1___24Anonymous__36 = Vvar__3__x__46 ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.Finite',axiom,
! [Vvar__0__U__3010,Vvar__1___24Anonymous__3011] :
( cType___24t(Vvar__0__U__3010)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__3010,Vvar__1___24Anonymous__3011)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(Vvar__0__U__3010,Vvar__1___24Anonymous__3011)
=> ( Vvar__1___24Anonymous__3011 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__3010)
| ? [Vvar__1__A__3015] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__3010,Vvar__1__A__3015)
& cCoq_2eSets_2eFinite__sets_2eFinite___24a2(Vvar__0__U__3010,Vvar__1__A__3015)
& ? [Vvar__3__x__3017] :
( t(Vvar__3__x__3017,Vvar__0__U__3010)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__3010,Vvar__1__A__3015,Vvar__3__x__3017)
& Vvar__1___24Anonymous__3011 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__3010,Vvar__1__A__3015,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__3010,Vvar__3__x__3017)) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Finite_sets.cardinal',axiom,
! [Vvar__0__U__188,Vvar__1___24Anonymous__189,Vvar__2___24Anonymous__190] :
( cType___24t(Vvar__0__U__188)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__188,Vvar__1___24Anonymous__189)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__190)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__188,Vvar__1___24Anonymous__189,Vvar__2___24Anonymous__190)
=> ( ( Vvar__2___24Anonymous__190 = cCoq_2eInit_2eDatatypes_2eO
& Vvar__1___24Anonymous__189 = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(Vvar__0__U__188) )
| ? [Vvar__1__A__194] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__188,Vvar__1__A__194)
& ? [Vvar__2__n__195] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__195)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(Vvar__0__U__188,Vvar__1__A__194,Vvar__2__n__195)
& ? [Vvar__4__x__197] :
( t(Vvar__4__x__197,Vvar__0__U__188)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__U__188,Vvar__1__A__194,Vvar__4__x__197)
& Vvar__2___24Anonymous__190 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__195)
& Vvar__1___24Anonymous__189 = cCoq_2eSets_2eEnsembles_2eUnion___24a3(Vvar__0__U__188,Vvar__1__A__194,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(Vvar__0__U__188,Vvar__4__x__197)) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.PO',axiom,
! [Vvar__0__U__3059,VX3060] :
( cType___24t(Vvar__0__U__3059)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__3059,VX3060)
=> ? [Vvar__1__Carrier__of__3062] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__3059,Vvar__1__Carrier__of__3062)
& ? [Vvar__2__Rel__of__3063] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__3059,Vvar__2__Rel__of__3063)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vvar__0__U__3059,Vvar__1__Carrier__of__3062)
& cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__3059,Vvar__2__Rel__of__3063)
& VX3060 = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(Vvar__0__U__3059,Vvar__1__Carrier__of__3062,Vvar__2__Rel__of__3063) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Partial_Order.covers',axiom,
! [Vvar__0__U__319,Vvar__1__p__320,Vvar__2__y__321,Vvar__3__x__322] :
( cType___24t(Vvar__0__U__319)
=> ( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vvar__0__U__319,Vvar__1__p__320)
=> ( t(Vvar__2__y__321,Vvar__0__U__319)
=> ( t(Vvar__3__x__322,Vvar__0__U__319)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(Vvar__0__U__319,Vvar__1__p__320,Vvar__2__y__321,Vvar__3__x__322)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__319,Vvar__1__p__320,Vvar__3__x__322,Vvar__2__y__321)
& ~ ? [Vvar__var__var__var__var__var__5__z__330__331__332__333__334__335] :
( t(Vvar__var__var__var__var__var__5__z__330__331__332__333__334__335,Vvar__0__U__319)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__319,Vvar__1__p__320,Vvar__3__x__322,Vvar__var__var__var__var__var__5__z__330__331__332__333__334__335)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(Vvar__0__U__319,Vvar__1__p__320,Vvar__var__var__var__var__var__5__z__330__331__332__333__334__335,Vvar__2__y__321) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Powerset.Power_set',axiom,
! [Vvar__0__U__3104,Vvar__1__A__3105,Vvar__1___24Anonymous__3106] :
( cType___24t(Vvar__0__U__3104)
=> ( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__3104,Vvar__1__A__3105)
=> ( c_24__type__3119___24t(Vvar__0__U__3104,Vvar__1__A__3105,Vvar__1___24Anonymous__3106,Vvar__1___24Anonymous__3106)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(Vvar__0__U__3104,Vvar__1__A__3105,Vvar__1___24Anonymous__3106)
=> ? [Vvar__2__X__3112] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__U__3104,Vvar__2__X__3112)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vvar__0__U__3104,Vvar__2__X__3112,Vvar__1__A__3105)
& Vvar__1___24Anonymous__3106 = Vvar__2__X__3112 ) ) ) ) ) ).
fof('$_inversion_Coq.Sets.Relations_1.Order',axiom,
! [Vvar__0__U__3146,Vvar__1__R__3147] :
( cType___24t(Vvar__0__U__3146)
=> ( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vvar__0__U__3146,Vvar__1__R__3147)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vvar__0__U__3146,Vvar__1__R__3147)
=> ( cCoq_2eSets_2eRelations__1_2eReflexive___24a2(Vvar__0__U__3146,Vvar__1__R__3147)
& cCoq_2eSets_2eRelations__1_2eTransitive___24a2(Vvar__0__U__3146,Vvar__1__R__3147)
& cCoq_2eSets_2eRelations__1_2eAntisymmetric___24a2(Vvar__0__U__3146,Vvar__1__R__3147)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
! [Vvar__0__A__28422,Vvar__1__R__28423,Vvar__2___24Anonymous__28428] :
( cType___24t(Vvar__0__A__28422)
=> ( c_24__type__28455___24t(Vvar__0__A__28422,Vvar__1__R__28423,Vvar__2___24Anonymous__28428,Vvar__1__R__28423)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28422,Vvar__2___24Anonymous__28428)
=> ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__28422,Vvar__1__R__28423,Vvar__2___24Anonymous__28428)
=> ( Vvar__2___24Anonymous__28428 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__28422)
| ? [Vvar__2__a__28442] :
( t(Vvar__2__a__28442,Vvar__0__A__28422)
& ? [Vvar__3__l__28443] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__28422,Vvar__3__l__28443)
& cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__28422,Vvar__1__R__28423,Vvar__3__l__28443)
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__28422,happ(Vvar__1__R__28423,Vvar__2__a__28442),Vvar__3__l__28443)
& Vvar__2___24Anonymous__28428 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__28422,Vvar__2__a__28442,Vvar__3__l__28443) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX3157] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX3157)
=> ? [Vvar__0___24Anonymous__3158] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__3158)
& ? [Vvar__1___24Anonymous__3159] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__3159)
& ? [Vvar__2___24Anonymous__3160] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__3160)
& ? [Vvar__3___24Anonymous__3161] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__3161)
& ? [Vvar__4___24Anonymous__3162] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__3162)
& ? [Vvar__5___24Anonymous__3163] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__3163)
& ? [Vvar__6___24Anonymous__3164] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__3164)
& ? [Vvar__7___24Anonymous__3165] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__3165)
& VX3157 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__3158,Vvar__1___24Anonymous__3159,Vvar__2___24Anonymous__3160,Vvar__3___24Anonymous__3161,Vvar__4___24Anonymous__3162,Vvar__5___24Anonymous__3163,Vvar__6___24Anonymous__3164,Vvar__7___24Anonymous__3165) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX11517] :
( cCoq_2eStrings_2eString_2estring___24t(VX11517)
=> ( VX11517 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__11518] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__11518)
& ? [Vvar__1___24Anonymous__11519] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__11519)
& VX11517 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__11518,Vvar__1___24Anonymous__11519) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339,VX18340] :
( cType___24t(Vvar__0__X__18327)
=> ( c_24__type__18400___24t(Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339,Vvar__1__lt__18328)
=> ( c_24__type__18419___24t(Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339,Vvar__2__eq__18333)
=> ( t(Vvar__3__x__18338,Vvar__0__X__18327)
=> ( t(Vvar__4__y__18339,Vvar__0__X__18327)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339,VX18340)
=> ( ( p(happ(happ(Vvar__1__lt__18328,Vvar__3__x__18338),Vvar__4__y__18339))
& VX18340 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339) )
| ( p(happ(happ(Vvar__2__eq__18333,Vvar__3__x__18338),Vvar__4__y__18339))
& VX18340 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339) )
| ( p(happ(happ(Vvar__1__lt__18328,Vvar__4__y__18339),Vvar__3__x__18338))
& VX18340 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__18327,Vvar__1__lt__18328,Vvar__2__eq__18333,Vvar__3__x__18338,Vvar__4__y__18339) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
! [Vvar__0___24Anonymous__29537,Vvar__1___24Anonymous__29538] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__29537)
=> ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__29538)
=> ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__29537,Vvar__1___24Anonymous__29538)
=> ( ? [Vvar__0__a__29540] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__29540)
& ? [Vvar__1__s__29541] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__29541)
& Vvar__1___24Anonymous__29538 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__29540,Vvar__1__s__29541)
& Vvar__0___24Anonymous__29537 = cCoq_2eStrings_2eString_2eEmptyString ) )
| ? [Vvar__0__a__29542] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__29542)
& ? [Vvar__1__s1__29543] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__29543)
& ? [Vvar__2__s2__29544] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__29544)
& cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__29543,Vvar__2__s2__29544)
& Vvar__1___24Anonymous__29538 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__29542,Vvar__2__s2__29544)
& Vvar__0___24Anonymous__29537 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__29542,Vvar__1__s1__29543) ) ) )
| ? [Vvar__0__a__29546] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__29546)
& ? [Vvar__1__b__29547] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__29547)
& ? [Vvar__2__s1__29548] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__29548)
& ? [Vvar__3__s2__29549] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__29549)
& cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__29546),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__29547))
& Vvar__1___24Anonymous__29538 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__29547,Vvar__3__s2__29549)
& Vvar__0___24Anonymous__29537 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__29546,Vvar__2__s1__29548) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX5068] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX5068)
=> ( VX5068 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX5068 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX5068 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.Fin.t',axiom,
! [Vvar__0___24Anonymous__16911,VX16912] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__16911)
=> ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__16911,VX16912)
=> ( ? [Vvar__0__n__16913] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__16913)
& Vvar__0___24Anonymous__16911 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__16913)
& VX16912 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__16913) )
| ? [Vvar__0__n__16914] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__16914)
& ? [Vvar__1___24Anonymous__16915] :
( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__16914,Vvar__1___24Anonymous__16915)
& Vvar__0___24Anonymous__16911 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__16914)
& VX16912 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__16914,Vvar__1___24Anonymous__16915) ) ) ) ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__11566,Vvar__1___24Anonymous__11567,VX11568] :
( cType___24t(Vvar__0__A__11566)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__11567)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__11566,Vvar__1___24Anonymous__11567,VX11568)
=> ( ( Vvar__1___24Anonymous__11567 = cCoq_2eInit_2eDatatypes_2eO
& VX11568 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__11566) )
| ? [Vvar__1__h__11571] :
( t(Vvar__1__h__11571,Vvar__0__A__11566)
& ? [Vvar__2__n__11572] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__11572)
& ? [Vvar__3___24Anonymous__11573] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__11566,Vvar__2__n__11572,Vvar__3___24Anonymous__11573)
& Vvar__1___24Anonymous__11567 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__11572)
& VX11568 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__11566,Vvar__1__h__11571,Vvar__2__n__11572,Vvar__3___24Anonymous__11573) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__12368,Vvar__1__b__12369,Vvar__2__d__12370] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__12368)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__12369)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__12370)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__12368,Vvar__1__b__12369,Vvar__2__d__12370)
=> ? [Vvar__3__u__12375] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__12375)
& ? [Vvar__4__v__12376] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__12376)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__12375,Vvar__0__a__12368),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__12376,Vvar__1__b__12369)) = Vvar__2__d__12370
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
! [Vvar__0__a__29245,Vvar__1__b__29246,VX29247] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__29245)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__29246)
=> ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__29245,Vvar__1__b__29246,VX29247)
=> ? [Vvar__2__u__29250] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__29250)
& ? [Vvar__3__v__29251] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__29251)
& ? [Vvar__4__d__29252] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__29252)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__29250,Vvar__0__a__29245),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__29251,Vvar__1__b__29246)) = Vvar__4__d__29252
& cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__29245,Vvar__1__b__29246,Vvar__4__d__29252)
& VX29247 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__29245,Vvar__1__b__29246,Vvar__2__u__29250,Vvar__3__v__29251,Vvar__4__d__29252) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__29217,Vvar__1__b__29218,Vvar__2__g__29219] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__29217)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__29218)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__29219)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__29217,Vvar__1__b__29218,Vvar__2__g__29219)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__29219,Vvar__0__a__29217)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__29219,Vvar__1__b__29218)
& ! [Vvar__var__var__var__var__5__x__29227__29230__29233__29236__29239] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__29227__29230__29233__29236__29239)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__29227__29230__29233__29236__29239,Vvar__0__a__29217)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__29227__29230__29233__29236__29239,Vvar__1__b__29218)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__29227__29230__29233__29236__29239,Vvar__2__g__29219) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
! [Vvar__0__x__29283,Vvar__1__p__29284,VX29285] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__29283)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__29284)
=> ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__29283,Vvar__1__p__29284,VX29285)
=> ? [Vvar__2__q__29288] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__29288)
& ? [Vvar__3__r__29289] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__29289)
& Vvar__0__x__29283 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__29288,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__29284)),Vvar__3__r__29289)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__29289))
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__29289,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__29284))
& VX29285 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__29283,Vvar__1__p__29284,Vvar__2__q__29288,Vvar__3__r__29289) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX14922] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX14922)
=> ( VX14922 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__14923] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14923)
& ? [Vvar__1___24Anonymous__14924] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__14924)
& VX14922 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__14923,Vvar__1___24Anonymous__14924) ) )
| ? [Vvar__0___24Anonymous__14925] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14925)
& ? [Vvar__1___24Anonymous__14926] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__14926)
& VX14922 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__14925,Vvar__1___24Anonymous__14926) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__14697,VX14698] :
( cType___24t(Vvar__0__C__14697)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,VX14698)
=> ( ? [Vvar__1___24Anonymous__14700] :
( t(Vvar__1___24Anonymous__14700,Vvar__0__C__14697)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__14697,Vvar__1___24Anonymous__14700) )
| ? [Vvar__1___24Anonymous__14702] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14702)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__14697,Vvar__1___24Anonymous__14702) )
| ? [Vvar__1___24Anonymous__14704] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__1___24Anonymous__14704)
& ? [Vvar__2___24Anonymous__14705] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__2___24Anonymous__14705)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__14697,Vvar__1___24Anonymous__14704,Vvar__2___24Anonymous__14705) ) )
| ? [Vvar__1___24Anonymous__14707] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__1___24Anonymous__14707)
& ? [Vvar__2___24Anonymous__14708] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__2___24Anonymous__14708)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__14697,Vvar__1___24Anonymous__14707,Vvar__2___24Anonymous__14708) ) )
| ? [Vvar__1___24Anonymous__14710] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__1___24Anonymous__14710)
& ? [Vvar__2___24Anonymous__14711] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__2___24Anonymous__14711)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__14697,Vvar__1___24Anonymous__14710,Vvar__2___24Anonymous__14711) ) )
| ? [Vvar__1___24Anonymous__14713] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__1___24Anonymous__14713)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__14697,Vvar__1___24Anonymous__14713) )
| ? [Vvar__1___24Anonymous__14715] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__14697,Vvar__1___24Anonymous__14715)
& ? [Vvar__2___24Anonymous__14716] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__14716)
& VX14698 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__14697,Vvar__1___24Anonymous__14715,Vvar__2___24Anonymous__14716) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__14864,VX14865] :
( cType___24t(Vvar__0__C__14864)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14864,VX14865)
=> ( ? [Vvar__1___24Anonymous__14867] :
( t(Vvar__1___24Anonymous__14867,Vvar__0__C__14864)
& VX14865 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__14864,Vvar__1___24Anonymous__14867) )
| ? [Vvar__1___24Anonymous__14869] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__14869)
& ? [Vvar__2___24Anonymous__14870] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14864,Vvar__2___24Anonymous__14870)
& VX14865 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__14864,Vvar__1___24Anonymous__14869,Vvar__2___24Anonymous__14870) ) )
| ? [Vvar__1___24Anonymous__14872] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14864,Vvar__1___24Anonymous__14872)
& ? [Vvar__2___24Anonymous__14873] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__14873)
& ? [Vvar__3___24Anonymous__14874] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__14864,Vvar__3___24Anonymous__14874)
& VX14865 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__14864,Vvar__1___24Anonymous__14872,Vvar__2___24Anonymous__14873,Vvar__3___24Anonymous__14874) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280] :
( cType___24t(Vvar__0__R__17249)
=> ( t(Vvar__1__rO__17250,Vvar__0__R__17249)
=> ( t(Vvar__2__rI__17251,Vvar__0__R__17249)
=> ( c_24__type__17681___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__3__rplus__17252)
=> ( c_24__type__17782___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__4__rtimes__17257)
=> ( c_24__type__17883___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__5__rminus__17262)
=> ( c_24__type__17973___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__6__ropp__17267)
=> ( c_24__type__18074___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__7__req__17270)
=> ( c_24__type__18175___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__8__rle__17275)
=> ( c_24__type__18276___24t(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280,Vvar__9__rlt__17280)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270,Vvar__8__rle__17275,Vvar__9__rlt__17280)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__17249,Vvar__7__req__17270)
& ! [Vvar__var__var__var__var__11__x1__17324__17330__17435__17441__17447] :
( t(Vvar__var__var__var__var__11__x1__17324__17330__17435__17441__17447,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__12__x2__17325__17331__17436__17442__17448] :
( t(Vvar__var__var__var__var__12__x2__17325__17331__17436__17442__17448,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__11__x1__17324__17330__17435__17441__17447),Vvar__var__var__var__var__12__x2__17325__17331__17436__17442__17448))
=> ! [Vvar__var__var__var__var__14__y1__17326__17332__17437__17443__17449] :
( t(Vvar__var__var__var__var__14__y1__17326__17332__17437__17443__17449,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__15__y2__17327__17333__17438__17444__17450] :
( t(Vvar__var__var__var__var__15__y2__17327__17333__17438__17444__17450,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__14__y1__17326__17332__17437__17443__17449),Vvar__var__var__var__var__15__y2__17327__17333__17438__17444__17450))
=> p(happ(happ(Vvar__7__req__17270,happ(happ(Vvar__3__rplus__17252,Vvar__var__var__var__var__11__x1__17324__17330__17435__17441__17447),Vvar__var__var__var__var__14__y1__17326__17332__17437__17443__17449)),happ(happ(Vvar__3__rplus__17252,Vvar__var__var__var__var__12__x2__17325__17331__17436__17442__17448),Vvar__var__var__var__var__15__y2__17327__17333__17438__17444__17450))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__17337__17343__17453__17459__17465] :
( t(Vvar__var__var__var__var__12__x1__17337__17343__17453__17459__17465,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__13__x2__17338__17344__17454__17460__17466] :
( t(Vvar__var__var__var__var__13__x2__17338__17344__17454__17460__17466,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__12__x1__17337__17343__17453__17459__17465),Vvar__var__var__var__var__13__x2__17338__17344__17454__17460__17466))
=> ! [Vvar__var__var__var__var__15__y1__17339__17345__17455__17461__17467] :
( t(Vvar__var__var__var__var__15__y1__17339__17345__17455__17461__17467,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__16__y2__17340__17346__17456__17462__17468] :
( t(Vvar__var__var__var__var__16__y2__17340__17346__17456__17462__17468,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__15__y1__17339__17345__17455__17461__17467),Vvar__var__var__var__var__16__y2__17340__17346__17456__17462__17468))
=> p(happ(happ(Vvar__7__req__17270,happ(happ(Vvar__4__rtimes__17257,Vvar__var__var__var__var__12__x1__17337__17343__17453__17459__17465),Vvar__var__var__var__var__15__y1__17339__17345__17455__17461__17467)),happ(happ(Vvar__4__rtimes__17257,Vvar__var__var__var__var__13__x2__17338__17344__17454__17460__17466),Vvar__var__var__var__var__16__y2__17340__17346__17456__17462__17468))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__17350__17353__17471__17474__17477] :
( t(Vvar__var__var__var__var__13__x1__17350__17353__17471__17474__17477,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__14__x2__17351__17354__17472__17475__17478] :
( t(Vvar__var__var__var__var__14__x2__17351__17354__17472__17475__17478,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__13__x1__17350__17353__17471__17474__17477),Vvar__var__var__var__var__14__x2__17351__17354__17472__17475__17478))
=> p(happ(happ(Vvar__7__req__17270,happ(Vvar__6__ropp__17267,Vvar__var__var__var__var__13__x1__17350__17353__17471__17474__17477)),happ(Vvar__6__ropp__17267,Vvar__var__var__var__var__14__x2__17351__17354__17472__17475__17478))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__17357__17363__17480__17486__17492] :
( t(Vvar__var__var__var__var__14__x1__17357__17363__17480__17486__17492,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__15__x2__17358__17364__17481__17487__17493] :
( t(Vvar__var__var__var__var__15__x2__17358__17364__17481__17487__17493,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__14__x1__17357__17363__17480__17486__17492),Vvar__var__var__var__var__15__x2__17358__17364__17481__17487__17493))
=> ! [Vvar__var__var__var__var__17__y1__17359__17365__17482__17488__17494] :
( t(Vvar__var__var__var__var__17__y1__17359__17365__17482__17488__17494,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__18__y2__17360__17366__17483__17489__17495] :
( t(Vvar__var__var__var__var__18__y2__17360__17366__17483__17489__17495,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__17__y1__17359__17365__17482__17488__17494),Vvar__var__var__var__var__18__y2__17360__17366__17483__17489__17495))
=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__var__14__x1__17357__17363__17480__17486__17492),Vvar__var__var__var__var__17__y1__17359__17365__17482__17488__17494))
<=> p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__var__15__x2__17358__17364__17481__17487__17493),Vvar__var__var__var__var__18__y2__17360__17366__17483__17489__17495)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__17370__17376__17498__17504__17510] :
( t(Vvar__var__var__var__var__15__x1__17370__17376__17498__17504__17510,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__16__x2__17371__17377__17499__17505__17511] :
( t(Vvar__var__var__var__var__16__x2__17371__17377__17499__17505__17511,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__15__x1__17370__17376__17498__17504__17510),Vvar__var__var__var__var__16__x2__17371__17377__17499__17505__17511))
=> ! [Vvar__var__var__var__var__18__y1__17372__17378__17500__17506__17512] :
( t(Vvar__var__var__var__var__18__y1__17372__17378__17500__17506__17512,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__19__y2__17373__17379__17501__17507__17513] :
( t(Vvar__var__var__var__var__19__y2__17373__17379__17501__17507__17513,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__18__y1__17372__17378__17500__17506__17512),Vvar__var__var__var__var__19__y2__17373__17379__17501__17507__17513))
=> ( p(happ(happ(Vvar__9__rlt__17280,Vvar__var__var__var__var__15__x1__17370__17376__17498__17504__17510),Vvar__var__var__var__var__18__y1__17372__17378__17500__17506__17512))
<=> p(happ(happ(Vvar__9__rlt__17280,Vvar__var__var__var__var__16__x2__17371__17377__17499__17505__17511),Vvar__var__var__var__var__19__y2__17373__17379__17501__17507__17513)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__17249,Vvar__1__rO__17250,Vvar__2__rI__17251,Vvar__3__rplus__17252,Vvar__4__rtimes__17257,Vvar__5__rminus__17262,Vvar__6__ropp__17267,Vvar__7__req__17270)
& ! [Vvar__var__var__var__17__n__17384__17385__17516__17517] :
( t(Vvar__var__var__var__17__n__17384__17385__17516__17517,Vvar__0__R__17249)
=> p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__17__n__17384__17385__17516__17517),Vvar__var__var__var__17__n__17384__17385__17516__17517)) )
& ! [Vvar__var__var__var__var__18__n__17387__17391__17518__17522__17526] :
( t(Vvar__var__var__var__var__18__n__17387__17391__17518__17522__17526,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__19__m__17388__17392__17519__17523__17527] :
( t(Vvar__var__var__var__var__19__m__17388__17392__17519__17523__17527,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__var__18__n__17387__17391__17518__17522__17526),Vvar__var__var__var__var__19__m__17388__17392__17519__17523__17527))
=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__var__19__m__17388__17392__17519__17523__17527),Vvar__var__var__var__var__18__n__17387__17391__17518__17522__17526))
=> p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__18__n__17387__17391__17518__17522__17526),Vvar__var__var__var__var__19__m__17388__17392__17519__17523__17527)) ) ) ) )
& ! [Vvar__var__var__var__19__n__17396__17401__17530__17535] :
( t(Vvar__var__var__var__19__n__17396__17401__17530__17535,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__20__m__17397__17402__17531__17536] :
( t(Vvar__var__var__var__20__m__17397__17402__17531__17536,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__21__p__17398__17403__17532__17537] :
( t(Vvar__var__var__var__21__p__17398__17403__17532__17537,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__19__n__17396__17401__17530__17535),Vvar__var__var__var__20__m__17397__17402__17531__17536))
=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__20__m__17397__17402__17531__17536),Vvar__var__var__var__21__p__17398__17403__17532__17537))
=> p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__19__n__17396__17401__17530__17535),Vvar__var__var__var__21__p__17398__17403__17532__17537)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__17407__17409__17540__17542__17544__17546] :
( t(Vvar__var__var__var__var__var__20__n__17407__17409__17540__17542__17544__17546,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__var__21__m__17408__17410__17541__17543__17545__17547] :
( t(Vvar__var__var__var__var__var__21__m__17408__17410__17541__17543__17545__17547,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__9__rlt__17280,Vvar__var__var__var__var__var__20__n__17407__17409__17540__17542__17544__17546),Vvar__var__var__var__var__var__21__m__17408__17410__17541__17543__17545__17547))
<=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__var__var__20__n__17407__17409__17540__17542__17544__17546),Vvar__var__var__var__var__var__21__m__17408__17410__17541__17543__17545__17547))
& ~ p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__var__20__n__17407__17409__17540__17542__17544__17546),Vvar__var__var__var__var__var__21__m__17408__17410__17541__17543__17545__17547)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__17412__17414__17548__17550__17552] :
( t(Vvar__var__var__var__var__21__n__17412__17414__17548__17550__17552,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__22__m__17413__17415__17549__17551__17553] :
( t(Vvar__var__var__var__var__22__m__17413__17415__17549__17551__17553,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__9__rlt__17280,Vvar__var__var__var__var__21__n__17412__17414__17548__17550__17552),Vvar__var__var__var__var__22__m__17413__17415__17549__17551__17553))
| p(happ(happ(Vvar__7__req__17270,Vvar__var__var__var__var__21__n__17412__17414__17548__17550__17552),Vvar__var__var__var__var__22__m__17413__17415__17549__17551__17553))
| p(happ(happ(Vvar__9__rlt__17280,Vvar__var__var__var__var__22__m__17413__17415__17549__17551__17553),Vvar__var__var__var__var__21__n__17412__17414__17548__17550__17552)) ) ) )
& ! [Vvar__var__var__var__var__22__n__17417__17421__17554__17558__17562] :
( t(Vvar__var__var__var__var__22__n__17417__17421__17554__17558__17562,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__23__m__17418__17422__17555__17559__17563] :
( t(Vvar__var__var__var__var__23__m__17418__17422__17555__17559__17563,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__24__p__17419__17423__17556__17560__17564] :
( t(Vvar__var__var__var__var__24__p__17419__17423__17556__17560__17564,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__8__rle__17275,Vvar__var__var__var__var__22__n__17417__17421__17554__17558__17562),Vvar__var__var__var__var__23__m__17418__17422__17555__17559__17563))
=> p(happ(happ(Vvar__8__rle__17275,happ(happ(Vvar__3__rplus__17252,Vvar__var__var__var__var__24__p__17419__17423__17556__17560__17564),Vvar__var__var__var__var__22__n__17417__17421__17554__17558__17562)),happ(happ(Vvar__3__rplus__17252,Vvar__var__var__var__var__24__p__17419__17423__17556__17560__17564),Vvar__var__var__var__var__23__m__17418__17422__17555__17559__17563))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__17426__17430__17566__17570__17574__17578] :
( t(Vvar__var__var__var__var__var__23__n__17426__17430__17566__17570__17574__17578,Vvar__0__R__17249)
=> ! [Vvar__var__var__var__var__var__24__m__17427__17431__17567__17571__17575__17579] :
( t(Vvar__var__var__var__var__var__24__m__17427__17431__17567__17571__17575__17579,Vvar__0__R__17249)
=> ( p(happ(happ(Vvar__9__rlt__17280,Vvar__1__rO__17250),Vvar__var__var__var__var__var__23__n__17426__17430__17566__17570__17574__17578))
=> ( p(happ(happ(Vvar__9__rlt__17280,Vvar__1__rO__17250),Vvar__var__var__var__var__var__24__m__17427__17431__17567__17571__17575__17579))
=> p(happ(happ(Vvar__9__rlt__17280,Vvar__1__rO__17250),happ(happ(Vvar__4__rtimes__17257,Vvar__var__var__var__var__var__23__n__17426__17430__17566__17570__17574__17578),Vvar__var__var__var__var__var__24__m__17427__17431__17567__17571__17575__17579))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__17270,Vvar__1__rO__17250),Vvar__2__rI__17251))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__24316,VX24317] :
( cType___24t(Vvar__0__T__24316)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__24316,VX24317)
=> ? [Vvar__1__Flhs__24319] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__24316,Vvar__1__Flhs__24319)
& ? [Vvar__2__Fop__24320] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__24320)
& ? [Vvar__3__Frhs__24321] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__24316,Vvar__3__Frhs__24321)
& VX24317 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__24316,Vvar__1__Flhs__24319,Vvar__2__Fop__24320,Vvar__3__Frhs__24321) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX24168] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX24168)
=> ( VX24168 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX24168 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX24168 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX24168 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX24315] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX24315)
=> ( VX24315 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX24315 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX24315 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX24315 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX24315 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX24315 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944] :
( cType___24t(Vvar__0__R__18875)
=> ( t(Vvar__1__rO__18876,Vvar__0__R__18875)
=> ( t(Vvar__2__rI__18877,Vvar__0__R__18875)
=> ( c_24__type__19408___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__3__rplus__18878)
=> ( c_24__type__19754___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__4__rtimes__18883)
=> ( c_24__type__20100___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__5__rminus__18888)
=> ( c_24__type__20423___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__6__ropp__18893)
=> ( c_24__type__20769___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__7__req__18896)
=> ( c_24__type__21115___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__8__rle__18901)
=> ( cType___24t(Vvar__9__C__18906)
=> ( t(Vvar__10__cO__18907,Vvar__9__C__18906)
=> ( t(Vvar__11__cI__18908,Vvar__9__C__18906)
=> ( c_24__type__21461___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__12__cplus__18909)
=> ( c_24__type__21807___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__13__ctimes__18914)
=> ( c_24__type__22153___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__14__cminus__18919)
=> ( c_24__type__22476___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__15__copp__18924)
=> ( c_24__type__22822___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__16__ceqb__18927)
=> ( c_24__type__23168___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__17__cleb__18932)
=> ( c_24__type__23491___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__18__phi__18937)
=> ( cType___24t(Vvar__19__E__18940)
=> ( c_24__type__23814___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__20__pow__phi__18941)
=> ( c_24__type__24160___24t(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944,Vvar__21__rpow__18944)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__8__rle__18901,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__17__cleb__18932,Vvar__18__phi__18937,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__18875,Vvar__1__rO__18876,Vvar__2__rI__18877,Vvar__3__rplus__18878,Vvar__4__rtimes__18883,Vvar__5__rminus__18888,Vvar__6__ropp__18893,Vvar__7__req__18896,Vvar__9__C__18906,Vvar__10__cO__18907,Vvar__11__cI__18908,Vvar__12__cplus__18909,Vvar__13__ctimes__18914,Vvar__14__cminus__18919,Vvar__15__copp__18924,Vvar__16__ceqb__18927,Vvar__18__phi__18937)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__18875,Vvar__2__rI__18877,Vvar__4__rtimes__18883,Vvar__7__req__18896,Vvar__19__E__18940,Vvar__20__pow__phi__18941,Vvar__21__rpow__18944)
& ! [Vvar__var__var__var__var__var__24__x__19027__19030__19040__19043__19046__19049] :
( t(Vvar__var__var__var__var__var__24__x__19027__19030__19040__19043__19046__19049,Vvar__9__C__18906)
=> ! [Vvar__var__var__var__var__var__25__y__19028__19031__19041__19044__19047__19050] :
( t(Vvar__var__var__var__var__var__25__y__19028__19031__19041__19044__19047__19050,Vvar__9__C__18906)
=> ( happ(happ(Vvar__16__ceqb__18927,Vvar__var__var__var__var__var__24__x__19027__19030__19040__19043__19046__19049),Vvar__var__var__var__var__var__25__y__19028__19031__19041__19044__19047__19050) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__18896,happ(Vvar__18__phi__18937,Vvar__var__var__var__var__var__24__x__19027__19030__19040__19043__19046__19049)),happ(Vvar__18__phi__18937,Vvar__var__var__var__var__var__25__y__19028__19031__19041__19044__19047__19050))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__19034__19037__19052__19055__19058__19061] :
( t(Vvar__var__var__var__var__var__25__x__19034__19037__19052__19055__19058__19061,Vvar__9__C__18906)
=> ! [Vvar__var__var__var__var__var__26__y__19035__19038__19053__19056__19059__19062] :
( t(Vvar__var__var__var__var__var__26__y__19035__19038__19053__19056__19059__19062,Vvar__9__C__18906)
=> ( happ(happ(Vvar__17__cleb__18932,Vvar__var__var__var__var__var__25__x__19034__19037__19052__19055__19058__19061),Vvar__var__var__var__var__var__26__y__19035__19038__19053__19056__19059__19062) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__18901,happ(Vvar__18__phi__18937,Vvar__var__var__var__var__var__25__x__19034__19037__19052__19055__19058__19061)),happ(Vvar__18__phi__18937,Vvar__var__var__var__var__var__26__y__19035__19038__19053__19056__19059__19062))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,VX28579] :
( cType___24t(Vvar__0__TA__28575)
=> ( cType___24t(Vvar__1__TX__28576)
=> ( cType___24t(Vvar__2__AA__28577)
=> ( cType___24t(Vvar__3__AF__28578)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,VX28579)
=> ( VX28579 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578)
| VX28579 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578)
| ? [Vvar__4___24Anonymous__28592] :
( t(Vvar__4___24Anonymous__28592,Vvar__1__TX__28576)
& VX28579 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28592) )
| ? [Vvar__4___24Anonymous__28597] :
( t(Vvar__4___24Anonymous__28597,Vvar__0__TA__28575)
& ? [Vvar__5___24Anonymous__28598] :
( t(Vvar__5___24Anonymous__28598,Vvar__2__AA__28577)
& VX28579 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28597,Vvar__5___24Anonymous__28598) ) )
| ? [Vvar__4___24Anonymous__28603] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28603)
& ? [Vvar__5___24Anonymous__28604] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__5___24Anonymous__28604)
& VX28579 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28603,Vvar__5___24Anonymous__28604) ) )
| ? [Vvar__4___24Anonymous__28609] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28609)
& ? [Vvar__5___24Anonymous__28610] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__5___24Anonymous__28610)
& VX28579 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28609,Vvar__5___24Anonymous__28610) ) )
| ? [Vvar__4___24Anonymous__28615] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28615)
& VX28579 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28615) )
| ? [Vvar__4___24Anonymous__28620] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28620)
& ? [Vvar__5___24Anonymous__28621] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__28578,Vvar__5___24Anonymous__28621)
& ? [Vvar__6___24Anonymous__28622] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__6___24Anonymous__28622)
& VX28579 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__28575,Vvar__1__TX__28576,Vvar__2__AA__28577,Vvar__3__AF__28578,Vvar__4___24Anonymous__28620,Vvar__5___24Anonymous__28621,Vvar__6___24Anonymous__28622) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__29324] :
( cProp___24t(Vvar__0___24Anonymous__29324)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__29324)
=> ( ? [Vvar__0__S__29326] :
( cType___24t(Vvar__0__S__29326)
& ? [Vvar__1__x__29327] :
( t(Vvar__1__x__29327,Vvar__0__S__29326)
& ? [Vvar__2__y__29328] :
( t(Vvar__2__y__29328,Vvar__0__S__29326)
& Vvar__0___24Anonymous__29324 = c_24__prop__29348___24a4(Vvar__0___24Anonymous__29324,Vvar__0__S__29326,Vvar__1__x__29327,Vvar__2__y__29328) ) ) )
| ? [Vvar__0__x__29329] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__29329)
& ? [Vvar__1__y__29330] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__29330)
& Vvar__0___24Anonymous__29324 = c_24__prop__29349___24a3(Vvar__0___24Anonymous__29324,Vvar__0__x__29329,Vvar__1__y__29330) ) )
| ? [Vvar__0__x__29331] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__29331)
& ? [Vvar__1__s__29332] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__29332)
& Vvar__0___24Anonymous__29324 = c_24__prop__29350___24a3(Vvar__0___24Anonymous__29324,Vvar__0__x__29331,Vvar__1__s__29332) ) )
| Vvar__0___24Anonymous__29324 = c_24True
| Vvar__0___24Anonymous__29324 = c_24False
| ? [Vvar__0__P__29333] :
( cProp___24t(Vvar__0__P__29333)
& ? [Vvar__1__Q__29334] :
( cProp___24t(Vvar__1__Q__29334)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29333)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29334)
& Vvar__0___24Anonymous__29324 = c_24__prop__29351___24a3(Vvar__0___24Anonymous__29324,Vvar__0__P__29333,Vvar__1__Q__29334) ) )
| ? [Vvar__0__P__29337] :
( cProp___24t(Vvar__0__P__29337)
& ? [Vvar__1__Q__29338] :
( cProp___24t(Vvar__1__Q__29338)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29337)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29338)
& Vvar__0___24Anonymous__29324 = c_24__prop__29352___24a3(Vvar__0___24Anonymous__29324,Vvar__0__P__29337,Vvar__1__Q__29338) ) )
| ? [Vvar__0__P__29341] :
( cProp___24t(Vvar__0__P__29341)
& ? [Vvar__1__Q__29342] :
( cProp___24t(Vvar__1__Q__29342)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29341)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29342)
& Vvar__0___24Anonymous__29324 = c_24__prop__29353___24a3(Vvar__0___24Anonymous__29324,Vvar__0__P__29341,Vvar__1__Q__29342) ) )
| ? [Vvar__0__P__29346] :
( cProp___24t(Vvar__0__P__29346)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29346)
& Vvar__0___24Anonymous__29324 = c_24__prop__29354___24a2(Vvar__0___24Anonymous__29324,Vvar__0__P__29346) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
! [Vvar__0__fr__29147,Vvar__1__env__29148,Vvar__2__env_27__29151,Vvar__3__x__29154] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__29147)
=> ( c_24__type__29175___24t(Vvar__0__fr__29147,Vvar__1__env__29148,Vvar__2__env_27__29151,Vvar__3__x__29154,Vvar__1__env__29148)
=> ( c_24__type__29184___24t(Vvar__0__fr__29147,Vvar__1__env__29148,Vvar__2__env_27__29151,Vvar__3__x__29154,Vvar__2__env_27__29151)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__29154)
=> ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__29147,Vvar__1__env__29148,Vvar__2__env_27__29151,Vvar__3__x__29154)
=> ( happ(Vvar__1__env__29148,Vvar__3__x__29154) = happ(Vvar__2__env_27__29151,Vvar__3__x__29154)
& happ(Vvar__1__env__29148,Vvar__3__x__29154) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__29151,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29147,Vvar__3__x__29154))),happ(Vvar__2__env_27__29151,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29147,Vvar__3__x__29154))))
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__29151,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29147,Vvar__3__x__29154))),cCoq_2eNumbers_2eBinNums_2eZ0)
& cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__29151,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29147,Vvar__3__x__29154))),cCoq_2eNumbers_2eBinNums_2eZ0)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__3595,VX3596] :
( cType___24t(Vvar__0__C__3595)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,VX3596)
=> ( VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__3595)
| VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__3595)
| ? [Vvar__1___24Anonymous__3600] :
( t(Vvar__1___24Anonymous__3600,Vvar__0__C__3595)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__3595,Vvar__1___24Anonymous__3600) )
| ? [Vvar__1___24Anonymous__3602] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3602)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__3595,Vvar__1___24Anonymous__3602) )
| ? [Vvar__1___24Anonymous__3604] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3604)
& ? [Vvar__2___24Anonymous__3605] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__2___24Anonymous__3605)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__3595,Vvar__1___24Anonymous__3604,Vvar__2___24Anonymous__3605) ) )
| ? [Vvar__1___24Anonymous__3607] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3607)
& ? [Vvar__2___24Anonymous__3608] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__2___24Anonymous__3608)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__3595,Vvar__1___24Anonymous__3607,Vvar__2___24Anonymous__3608) ) )
| ? [Vvar__1___24Anonymous__3610] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3610)
& ? [Vvar__2___24Anonymous__3611] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__2___24Anonymous__3611)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__3595,Vvar__1___24Anonymous__3610,Vvar__2___24Anonymous__3611) ) )
| ? [Vvar__1___24Anonymous__3613] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3613)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__3595,Vvar__1___24Anonymous__3613) )
| ? [Vvar__1___24Anonymous__3615] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3615)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__3595,Vvar__1___24Anonymous__3615) )
| ? [Vvar__1___24Anonymous__3617] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3617)
& ? [Vvar__2___24Anonymous__3618] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__2___24Anonymous__3618)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__3595,Vvar__1___24Anonymous__3617,Vvar__2___24Anonymous__3618) ) )
| ? [Vvar__1___24Anonymous__3620] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__3595,Vvar__1___24Anonymous__3620)
& ? [Vvar__2___24Anonymous__3621] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__3621)
& VX3596 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__3595,Vvar__1___24Anonymous__3620,Vvar__2___24Anonymous__3621) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057] :
( cType___24t(Vvar__0__R__15028)
=> ( t(Vvar__1__rO__15029,Vvar__0__R__15028)
=> ( t(Vvar__2__rI__15030,Vvar__0__R__15028)
=> ( c_24__type__15222___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__3__radd__15031)
=> ( c_24__type__15315___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__4__rmul__15036)
=> ( c_24__type__15408___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__5__rsub__15041)
=> ( c_24__type__15490___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__6__ropp__15046)
=> ( c_24__type__15583___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__7__rdiv__15049)
=> ( c_24__type__15665___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__8__rinv__15054)
=> ( c_24__type__15758___24t(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057,Vvar__9__req__15057)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__7__rdiv__15049,Vvar__8__rinv__15054,Vvar__9__req__15057)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__15028,Vvar__1__rO__15029,Vvar__2__rI__15030,Vvar__3__radd__15031,Vvar__4__rmul__15036,Vvar__5__rsub__15041,Vvar__6__ropp__15046,Vvar__9__req__15057)
& ~ p(happ(happ(Vvar__9__req__15057,Vvar__2__rI__15030),Vvar__1__rO__15029))
& ! [Vvar__var__var__var__var__var__var__12__p__15100__15102__15109__15111__15113__15115__15117] :
( t(Vvar__var__var__var__var__var__var__12__p__15100__15102__15109__15111__15113__15115__15117,Vvar__0__R__15028)
=> ! [Vvar__var__var__var__var__var__var__13__q__15101__15103__15110__15112__15114__15116__15118] :
( t(Vvar__var__var__var__var__var__var__13__q__15101__15103__15110__15112__15114__15116__15118,Vvar__0__R__15028)
=> p(happ(happ(Vvar__9__req__15057,happ(happ(Vvar__7__rdiv__15049,Vvar__var__var__var__var__var__var__12__p__15100__15102__15109__15111__15113__15115__15117),Vvar__var__var__var__var__var__var__13__q__15101__15103__15110__15112__15114__15116__15118)),happ(happ(Vvar__4__rmul__15036,Vvar__var__var__var__var__var__var__12__p__15100__15102__15109__15111__15113__15115__15117),happ(Vvar__8__rinv__15054,Vvar__var__var__var__var__var__var__13__q__15101__15103__15110__15112__15114__15116__15118)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__15105__15107__15119__15121__15123__15125__15127__15129] :
( t(Vvar__var__var__var__var__var__var__var__13__p__15105__15107__15119__15121__15123__15125__15127__15129,Vvar__0__R__15028)
=> ( ~ p(happ(happ(Vvar__9__req__15057,Vvar__var__var__var__var__var__var__var__13__p__15105__15107__15119__15121__15123__15125__15127__15129),Vvar__1__rO__15029))
=> p(happ(happ(Vvar__9__req__15057,happ(happ(Vvar__4__rmul__15036,happ(Vvar__8__rinv__15054,Vvar__var__var__var__var__var__var__var__13__p__15105__15107__15119__15121__15123__15125__15127__15129)),Vvar__var__var__var__var__var__var__var__13__p__15105__15107__15119__15121__15123__15125__15127__15129)),Vvar__2__rI__15030)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
! [Vvar__0__C__4231,VX4232] :
( cType___24t(Vvar__0__C__4231)
=> ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__4231,VX4232)
=> ? [Vvar__1__num__4234] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4231,Vvar__1__num__4234)
& ? [Vvar__2__denum__4235] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__4231,Vvar__2__denum__4235)
& ? [Vvar__3__condition__4236] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__4231),Vvar__3__condition__4236)
& VX4232 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__4231,Vvar__1__num__4234,Vvar__2__denum__4235,Vvar__3__condition__4236) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [Vvar__0__C__15764,VX15765] :
( cType___24t(Vvar__0__C__15764)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__15764,VX15765)
=> ? [Vvar__1__rsplit__left__15767] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15764,Vvar__1__rsplit__left__15767)
& ? [Vvar__2__rsplit__common__15768] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15764,Vvar__2__rsplit__common__15768)
& ? [Vvar__3__rsplit__right__15769] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__15764,Vvar__3__rsplit__right__15769)
& VX15765 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__15764,Vvar__1__rsplit__left__15767,Vvar__2__rsplit__common__15768,Vvar__3__rsplit__right__15769) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX5294] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX5294)
=> ( VX5294 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__5295] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5295)
& ? [Vvar__1___24Anonymous__5296] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__5296)
& VX5294 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__5295,Vvar__1___24Anonymous__5296) ) )
| ? [Vvar__0___24Anonymous__5297] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5297)
& ? [Vvar__1___24Anonymous__5298] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__5298)
& VX5294 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__5297,Vvar__1___24Anonymous__5298) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__5315,VX5316] :
( cType___24t(Vvar__0__C__5315)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,VX5316)
=> ( VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__5315)
| VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__5315)
| ? [Vvar__1___24Anonymous__5320] :
( t(Vvar__1___24Anonymous__5320,Vvar__0__C__5315)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__5315,Vvar__1___24Anonymous__5320) )
| ? [Vvar__1___24Anonymous__5322] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5322)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__5315,Vvar__1___24Anonymous__5322) )
| ? [Vvar__1___24Anonymous__5324] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__1___24Anonymous__5324)
& ? [Vvar__2___24Anonymous__5325] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__2___24Anonymous__5325)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__5315,Vvar__1___24Anonymous__5324,Vvar__2___24Anonymous__5325) ) )
| ? [Vvar__1___24Anonymous__5327] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__1___24Anonymous__5327)
& ? [Vvar__2___24Anonymous__5328] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__2___24Anonymous__5328)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__5315,Vvar__1___24Anonymous__5327,Vvar__2___24Anonymous__5328) ) )
| ? [Vvar__1___24Anonymous__5330] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__1___24Anonymous__5330)
& ? [Vvar__2___24Anonymous__5331] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__2___24Anonymous__5331)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__5315,Vvar__1___24Anonymous__5330,Vvar__2___24Anonymous__5331) ) )
| ? [Vvar__1___24Anonymous__5333] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__1___24Anonymous__5333)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__5315,Vvar__1___24Anonymous__5333) )
| ? [Vvar__1___24Anonymous__5335] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__5315,Vvar__1___24Anonymous__5335)
& ? [Vvar__2___24Anonymous__5336] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__5336)
& VX5316 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__5315,Vvar__1___24Anonymous__5335,Vvar__2___24Anonymous__5336) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__5115,VX5116] :
( cType___24t(Vvar__0__C__5115)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5115,VX5116)
=> ( ? [Vvar__1___24Anonymous__5118] :
( t(Vvar__1___24Anonymous__5118,Vvar__0__C__5115)
& VX5116 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__5115,Vvar__1___24Anonymous__5118) )
| ? [Vvar__1___24Anonymous__5120] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__5120)
& ? [Vvar__2___24Anonymous__5121] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5115,Vvar__2___24Anonymous__5121)
& VX5116 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__5115,Vvar__1___24Anonymous__5120,Vvar__2___24Anonymous__5121) ) )
| ? [Vvar__1___24Anonymous__5123] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5115,Vvar__1___24Anonymous__5123)
& ? [Vvar__2___24Anonymous__5124] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__5124)
& ? [Vvar__3___24Anonymous__5125] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__5115,Vvar__3___24Anonymous__5125)
& VX5116 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__5115,Vvar__1___24Anonymous__5123,Vvar__2___24Anonymous__5124,Vvar__3___24Anonymous__5125) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668] :
( cType___24t(Vvar__0__R__24647)
=> ( t(Vvar__1__rO__24648,Vvar__0__R__24647)
=> ( t(Vvar__2__rI__24649,Vvar__0__R__24647)
=> ( c_24__type__24896___24t(Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668,Vvar__3__radd__24650)
=> ( c_24__type__24959___24t(Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668,Vvar__4__rmul__24655)
=> ( c_24__type__25022___24t(Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668,Vvar__5__rsub__24660)
=> ( c_24__type__25076___24t(Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668,Vvar__6__ropp__24665)
=> ( c_24__type__25139___24t(Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668,Vvar__7__req__24668)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__24647,Vvar__1__rO__24648,Vvar__2__rI__24649,Vvar__3__radd__24650,Vvar__4__rmul__24655,Vvar__5__rsub__24660,Vvar__6__ropp__24665,Vvar__7__req__24668)
=> ( ! [Vvar__var__var__var__var__var__8__x__24701__24702__24755__24756__24757__24758] :
( t(Vvar__var__var__var__var__var__8__x__24701__24702__24755__24756__24757__24758,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__3__radd__24650,Vvar__1__rO__24648),Vvar__var__var__var__var__var__8__x__24701__24702__24755__24756__24757__24758)),Vvar__var__var__var__var__var__8__x__24701__24702__24755__24756__24757__24758)) )
& ! [Vvar__var__var__var__var__9__x__24704__24706__24759__24761__24763] :
( t(Vvar__var__var__var__var__9__x__24704__24706__24759__24761__24763,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__10__y__24705__24707__24760__24762__24764] :
( t(Vvar__var__var__var__var__10__y__24705__24707__24760__24762__24764,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__9__x__24704__24706__24759__24761__24763),Vvar__var__var__var__var__10__y__24705__24707__24760__24762__24764)),happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__10__y__24705__24707__24760__24762__24764),Vvar__var__var__var__var__9__x__24704__24706__24759__24761__24763))) ) )
& ! [Vvar__var__var__var__var__10__x__24709__24712__24765__24768__24771] :
( t(Vvar__var__var__var__var__10__x__24709__24712__24765__24768__24771,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__11__y__24710__24713__24766__24769__24772] :
( t(Vvar__var__var__var__var__11__y__24710__24713__24766__24769__24772,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__12__z__24711__24714__24767__24770__24773] :
( t(Vvar__var__var__var__var__12__z__24711__24714__24767__24770__24773,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__10__x__24709__24712__24765__24768__24771),happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__11__y__24710__24713__24766__24769__24772),Vvar__var__var__var__var__12__z__24711__24714__24767__24770__24773))),happ(happ(Vvar__3__radd__24650,happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__10__x__24709__24712__24765__24768__24771),Vvar__var__var__var__var__11__y__24710__24713__24766__24769__24772)),Vvar__var__var__var__var__12__z__24711__24714__24767__24770__24773))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__24716__24717__24774__24775__24776__24777] :
( t(Vvar__var__var__var__var__var__11__x__24716__24717__24774__24775__24776__24777,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__4__rmul__24655,Vvar__2__rI__24649),Vvar__var__var__var__var__var__11__x__24716__24717__24774__24775__24776__24777)),Vvar__var__var__var__var__var__11__x__24716__24717__24774__24775__24776__24777)) )
& ! [Vvar__var__var__var__var__var__12__x__24719__24720__24778__24779__24780__24781] :
( t(Vvar__var__var__var__var__var__12__x__24719__24720__24778__24779__24780__24781,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__4__rmul__24655,Vvar__1__rO__24648),Vvar__var__var__var__var__var__12__x__24719__24720__24778__24779__24780__24781)),Vvar__1__rO__24648)) )
& ! [Vvar__var__var__var__var__13__x__24722__24724__24782__24784__24786] :
( t(Vvar__var__var__var__var__13__x__24722__24724__24782__24784__24786,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__14__y__24723__24725__24783__24785__24787] :
( t(Vvar__var__var__var__var__14__y__24723__24725__24783__24785__24787,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__13__x__24722__24724__24782__24784__24786),Vvar__var__var__var__var__14__y__24723__24725__24783__24785__24787)),happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__14__y__24723__24725__24783__24785__24787),Vvar__var__var__var__var__13__x__24722__24724__24782__24784__24786))) ) )
& ! [Vvar__var__var__var__var__14__x__24727__24730__24788__24791__24794] :
( t(Vvar__var__var__var__var__14__x__24727__24730__24788__24791__24794,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__15__y__24728__24731__24789__24792__24795] :
( t(Vvar__var__var__var__var__15__y__24728__24731__24789__24792__24795,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__16__z__24729__24732__24790__24793__24796] :
( t(Vvar__var__var__var__var__16__z__24729__24732__24790__24793__24796,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__14__x__24727__24730__24788__24791__24794),happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__15__y__24728__24731__24789__24792__24795),Vvar__var__var__var__var__16__z__24729__24732__24790__24793__24796))),happ(happ(Vvar__4__rmul__24655,happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__14__x__24727__24730__24788__24791__24794),Vvar__var__var__var__var__15__y__24728__24731__24789__24792__24795)),Vvar__var__var__var__var__16__z__24729__24732__24790__24793__24796))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__24734__24737__24797__24800__24803__24806] :
( t(Vvar__var__var__var__var__var__15__x__24734__24737__24797__24800__24803__24806,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__var__16__y__24735__24738__24798__24801__24804__24807] :
( t(Vvar__var__var__var__var__var__16__y__24735__24738__24798__24801__24804__24807,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__var__17__z__24736__24739__24799__24802__24805__24808] :
( t(Vvar__var__var__var__var__var__17__z__24736__24739__24799__24802__24805__24808,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__4__rmul__24655,happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__var__15__x__24734__24737__24797__24800__24803__24806),Vvar__var__var__var__var__var__16__y__24735__24738__24798__24801__24804__24807)),Vvar__var__var__var__var__var__17__z__24736__24739__24799__24802__24805__24808)),happ(happ(Vvar__3__radd__24650,happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__var__15__x__24734__24737__24797__24800__24803__24806),Vvar__var__var__var__var__var__17__z__24736__24739__24799__24802__24805__24808)),happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__var__16__y__24735__24738__24798__24801__24804__24807),Vvar__var__var__var__var__var__17__z__24736__24739__24799__24802__24805__24808)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__24741__24743__24809__24811__24813__24815] :
( t(Vvar__var__var__var__var__var__16__x__24741__24743__24809__24811__24813__24815,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__var__17__y__24742__24744__24810__24812__24814__24816] :
( t(Vvar__var__var__var__var__var__17__y__24742__24744__24810__24812__24814__24816,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(Vvar__6__ropp__24665,happ(happ(Vvar__4__rmul__24655,Vvar__var__var__var__var__var__16__x__24741__24743__24809__24811__24813__24815),Vvar__var__var__var__var__var__17__y__24742__24744__24810__24812__24814__24816))),happ(happ(Vvar__4__rmul__24655,happ(Vvar__6__ropp__24665,Vvar__var__var__var__var__var__16__x__24741__24743__24809__24811__24813__24815)),Vvar__var__var__var__var__var__17__y__24742__24744__24810__24812__24814__24816))) ) )
& ! [Vvar__var__var__var__var__var__17__x__24746__24748__24817__24819__24821__24823] :
( t(Vvar__var__var__var__var__var__17__x__24746__24748__24817__24819__24821__24823,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__var__18__y__24747__24749__24818__24820__24822__24824] :
( t(Vvar__var__var__var__var__var__18__y__24747__24749__24818__24820__24822__24824,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(Vvar__6__ropp__24665,happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__var__17__x__24746__24748__24817__24819__24821__24823),Vvar__var__var__var__var__var__18__y__24747__24749__24818__24820__24822__24824))),happ(happ(Vvar__3__radd__24650,happ(Vvar__6__ropp__24665,Vvar__var__var__var__var__var__17__x__24746__24748__24817__24819__24821__24823)),happ(Vvar__6__ropp__24665,Vvar__var__var__var__var__var__18__y__24747__24749__24818__24820__24822__24824)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__24751__24753__24825__24827__24829__24831__24833] :
( t(Vvar__var__var__var__var__var__var__18__x__24751__24753__24825__24827__24829__24831__24833,Vvar__0__R__24647)
=> ! [Vvar__var__var__var__var__var__var__19__y__24752__24754__24826__24828__24830__24832__24834] :
( t(Vvar__var__var__var__var__var__var__19__y__24752__24754__24826__24828__24830__24832__24834,Vvar__0__R__24647)
=> p(happ(happ(Vvar__7__req__24668,happ(happ(Vvar__5__rsub__24660,Vvar__var__var__var__var__var__var__18__x__24751__24753__24825__24827__24829__24831__24833),Vvar__var__var__var__var__var__var__19__y__24752__24754__24826__24828__24830__24832__24834)),happ(happ(Vvar__3__radd__24650,Vvar__var__var__var__var__var__var__18__x__24751__24753__24825__24827__24829__24831__24833),happ(Vvar__6__ropp__24665,Vvar__var__var__var__var__var__var__19__y__24752__24754__24826__24828__24830__24832__24834)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285] :
( cType___24t(Vvar__0__R__27265)
=> ( c_24__type__27405___24t(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285,Vvar__1__req__27266)
=> ( cType___24t(Vvar__2__C__27271)
=> ( c_24__type__27455___24t(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285,Vvar__3__cadd__27272)
=> ( c_24__type__27505___24t(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285,Vvar__4__cmul__27277)
=> ( c_24__type__27547___24t(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285,Vvar__5__phi__27282)
=> ( c_24__type__27597___24t(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285,Vvar__6__cdiv__27285)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__27317__27322__27327__27332__27337__27342__27347__27352] :
( t(Vvar__var__var__var__var__var__var__var__7__a__27317__27322__27327__27332__27337__27342__27347__27352,Vvar__2__C__27271)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__27318__27323__27328__27333__27338__27343__27348__27353] :
( t(Vvar__var__var__var__var__var__var__var__8__b__27318__27323__27328__27333__27338__27343__27348__27353,Vvar__2__C__27271)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2427660___24a9(Vvar__0__R__27265,Vvar__1__req__27266,Vvar__2__C__27271,Vvar__3__cadd__27272,Vvar__4__cmul__27277,Vvar__5__phi__27282,Vvar__6__cdiv__27285,Vvar__var__var__var__var__var__var__var__7__a__27317__27322__27327__27332__27337__27342__27347__27352,Vvar__var__var__var__var__var__var__var__8__b__27318__27323__27328__27333__27338__27343__27348__27353) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__3__req__27687,Vvar__4__Cpow__27692,Vvar__5__Cp__phi__27693,Vvar__6__rpow__27696] :
( cType___24t(Vvar__0__R__27680)
=> ( t(Vvar__1__rI__27681,Vvar__0__R__27680)
=> ( c_24__type__27782___24t(Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__3__req__27687,Vvar__4__Cpow__27692,Vvar__5__Cp__phi__27693,Vvar__6__rpow__27696,Vvar__2__rmul__27682)
=> ( c_24__type__27826___24t(Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__3__req__27687,Vvar__4__Cpow__27692,Vvar__5__Cp__phi__27693,Vvar__6__rpow__27696,Vvar__3__req__27687)
=> ( cType___24t(Vvar__4__Cpow__27692)
=> ( c_24__type__27862___24t(Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__3__req__27687,Vvar__4__Cpow__27692,Vvar__5__Cp__phi__27693,Vvar__6__rpow__27696,Vvar__5__Cp__phi__27693)
=> ( c_24__type__27906___24t(Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__3__req__27687,Vvar__4__Cpow__27692,Vvar__5__Cp__phi__27693,Vvar__6__rpow__27696,Vvar__6__rpow__27696)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__3__req__27687,Vvar__4__Cpow__27692,Vvar__5__Cp__phi__27693,Vvar__6__rpow__27696)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__27724__27726__27728__27730__27732__27734__27736__27738] :
( t(Vvar__var__var__var__var__var__var__var__7__r__27724__27726__27728__27730__27732__27734__27736__27738,Vvar__0__R__27680)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__27725__27727__27729__27731__27733__27735__27737__27739] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__27725__27727__27729__27731__27733__27735__27737__27739)
=> p(happ(happ(Vvar__3__req__27687,happ(happ(Vvar__6__rpow__27696,Vvar__var__var__var__var__var__var__var__7__r__27724__27726__27728__27730__27732__27734__27736__27738),happ(Vvar__5__Cp__phi__27693,Vvar__var__var__var__var__var__var__var__8__n__27725__27727__27729__27731__27733__27735__27737__27739))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__27680,Vvar__1__rI__27681,Vvar__2__rmul__27682,Vvar__var__var__var__var__var__var__var__7__r__27724__27726__27728__27730__27732__27734__27736__27738,Vvar__var__var__var__var__var__var__var__8__n__27725__27727__27729__27731__27733__27735__27737__27739))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951] :
( cType___24t(Vvar__0__R__25937)
=> ( c_24__type__26042___24t(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951,Vvar__1__radd__25938)
=> ( c_24__type__26072___24t(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951,Vvar__2__rmul__25943)
=> ( c_24__type__26096___24t(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951,Vvar__3__ropp__25948)
=> ( c_24__type__26126___24t(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951,Vvar__4__req__25951)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__26156___24a5(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25937,c_24__type__26180___24a5(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951),Vvar__4__req__25951,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25937,Vvar__0__R__25937,Vvar__4__req__25951,Vvar__4__req__25951)),Vvar__1__radd__25938)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__26213___24a5(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25937,c_24__type__26237___24a5(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951),Vvar__4__req__25951,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25937,Vvar__0__R__25937,Vvar__4__req__25951,Vvar__4__req__25951)),Vvar__2__rmul__25943)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__26264___24a5(Vvar__0__R__25937,Vvar__1__radd__25938,Vvar__2__rmul__25943,Vvar__3__ropp__25948,Vvar__4__req__25951),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25937,Vvar__0__R__25937,Vvar__4__req__25951,Vvar__4__req__25951),Vvar__3__ropp__25948)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
! [VX27910] :
( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX27910)
=> ( VX27910 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
| ? [Vvar__0__R__27911] :
( cType___24t(Vvar__0__R__27911)
& ? [Vvar__1__req__27912] :
( c_24__type__3131___24t(Vvar__0__R__27911,Vvar__1__req__27912)
& ? [Vvar__2__reqb__27917] :
( c_24__type__4744___24t(Vvar__0__R__27911,Vvar__2__reqb__27917)
& ! [Vvar__var__3__x__27923__27926] :
( t(Vvar__var__3__x__27923__27926,Vvar__0__R__27911)
=> ! [Vvar__var__4__y__27924__27927] :
( t(Vvar__var__4__y__27924__27927,Vvar__0__R__27911)
=> ( happ(happ(Vvar__2__reqb__27917,Vvar__var__3__x__27923__27926),Vvar__var__4__y__27924__27927) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__1__req__27912,Vvar__var__3__x__27923__27926),Vvar__var__4__y__27924__27927)) ) ) )
& VX27910 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__27911,Vvar__1__req__27912,Vvar__2__reqb__27917) ) ) )
| ? [Vvar__0__R__27929] :
( cType___24t(Vvar__0__R__27929)
& ? [Vvar__1__rO__27930] :
( t(Vvar__1__rO__27930,Vvar__0__R__27929)
& ? [Vvar__2__rI__27931] :
( t(Vvar__2__rI__27931,Vvar__0__R__27929)
& ? [Vvar__3__radd__27932] :
( c_24__type__4198___24t(Vvar__0__R__27929,Vvar__3__radd__27932)
& ? [Vvar__4__rmul__27937] :
( c_24__type__4198___24t(Vvar__0__R__27929,Vvar__4__rmul__27937)
& ? [Vvar__5__rsub__27942] :
( c_24__type__4198___24t(Vvar__0__R__27929,Vvar__5__rsub__27942)
& ? [Vvar__6__ropp__27947] :
( c_24__type__4207___24t(Vvar__0__R__27929,Vvar__6__ropp__27947)
& ? [Vvar__7__req__27950] :
( c_24__type__3131___24t(Vvar__0__R__27929,Vvar__7__req__27950)
& ? [Vvar__8__C__27955] :
( cType___24t(Vvar__8__C__27955)
& ? [Vvar__9__cO__27956] :
( t(Vvar__9__cO__27956,Vvar__8__C__27955)
& ? [Vvar__10__cI__27957] :
( t(Vvar__10__cI__27957,Vvar__8__C__27955)
& ? [Vvar__11__cadd__27958] :
( c_24__type__6444___24t(Vvar__0__R__27929,Vvar__8__C__27955,Vvar__11__cadd__27958)
& ? [Vvar__12__cmul__27963] :
( c_24__type__6444___24t(Vvar__0__R__27929,Vvar__8__C__27955,Vvar__12__cmul__27963)
& ? [Vvar__13__csub__27968] :
( c_24__type__6444___24t(Vvar__0__R__27929,Vvar__8__C__27955,Vvar__13__csub__27968)
& ? [Vvar__14__copp__27973] :
( c_24__type__6458___24t(Vvar__0__R__27929,Vvar__8__C__27955,Vvar__14__copp__27973)
& ? [Vvar__15__ceqb__27976] :
( c_24__type__6465___24t(Vvar__0__R__27929,Vvar__8__C__27955,Vvar__15__ceqb__27976)
& ? [Vvar__16__phi__27981] :
( c_24__type__4215___24t(Vvar__0__R__27929,Vvar__8__C__27955,Vvar__16__phi__27981)
& cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__27929,Vvar__1__rO__27930,Vvar__2__rI__27931,Vvar__3__radd__27932,Vvar__4__rmul__27937,Vvar__5__rsub__27942,Vvar__6__ropp__27947,Vvar__7__req__27950,Vvar__8__C__27955,Vvar__9__cO__27956,Vvar__10__cI__27957,Vvar__11__cadd__27958,Vvar__12__cmul__27963,Vvar__13__csub__27968,Vvar__14__copp__27973,Vvar__15__ceqb__27976,Vvar__16__phi__27981)
& VX27910 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__27929,Vvar__1__rO__27930,Vvar__2__rI__27931,Vvar__3__radd__27932,Vvar__4__rmul__27937,Vvar__5__rsub__27942,Vvar__6__ropp__27947,Vvar__7__req__27950,Vvar__8__C__27955,Vvar__9__cO__27956,Vvar__10__cI__27957,Vvar__11__cadd__27958,Vvar__12__cmul__27963,Vvar__13__csub__27968,Vvar__14__copp__27973,Vvar__15__ceqb__27976,Vvar__16__phi__27981) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542] :
( cType___24t(Vvar__0__R__6490)
=> ( t(Vvar__1__rO__6491,Vvar__0__R__6490)
=> ( t(Vvar__2__rI__6492,Vvar__0__R__6490)
=> ( c_24__type__6886___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__3__radd__6493)
=> ( c_24__type__7099___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__4__rmul__6498)
=> ( c_24__type__7312___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__5__rsub__6503)
=> ( c_24__type__7507___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__6__ropp__6508)
=> ( c_24__type__7720___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__7__req__6511)
=> ( cType___24t(Vvar__8__C__6516)
=> ( t(Vvar__9__cO__6517,Vvar__8__C__6516)
=> ( t(Vvar__10__cI__6518,Vvar__8__C__6516)
=> ( c_24__type__7933___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__11__cadd__6519)
=> ( c_24__type__8146___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__12__cmul__6524)
=> ( c_24__type__8359___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__13__csub__6529)
=> ( c_24__type__8554___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__14__copp__6534)
=> ( c_24__type__8767___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__15__ceqb__6537)
=> ( c_24__type__8962___24t(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542,Vvar__16__phi__6542)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__6490,Vvar__1__rO__6491,Vvar__2__rI__6492,Vvar__3__radd__6493,Vvar__4__rmul__6498,Vvar__5__rsub__6503,Vvar__6__ropp__6508,Vvar__7__req__6511,Vvar__8__C__6516,Vvar__9__cO__6517,Vvar__10__cI__6518,Vvar__11__cadd__6519,Vvar__12__cmul__6524,Vvar__13__csub__6529,Vvar__14__copp__6534,Vvar__15__ceqb__6537,Vvar__16__phi__6542)
=> ( p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,Vvar__9__cO__6517)),Vvar__1__rO__6491))
& p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,Vvar__10__cI__6518)),Vvar__2__rI__6492))
& ! [Vvar__var__var__var__var__var__var__19__x__6604__6606__6628__6630__6632__6634__6636] :
( t(Vvar__var__var__var__var__var__var__19__x__6604__6606__6628__6630__6632__6634__6636,Vvar__8__C__6516)
=> ! [Vvar__var__var__var__var__var__var__20__y__6605__6607__6629__6631__6633__6635__6637] :
( t(Vvar__var__var__var__var__var__var__20__y__6605__6607__6629__6631__6633__6635__6637,Vvar__8__C__6516)
=> p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,happ(happ(Vvar__11__cadd__6519,Vvar__var__var__var__var__var__var__19__x__6604__6606__6628__6630__6632__6634__6636),Vvar__var__var__var__var__var__var__20__y__6605__6607__6629__6631__6633__6635__6637))),happ(happ(Vvar__3__radd__6493,happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__19__x__6604__6606__6628__6630__6632__6634__6636)),happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__20__y__6605__6607__6629__6631__6633__6635__6637)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__6609__6611__6638__6640__6642__6644__6646] :
( t(Vvar__var__var__var__var__var__var__20__x__6609__6611__6638__6640__6642__6644__6646,Vvar__8__C__6516)
=> ! [Vvar__var__var__var__var__var__var__21__y__6610__6612__6639__6641__6643__6645__6647] :
( t(Vvar__var__var__var__var__var__var__21__y__6610__6612__6639__6641__6643__6645__6647,Vvar__8__C__6516)
=> p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,happ(happ(Vvar__13__csub__6529,Vvar__var__var__var__var__var__var__20__x__6609__6611__6638__6640__6642__6644__6646),Vvar__var__var__var__var__var__var__21__y__6610__6612__6639__6641__6643__6645__6647))),happ(happ(Vvar__5__rsub__6503,happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__20__x__6609__6611__6638__6640__6642__6644__6646)),happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__21__y__6610__6612__6639__6641__6643__6645__6647)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__6614__6616__6648__6650__6652__6654__6656] :
( t(Vvar__var__var__var__var__var__var__21__x__6614__6616__6648__6650__6652__6654__6656,Vvar__8__C__6516)
=> ! [Vvar__var__var__var__var__var__var__22__y__6615__6617__6649__6651__6653__6655__6657] :
( t(Vvar__var__var__var__var__var__var__22__y__6615__6617__6649__6651__6653__6655__6657,Vvar__8__C__6516)
=> p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,happ(happ(Vvar__12__cmul__6524,Vvar__var__var__var__var__var__var__21__x__6614__6616__6648__6650__6652__6654__6656),Vvar__var__var__var__var__var__var__22__y__6615__6617__6649__6651__6653__6655__6657))),happ(happ(Vvar__4__rmul__6498,happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__21__x__6614__6616__6648__6650__6652__6654__6656)),happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__22__y__6615__6617__6649__6651__6653__6655__6657)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__6619__6620__6658__6659__6660__6661__6662] :
( t(Vvar__var__var__var__var__var__var__22__x__6619__6620__6658__6659__6660__6661__6662,Vvar__8__C__6516)
=> p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,happ(Vvar__14__copp__6534,Vvar__var__var__var__var__var__var__22__x__6619__6620__6658__6659__6660__6661__6662))),happ(Vvar__6__ropp__6508,happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__var__22__x__6619__6620__6658__6659__6660__6661__6662)))) )
& ! [Vvar__var__var__var__var__var__23__x__6622__6625__6663__6666__6669__6672] :
( t(Vvar__var__var__var__var__var__23__x__6622__6625__6663__6666__6669__6672,Vvar__8__C__6516)
=> ! [Vvar__var__var__var__var__var__24__y__6623__6626__6664__6667__6670__6673] :
( t(Vvar__var__var__var__var__var__24__y__6623__6626__6664__6667__6670__6673,Vvar__8__C__6516)
=> ( happ(happ(Vvar__15__ceqb__6537,Vvar__var__var__var__var__var__23__x__6622__6625__6663__6666__6669__6672),Vvar__var__var__var__var__var__24__y__6623__6626__6664__6667__6670__6673) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__6511,happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__23__x__6622__6625__6663__6666__6669__6672)),happ(Vvar__16__phi__6542,Vvar__var__var__var__var__var__24__y__6623__6626__6664__6667__6670__6673))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
! [Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303] :
( cType___24t(Vvar__0__R__26267)
=> ( t(Vvar__1__rO__26268,Vvar__0__R__26267)
=> ( t(Vvar__2__rI__26269,Vvar__0__R__26267)
=> ( c_24__type__26520___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__3__radd__26270)
=> ( c_24__type__26645___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__4__rmul__26275)
=> ( c_24__type__26770___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__5__req__26280)
=> ( cType___24t(Vvar__6__C__26285)
=> ( t(Vvar__7__cO__26286,Vvar__6__C__26285)
=> ( t(Vvar__8__cI__26287,Vvar__6__C__26285)
=> ( c_24__type__26895___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__9__cadd__26288)
=> ( c_24__type__27020___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__10__cmul__26293)
=> ( c_24__type__27145___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__11__ceqb__26298)
=> ( c_24__type__27256___24t(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303,Vvar__12__phi__26303)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__26267,Vvar__1__rO__26268,Vvar__2__rI__26269,Vvar__3__radd__26270,Vvar__4__rmul__26275,Vvar__5__req__26280,Vvar__6__C__26285,Vvar__7__cO__26286,Vvar__8__cI__26287,Vvar__9__cadd__26288,Vvar__10__cmul__26293,Vvar__11__ceqb__26298,Vvar__12__phi__26303)
=> ( p(happ(happ(Vvar__5__req__26280,happ(Vvar__12__phi__26303,Vvar__7__cO__26286)),Vvar__1__rO__26268))
& p(happ(happ(Vvar__5__req__26280,happ(Vvar__12__phi__26303,Vvar__8__cI__26287)),Vvar__2__rI__26269))
& ! [Vvar__var__var__var__var__var__var__15__x__26349__26351__26365__26367__26369__26371__26373] :
( t(Vvar__var__var__var__var__var__var__15__x__26349__26351__26365__26367__26369__26371__26373,Vvar__6__C__26285)
=> ! [Vvar__var__var__var__var__var__var__16__y__26350__26352__26366__26368__26370__26372__26374] :
( t(Vvar__var__var__var__var__var__var__16__y__26350__26352__26366__26368__26370__26372__26374,Vvar__6__C__26285)
=> p(happ(happ(Vvar__5__req__26280,happ(Vvar__12__phi__26303,happ(happ(Vvar__9__cadd__26288,Vvar__var__var__var__var__var__var__15__x__26349__26351__26365__26367__26369__26371__26373),Vvar__var__var__var__var__var__var__16__y__26350__26352__26366__26368__26370__26372__26374))),happ(happ(Vvar__3__radd__26270,happ(Vvar__12__phi__26303,Vvar__var__var__var__var__var__var__15__x__26349__26351__26365__26367__26369__26371__26373)),happ(Vvar__12__phi__26303,Vvar__var__var__var__var__var__var__16__y__26350__26352__26366__26368__26370__26372__26374)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__26354__26356__26375__26377__26379__26381__26383] :
( t(Vvar__var__var__var__var__var__var__16__x__26354__26356__26375__26377__26379__26381__26383,Vvar__6__C__26285)
=> ! [Vvar__var__var__var__var__var__var__17__y__26355__26357__26376__26378__26380__26382__26384] :
( t(Vvar__var__var__var__var__var__var__17__y__26355__26357__26376__26378__26380__26382__26384,Vvar__6__C__26285)
=> p(happ(happ(Vvar__5__req__26280,happ(Vvar__12__phi__26303,happ(happ(Vvar__10__cmul__26293,Vvar__var__var__var__var__var__var__16__x__26354__26356__26375__26377__26379__26381__26383),Vvar__var__var__var__var__var__var__17__y__26355__26357__26376__26378__26380__26382__26384))),happ(happ(Vvar__4__rmul__26275,happ(Vvar__12__phi__26303,Vvar__var__var__var__var__var__var__16__x__26354__26356__26375__26377__26379__26381__26383)),happ(Vvar__12__phi__26303,Vvar__var__var__var__var__var__var__17__y__26355__26357__26376__26378__26380__26382__26384)))) ) )
& ! [Vvar__var__var__var__var__var__17__x__26359__26362__26385__26388__26391__26394] :
( t(Vvar__var__var__var__var__var__17__x__26359__26362__26385__26388__26391__26394,Vvar__6__C__26285)
=> ! [Vvar__var__var__var__var__var__18__y__26360__26363__26386__26389__26392__26395] :
( t(Vvar__var__var__var__var__var__18__y__26360__26363__26386__26389__26392__26395,Vvar__6__C__26285)
=> ( happ(happ(Vvar__11__ceqb__26298,Vvar__var__var__var__var__var__17__x__26359__26362__26385__26388__26391__26394),Vvar__var__var__var__var__var__18__y__26360__26363__26386__26389__26392__26395) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__5__req__26280,happ(Vvar__12__phi__26303,Vvar__var__var__var__var__var__17__x__26359__26362__26385__26388__26391__26394)),happ(Vvar__12__phi__26303,Vvar__var__var__var__var__var__18__y__26360__26363__26386__26389__26392__26395))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
! [Vvar__0__C__56276,Vvar__1__copp__56277,Vvar__2__ceqb__56280,Vvar__3__get__sign__56285] :
( cType___24t(Vvar__0__C__56276)
=> ( c_24__type__56332___24t(Vvar__0__C__56276,Vvar__1__copp__56277,Vvar__2__ceqb__56280,Vvar__3__get__sign__56285,Vvar__1__copp__56277)
=> ( c_24__type__56351___24t(Vvar__0__C__56276,Vvar__1__copp__56277,Vvar__2__ceqb__56280,Vvar__3__get__sign__56285,Vvar__2__ceqb__56280)
=> ( c_24__type__56365___24t(Vvar__0__C__56276,Vvar__1__copp__56277,Vvar__2__ceqb__56280,Vvar__3__get__sign__56285,Vvar__3__get__sign__56285)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__56276,Vvar__1__copp__56277,Vvar__2__ceqb__56280,Vvar__3__get__sign__56285)
=> ( ! [Vvar__var__var__var__var__var__4__c__56302__56305__56308__56311__56314__56317] :
( t(Vvar__var__var__var__var__var__4__c__56302__56305__56308__56311__56314__56317,Vvar__0__C__56276)
=> ! [Vvar__var__var__var__var__var__5__c_27__56303__56306__56309__56312__56315__56318] :
( t(Vvar__var__var__var__var__var__5__c_27__56303__56306__56309__56312__56315__56318,Vvar__0__C__56276)
=> ( happ(Vvar__3__get__sign__56285,Vvar__var__var__var__var__var__4__c__56302__56305__56308__56311__56314__56317) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__56276,Vvar__var__var__var__var__var__5__c_27__56303__56306__56309__56312__56315__56318)
=> happ(happ(Vvar__2__ceqb__56280,Vvar__var__var__var__var__var__4__c__56302__56305__56308__56311__56314__56317),happ(Vvar__1__copp__56277,Vvar__var__var__var__var__var__5__c_27__56303__56306__56309__56312__56315__56318)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726] :
( cType___24t(Vvar__0__R__25715)
=> ( c_24__type__25801___24t(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726,Vvar__1__radd__25716)
=> ( c_24__type__25824___24t(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726,Vvar__2__rmul__25721)
=> ( c_24__type__25847___24t(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726,Vvar__3__req__25726)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__25870___24a4(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25715,c_24__type__25888___24a4(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726),Vvar__3__req__25726,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25715,Vvar__0__R__25715,Vvar__3__req__25726,Vvar__3__req__25726)),Vvar__1__radd__25716)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__25914___24a4(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25715,c_24__type__25932___24a4(Vvar__0__R__25715,Vvar__1__radd__25716,Vvar__2__rmul__25721,Vvar__3__req__25726),Vvar__3__req__25726,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__25715,Vvar__0__R__25715,Vvar__3__req__25726,Vvar__3__req__25726)),Vvar__2__rmul__25721)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction',axiom,
! [Vvar__0__X__70,Vvar__1__P__71,Vvar__2__x__74] :
( cType___24t(Vvar__0__X__70)
=> ( c_24__type__86___24t(Vvar__0__X__70,Vvar__1__P__71,Vvar__2__x__74,Vvar__1__P__71)
=> ( t(Vvar__2__x__74,Vvar__0__X__70)
=> ( cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(Vvar__0__X__70,Vvar__1__P__71,Vvar__2__x__74)
=> ( p(happ(Vvar__1__P__71,Vvar__2__x__74))
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyIntersection',axiom,
! [Vvar__0__T__281,Vvar__1__F__282,Vvar__1___24Anonymous__283] :
( cType___24t(Vvar__0__T__281)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__281,Vvar__1__F__282)
=> ( t(Vvar__1___24Anonymous__283,Vvar__0__T__281)
=> ( cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(Vvar__0__T__281,Vvar__1__F__282,Vvar__1___24Anonymous__283)
=> ? [Vvar__2__x__287] :
( t(Vvar__2__x__287,Vvar__0__T__281)
& ! [Vvar__var__var__var__3__S__289__291__293__295] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__281,Vvar__var__var__var__3__S__289__291__293__295)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__281),Vvar__1__F__282,Vvar__var__var__var__3__S__289__291__293__295)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__281,Vvar__var__var__var__3__S__289__291__293__295,Vvar__2__x__287) ) )
& Vvar__1___24Anonymous__283 = Vvar__2__x__287 ) ) ) ) ) ).
fof('$_inversion_ZornsLemma.Families.FamilyUnion',axiom,
! [Vvar__0__T__271,Vvar__1__F__272,Vvar__1___24Anonymous__273] :
( cType___24t(Vvar__0__T__271)
=> ( cZornsLemma_2eFamilies_2eFamily___24t(Vvar__0__T__271,Vvar__1__F__272)
=> ( t(Vvar__1___24Anonymous__273,Vvar__0__T__271)
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a3(Vvar__0__T__271,Vvar__1__F__272,Vvar__1___24Anonymous__273)
=> ? [Vvar__2__S__277] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vvar__0__T__271,Vvar__2__S__277)
& ? [Vvar__3__x__278] :
( t(Vvar__3__x__278,Vvar__0__T__271)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vvar__0__T__271),Vvar__1__F__272,Vvar__2__S__277)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(Vvar__0__T__271,Vvar__2__S__277,Vvar__3__x__278)
& Vvar__1___24Anonymous__273 = Vvar__3__x__278 ) ) ) ) ) ) ).
fof('$_lam_1138',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1138___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eSets_2eCpo_2eLub__rect___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) ).
fof('$_lam_141',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__141___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_1420',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1420___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eSets_2eCpo_2eGlb__rect___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) ).
fof('$_lam_1928',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1928___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_2595',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2595___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eSets_2eCpo_2eComplete__rect___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_2859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2859___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_29604',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__29604___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))) ) ).
fof('$_lam_2997',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2997___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_31939',axiom,
! [Vv__CANONICAL__0] : c_24__lam__31939___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2enat ).
fof('$_lam_31940',axiom,
! [Vv__CANONICAL__0] : c_24__lam__31940___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eNat_2edouble ).
fof('$_lam_33928',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__33928___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> Vv__CANONICAL__2 = Vv__CANONICAL__1 ) ).
fof('$_lam_574',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__574___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eSets_2eCpo_2eUpper__Bound__rect___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) ).
fof('$_lam_856',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__856___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eSets_2eCpo_2eLower__Bound__rect___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) ).
fof('$_lam_95',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__95___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ).
fof('$_prop_14155',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__14155___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_14419',axiom,
! [V7__A] :
( p(c_24__prop__14419___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_29348',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__S__29326,Vvar__1__x__29327,Vvar__2__y__29328] :
( p(c_24__prop__29348___24a4(Vvar__0___24Anonymous__29324,Vvar__0__S__29326,Vvar__1__x__29327,Vvar__2__y__29328))
<=> Vvar__1__x__29327 = Vvar__2__y__29328 ) ).
fof('$_prop_29349',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__x__29329,Vvar__1__y__29330] :
( p(c_24__prop__29349___24a3(Vvar__0___24Anonymous__29324,Vvar__0__x__29329,Vvar__1__y__29330))
<=> Vvar__0__x__29329 = Vvar__1__y__29330 ) ).
fof('$_prop_29350',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__x__29331,Vvar__1__s__29332] :
( p(c_24__prop__29350___24a3(Vvar__0___24Anonymous__29324,Vvar__0__x__29331,Vvar__1__s__29332))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__29331,Vvar__1__s__29332) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_29351',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__P__29333,Vvar__1__Q__29334] :
( p(c_24__prop__29351___24a3(Vvar__0___24Anonymous__29324,Vvar__0__P__29333,Vvar__1__Q__29334))
<=> ( p(Vvar__0__P__29333)
& p(Vvar__1__Q__29334) ) ) ).
fof('$_prop_29352',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__P__29337,Vvar__1__Q__29338] :
( p(c_24__prop__29352___24a3(Vvar__0___24Anonymous__29324,Vvar__0__P__29337,Vvar__1__Q__29338))
<=> ( p(Vvar__0__P__29337)
| p(Vvar__1__Q__29338) ) ) ).
fof('$_prop_29353',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__P__29341,Vvar__1__Q__29342] :
( p(c_24__prop__29353___24a3(Vvar__0___24Anonymous__29324,Vvar__0__P__29341,Vvar__1__Q__29342))
<=> ( p(Vvar__0__P__29341)
=> p(Vvar__1__Q__29342) ) ) ).
fof('$_prop_29354',axiom,
! [Vvar__0___24Anonymous__29324,Vvar__0__P__29346] :
( p(c_24__prop__29354___24a2(Vvar__0___24Anonymous__29324,Vvar__0__P__29346))
<=> ~ p(Vvar__0__P__29346) ) ).
fof('$_prop_29371',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__29371___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_32772',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__32772___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_32774',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__32774___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_33910',axiom,
! [V0__X,V1__x] :
( p(c_24__prop__33910___24a2(V0__X,V1__x))
<=> V1__x = V1__x ) ).
fof('$_prop_3584',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__3584___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 = Vv__CANONICAL__2 ) ).
fof('$_prop_3585',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__3585___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> Vv__CANONICAL__1 != Vv__CANONICAL__2 ) ).
fof('$_prop_55887',axiom,
! [V6__A] :
( p(c_24__prop__55887___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_55955',axiom,
! [V6__A] :
( p(c_24__prop__55955___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_56053',axiom,
! [V7__A] :
( p(c_24__prop__56053___24a1(V7__A))
<=> ~ ~ p(V7__A) ) ).
fof('$_prop_56054',axiom,
! [V7__A] :
( p(c_24__prop__56054___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_56467',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56467___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).
fof('$_prop_56468',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__56468___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> Vv__CANONICAL__0 != Vv__CANONICAL__1 ) ).
fof('$_type_104',axiom,
! [Vvar__105] :
( c_24__type__104___24t(Vvar__105)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__108___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__105,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1077',axiom,
! [Vvar__1078] :
( c_24__type__1077___24t(Vvar__1078)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1103___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ( cCoq_2eSets_2eCpo_2eLub___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(happ(happ(Vvar__1078,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__4) ) ) ) ) ) ) ) ) ).
fof('$_type_108',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__109] :
( c_24__type__108___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__109)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__109,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_1103',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1104] :
( c_24__type__1103___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1104)
<=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__6) ) )
=> t(Vvar__1104,Vv__CANONICAL__4) ) ) ) ).
fof('$_type_11497',axiom,
! [Vvar__11498] :
( c_24__type__11497___24t(Vvar__11498)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__11498,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11527',axiom,
! [Vvar__11528] :
( c_24__type__11527___24t(Vvar__11528)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cCoq_2eStrings_2eString_2estring___24t(happ(happ(Vvar__11528,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11575',axiom,
! [Vvar__11576] :
( c_24__type__11575___24t(Vvar__11576)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__11576,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11592',axiom,
! [Vvar__11593] :
( c_24__type__11592___24t(Vvar__11593)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__11593,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11600',axiom,
! [Vvar__11601] :
( c_24__type__11600___24t(Vvar__11601)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__11601,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_12',axiom,
! [Vvar__13] :
( c_24__type__12___24t(Vvar__13)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__13,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12354',axiom,
! [Vvar__12355] :
( c_24__type__12354___24t(Vvar__12355)
<=> ! [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__12355,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12388',axiom,
! [Vvar__12389] :
( c_24__type__12388___24t(Vvar__12389)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__12389,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12391',axiom,
! [Vvar__12392] :
( c_24__type__12391___24t(Vvar__12392)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__12392,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12403',axiom,
! [Vvar__12404] :
( c_24__type__12403___24t(Vvar__12404)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(happ(Vvar__12404,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12426',axiom,
! [Vvar__12427] :
( c_24__type__12426___24t(Vvar__12427)
<=> ! [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__12427,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12435',axiom,
! [Vvar__12436] :
( c_24__type__12435___24t(Vvar__12436)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__12436,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12486',axiom,
! [Vvar__12487] :
( c_24__type__12486___24t(Vvar__12487)
<=> ! [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__12487,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12489',axiom,
! [Vvar__12490] :
( c_24__type__12489___24t(Vvar__12490)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__12490,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12495',axiom,
! [Vvar__12496] :
( c_24__type__12495___24t(Vvar__12496)
<=> ! [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__12496,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12499',axiom,
! [Vvar__12500] :
( c_24__type__12499___24t(Vvar__12500)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12500,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12582',axiom,
! [Vvar__12583] :
( c_24__type__12582___24t(Vvar__12583)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12435___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12435___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12583,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12593',axiom,
! [Vvar__12594] :
( c_24__type__12593___24t(Vvar__12594)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__12594,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12599',axiom,
! [Vvar__12600] :
( c_24__type__12599___24t(Vvar__12600)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__12600,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12603',axiom,
! [Vvar__12604] :
( c_24__type__12603___24t(Vvar__12604)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__12593___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__12593___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__12604,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12640',axiom,
! [Vvar__12641] :
( c_24__type__12640___24t(Vvar__12641)
<=> ! [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__12641,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12650',axiom,
! [Vvar__12651] :
( c_24__type__12650___24t(Vvar__12651)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__12651,Vv__CANONICAL__0)) ) ) ).
fof('$_type_127',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__128] :
( c_24__type__127___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__128)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__128,Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ).
fof('$_type_12701',axiom,
! [Vvar__12702] :
( c_24__type__12701___24t(Vvar__12702)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4207___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__12702,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12725',axiom,
! [Vvar__12726] :
( c_24__type__12725___24t(Vvar__12726)
<=> ! [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__12726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12820',axiom,
! [Vvar__12821] :
( c_24__type__12820___24t(Vvar__12821)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(Vvar__12821,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_12825',axiom,
! [Vvar__12826] :
( c_24__type__12825___24t(Vvar__12826)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__12826,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12832',axiom,
! [Vvar__12833] :
( c_24__type__12832___24t(Vvar__12833)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__12833,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12835',axiom,
! [Vvar__12836] :
( c_24__type__12835___24t(Vvar__12836)
<=> ! [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__12836,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12844',axiom,
! [Vvar__12845] :
( c_24__type__12844___24t(Vvar__12845)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__12845,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12886',axiom,
! [Vvar__12887] :
( c_24__type__12886___24t(Vvar__12887)
<=> ! [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__12887,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12935',axiom,
! [Vvar__12936] :
( c_24__type__12935___24t(Vvar__12936)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__12936,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13531',axiom,
! [Vvar__13532] :
( c_24__type__13531___24t(Vvar__13532)
<=> ! [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__13532,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13567',axiom,
! [Vvar__13568] :
( c_24__type__13567___24t(Vvar__13568)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__13568,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1359',axiom,
! [Vvar__1360] :
( c_24__type__1359___24t(Vvar__1360)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__1385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ( cCoq_2eSets_2eCpo_2eGlb___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(happ(happ(Vvar__1360,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__4) ) ) ) ) ) ) ) ) ).
fof('$_type_1385',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1386] :
( c_24__type__1385___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__1386)
<=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__3) ) )
=> t(Vvar__1386,Vv__CANONICAL__4) ) ) ) ).
fof('$_type_14149',axiom,
! [Vvar__14150] :
( c_24__type__14149___24t(Vvar__14150)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__14150,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14224',axiom,
! [Vvar__14225] :
( c_24__type__14224___24t(Vvar__14225)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__14225,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14234',axiom,
! [Vvar__14235] :
( c_24__type__14234___24t(Vvar__14235)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__14235,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14248',axiom,
! [Vvar__14249] :
( c_24__type__14248___24t(Vvar__14249)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__14249,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14322',axiom,
! [Vv__CANONICAL__0,Vvar__14323] :
( c_24__type__14322___24t(Vv__CANONICAL__0,Vvar__14323)
<=> ( p(Vv__CANONICAL__0)
=> cProp___24t(Vvar__14323) ) ) ).
fof('$_type_14331',axiom,
! [Vvar__14332] :
( c_24__type__14331___24t(Vvar__14332)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__14332,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14394',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14395] :
( c_24__type__14394___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14395)
<=> ( p(happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2))
=> cProp___24t(Vvar__14395) ) ) ).
fof('$_type_14499',axiom,
! [Vvar__14500] :
( c_24__type__14499___24t(Vvar__14500)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__14500,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14501',axiom,
! [Vvar__14502] :
( c_24__type__14501___24t(Vvar__14502)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__14502,Vv__CANONICAL__0)) ) ) ).
fof('$_type_14862',axiom,
! [Vvar__14863] :
( c_24__type__14862___24t(Vvar__14863)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__14863,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14912',axiom,
! [Vvar__14913] :
( c_24__type__14912___24t(Vvar__14913)
<=> ! [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__14913,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14920',axiom,
! [Vvar__14921] :
( c_24__type__14920___24t(Vvar__14921)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__14921,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_14972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14973] :
( c_24__type__14972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__14973)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__14973,Vv__CANONICAL__6)) ) ) ).
fof('$_type_15000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__15001] :
( c_24__type__15000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__15001)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__15001,Vv__CANONICAL__6)) ) ) ).
fof('$_type_15009',axiom,
! [Vvar__15010] :
( c_24__type__15009___24t(Vvar__15010)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___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__15010,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_15018',axiom,
! [Vvar__15019] :
( c_24__type__15018___24t(Vvar__15019)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(happ(happ(Vvar__15019,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_15222',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__15223] :
( c_24__type__15222___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__15223)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15223,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15316] :
( c_24__type__15315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15316)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15316,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15408',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__15409] :
( c_24__type__15408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__15409)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15409,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15490',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15491] :
( c_24__type__15490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15491)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__15491,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_15583',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__15584] :
( c_24__type__15583___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__15584)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__15584,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_15665',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15666] :
( c_24__type__15665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__15666)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__15666,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_15758',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__15759] :
( c_24__type__15758___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__15759)
<=> ! [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__15759,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_159',axiom,
! [Vvar__160] :
( c_24__type__159___24t(Vvar__160)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__160,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17',axiom,
! [Vvar__18] :
( c_24__type__17___24t(Vvar__18)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__18,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17014',axiom,
! [Vvar__17015] :
( c_24__type__17014___24t(Vvar__17015)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__17015,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17039',axiom,
! [Vvar__17040] :
( c_24__type__17039___24t(Vvar__17040)
<=> ! [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__17040,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_17063',axiom,
! [Vvar__17064] :
( c_24__type__17063___24t(Vvar__17064)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__17070___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(happ(happ(happ(happ(Vvar__17064,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_17070',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17071] :
( c_24__type__17070___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17071)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__17071,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17094',axiom,
! [Vvar__17095] :
( c_24__type__17094___24t(Vvar__17095)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__17101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__17095,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_17101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17102] :
( c_24__type__17101___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__17102)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17102,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17149] :
( c_24__type__17148___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__17149)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__17149,Vv__CANONICAL__3)) ) ) ).
fof('$_type_17681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__17682] :
( c_24__type__17681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__17682)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17682,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__17783] :
( c_24__type__17782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__17783)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17783,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17883',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__17884] :
( c_24__type__17883___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__17884)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__17884,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_17973',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__17974] :
( c_24__type__17973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__17974)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__17974,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_18074',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__18075] :
( c_24__type__18074___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__18075)
<=> ! [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__18075,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_18175',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18176] :
( c_24__type__18175___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__18176)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18176,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_18276',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__18277] :
( c_24__type__18276___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__18277)
<=> ! [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__18277,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_18400',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18401] :
( c_24__type__18400___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18401)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__18401,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_18419',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18420] :
( c_24__type__18419___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__18420)
<=> ! [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__18420,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_18439',axiom,
! [Vvar__18440] :
( c_24__type__18439___24t(Vvar__18440)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__18440,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_18520',axiom,
! [Vv__CANONICAL__0,Vvar__18521] :
( c_24__type__18520___24t(Vv__CANONICAL__0,Vvar__18521)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__18521,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_18547',axiom,
! [Vvar__18548] :
( c_24__type__18547___24t(Vvar__18548)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eQArith_2eQArith__base_2eQ___24t(happ(happ(Vvar__18548,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1868',axiom,
! [Vvar__1869] :
( c_24__type__1868___24t(Vvar__1869)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__1896___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(happ(happ(Vvar__1869,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ) ) ) ) ) ).
fof('$_type_18727',axiom,
! [Vvar__18728] :
( c_24__type__18727___24t(Vvar__18728)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__18728,Vv__CANONICAL__0)) ) ) ).
fof('$_type_18772',axiom,
! [Vvar__18773] :
( c_24__type__18772___24t(Vvar__18773)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___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__18773,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_18841',axiom,
! [Vvar__18842] :
( c_24__type__18841___24t(Vvar__18842)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__18842,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1896',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1897] :
( c_24__type__1896___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__1897)
<=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,cCoq_2eSets_2eEnsembles_2eCouple___24a3(Vv__CANONICAL__0,Vv__CANONICAL__5,Vv__CANONICAL__6),Vv__CANONICAL__2)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__5) ) ) ) ) )
=> t(Vvar__1897,Vv__CANONICAL__3) ) ) ).
fof('$_type_19408',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19409] :
( c_24__type__19408___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__19409)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19409,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_19754',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19755] :
( c_24__type__19754___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__19755)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__19755,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2',axiom,
! [Vvar__3] :
( c_24__type__2___24t(Vvar__3)
<=> ! [Vv__CANONICAL__0] :
( cX___24t(Vv__CANONICAL__0)
=> cY___24t(happ(Vvar__3,Vv__CANONICAL__0)) ) ) ).
fof('$_type_20100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20101] :
( c_24__type__20100___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20101)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__20101,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_202',axiom,
! [Vv__CANONICAL__0,Vvar__203] :
( c_24__type__202___24t(Vv__CANONICAL__0,Vvar__203)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__203,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20423',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20424] :
( c_24__type__20423___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__20424)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__20424,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_20769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__20770] :
( c_24__type__20769___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__20770)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__20770,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_21115',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21116] :
( c_24__type__21115___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21116)
<=> ! [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__21116,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_21461',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__21462] :
( c_24__type__21461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__21462)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__21462,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_21807',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21808] :
( c_24__type__21807___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__21808)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__21808,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_22153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22154] :
( c_24__type__22153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22154)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__22154,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_22476',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__22477] :
( c_24__type__22476___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__22477)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__22477,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_22822',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22823] :
( c_24__type__22822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__22823)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__22823,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_23168',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23169] :
( c_24__type__23168___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23169)
<=> ! [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__23169,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_23491',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23492] :
( c_24__type__23491___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23492)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__23492,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_23814',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23815] :
( c_24__type__23814___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23815)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__23815,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_24160',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24161] :
( c_24__type__24160___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24161)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__24161,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24330',axiom,
! [Vvar__24331] :
( c_24__type__24330___24t(Vvar__24331)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__24331,Vv__CANONICAL__0)) ) ) ).
fof('$_type_24339',axiom,
! [Vvar__24340] :
( c_24__type__24339___24t(Vvar__24340)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__24340,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_24357',axiom,
! [Vvar__24358] :
( c_24__type__24357___24t(Vvar__24358)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4198___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__24358,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_24378',axiom,
! [Vvar__24379] :
( c_24__type__24378___24t(Vvar__24379)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4198___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__24379,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_24896',axiom,
! [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__24897] :
( c_24__type__24896___24t(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__24897)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24897,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24959',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24960] :
( c_24__type__24959___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__24960)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24960,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25022',axiom,
! [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__25023] :
( c_24__type__25022___24t(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__25023)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25023,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__25077] :
( c_24__type__25076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__25077)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__25077,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_25139',axiom,
! [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__25140] :
( c_24__type__25139___24t(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__25140)
<=> ! [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__25140,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_2542',axiom,
! [Vvar__2543] :
( c_24__type__2542___24t(Vvar__2543)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2569___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eCpo_2eComplete___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(Vvar__2543,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ) ) ) ) ).
fof('$_type_2569',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2570] :
( c_24__type__2569___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2570)
<=> ( ? [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
& cCoq_2eSets_2eCpo_2eBottom___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) )
=> ( ! [Vv__CANONICAL__4] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ? [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__6) ) ) )
=> t(Vvar__2570,Vv__CANONICAL__2) ) ) ) ).
fof('$_type_25801',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25802] :
( c_24__type__25801___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25802)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25802,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25824',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25825] :
( c_24__type__25824___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25825)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25825,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25847',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25848] :
( c_24__type__25847___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25848)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25848,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_25870',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25871] :
( c_24__type__25870___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25871)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25871,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25888',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25889] :
( c_24__type__25888___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25889)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__25889,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_25914',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25915] :
( c_24__type__25914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25915)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__25915,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_25932',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25933] :
( c_24__type__25932___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__25933)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__25933,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_26042',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26043] :
( c_24__type__26042___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26043)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26043,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26072',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26073] :
( c_24__type__26072___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26073)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26073,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26096',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26097] :
( c_24__type__26096___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26097)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__26097,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_26126',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26127] :
( c_24__type__26126___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26127)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26127,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_26156',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26157] :
( c_24__type__26156___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26157)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26157,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26180',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26181] :
( c_24__type__26180___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26181)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__26181,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_26213',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26214] :
( c_24__type__26213___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26214)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26214,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26237',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26238] :
( c_24__type__26237___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26238)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__26238,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_26264',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26265] :
( c_24__type__26264___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__26265)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__26265,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_26520',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26521] :
( c_24__type__26520___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26521)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26521,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__26646] :
( c_24__type__26645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__26646)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__26646,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_26770',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26771] :
( c_24__type__26770___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__26771)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__26771,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_26895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__26896] :
( c_24__type__26895___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__26896)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__26896,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_27020',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__27021] :
( c_24__type__27020___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__27021)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__14] :
( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
=> t(happ(happ(Vvar__27021,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).
fof('$_type_27145',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27146] :
( c_24__type__27145___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__27146)
<=> ! [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__27146,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).
fof('$_type_27256',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__27257] :
( c_24__type__27256___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vvar__27257)
<=> ! [Vv__CANONICAL__13] :
( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
=> t(happ(Vvar__27257,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).
fof('$_type_27405',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27406] :
( c_24__type__27405___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27406)
<=> ! [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__27406,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_27455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27456] :
( c_24__type__27455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27456)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__27456,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27505',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27506] :
( c_24__type__27505___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27506)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__27506,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_27547',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27548] :
( c_24__type__27547___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27548)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__27548,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_27597',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27598] :
( c_24__type__27597___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27598)
<=> ! [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__27598,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_27673',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27674] :
( c_24__type__27673___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27674)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__27674,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_27782',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27783] :
( c_24__type__27782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27783)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__27783,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_27826',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27827] :
( c_24__type__27826___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27827)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__27827,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_27862',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27863] :
( c_24__type__27862___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27863)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__27863,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_27906',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27907] :
( c_24__type__27906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__27907)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__27907,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_2801',axiom,
! [Vvar__2802] :
( c_24__type__2801___24t(Vvar__2802)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__2829___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> t(happ(happ(happ(happ(Vvar__2802,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ) ) ) ) ).
fof('$_type_28120',axiom,
! [Vvar__28121] :
( c_24__type__28120___24t(Vvar__28121)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__28121,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28163] :
( c_24__type__28162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__28163)
<=> ! [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__28163,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_28257',axiom,
! [Vvar__28258] :
( c_24__type__28257___24t(Vvar__28258)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3131___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__28267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__28258,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28267',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28268] :
( c_24__type__28267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28268)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__28268,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_2829',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2830] :
( c_24__type__2829___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2830)
<=> ( ! [Vv__CANONICAL__3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(Vv__CANONICAL__0,Vv__CANONICAL__3,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> ( ? [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__5) )
=> ? [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
& cCoq_2eSets_2eCpo_2eLub___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) )
=> t(Vvar__2830,Vv__CANONICAL__2) ) ) ).
fof('$_type_28455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28456] :
( c_24__type__28455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__28456)
<=> ! [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__28456,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_28471',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28472] :
( c_24__type__28471___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28472)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__28472,Vv__CANONICAL__2)) ) ) ).
fof('$_type_28475',axiom,
! [Vvar__28476] :
( c_24__type__28475___24t(Vvar__28476)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__28476,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28493',axiom,
! [Vvar__28494] :
( c_24__type__28493___24t(Vvar__28494)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__28494,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_28510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28511] :
( c_24__type__28510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__28511)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__28511,Vv__CANONICAL__2)) ) ) ).
fof('$_type_28514',axiom,
! [Vvar__28515] :
( c_24__type__28514___24t(Vvar__28515)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__28515,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28532',axiom,
! [Vvar__28533] :
( c_24__type__28532___24t(Vvar__28533)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___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__28533,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_28538',axiom,
! [Vvar__28539] :
( c_24__type__28538___24t(Vvar__28539)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__28539,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_28543',axiom,
! [Vvar__28544] :
( c_24__type__28543___24t(Vvar__28544)
<=> ! [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__28544,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_28555',axiom,
! [Vvar__28556] :
( c_24__type__28555___24t(Vvar__28556)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__28556,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28629',axiom,
! [Vvar__28630] :
( c_24__type__28629___24t(Vvar__28630)
<=> ! [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__28630,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2908',axiom,
! [Vvar__2909] :
( c_24__type__2908___24t(Vvar__2909)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__2909,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29092] :
( c_24__type__29091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__29092)
<=> ! [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__29092,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_29099',axiom,
! [Vvar__29100] :
( c_24__type__29099___24t(Vvar__29100)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29100,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29175',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29176] :
( c_24__type__29175___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29176)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29176,Vv__CANONICAL__4)) ) ) ).
fof('$_type_29184',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29185] :
( c_24__type__29184___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29185)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29185,Vv__CANONICAL__4)) ) ) ).
fof('$_type_29189',axiom,
! [Vvar__29190] :
( c_24__type__29189___24t(Vvar__29190)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__29190,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_29305',axiom,
! [Vvar__29306] :
( c_24__type__29305___24t(Vvar__29306)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29306,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2944',axiom,
! [Vvar__2945] :
( c_24__type__2944___24t(Vvar__2945)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(happ(happ(Vvar__2945,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__3) ) ) ) ) ) ) ) ).
fof('$_type_29528',axiom,
! [Vvar__29529] :
( c_24__type__29528___24t(Vvar__29529)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29529,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29531',axiom,
! [Vvar__29532] :
( c_24__type__29531___24t(Vvar__29532)
<=> ! [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__29532,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2954',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2955] :
( c_24__type__2954___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2955)
<=> ( ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__4) )
=> t(Vvar__2955,Vv__CANONICAL__3) ) ) ).
fof('$_type_29557',axiom,
! [Vvar__29558] :
( c_24__type__29557___24t(Vvar__29558)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29558,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29561',axiom,
! [Vvar__29562] :
( c_24__type__29561___24t(Vvar__29562)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__29562,Vv__CANONICAL__0)) ) ) ).
fof('$_type_29591',axiom,
! [Vvar__29592] :
( c_24__type__29591___24t(Vvar__29592)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__14149___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__14149___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__29592,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2990',axiom,
! [Vvar__2991] :
( c_24__type__2990___24t(Vvar__2991)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__2991,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3020',axiom,
! [Vv__CANONICAL__0,Vvar__3021] :
( c_24__type__3020___24t(Vv__CANONICAL__0,Vvar__3021)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__3021,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30323',axiom,
! [Vv__CANONICAL__0,Vvar__30324] :
( c_24__type__30323___24t(Vv__CANONICAL__0,Vvar__30324)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__30324,Vv__CANONICAL__1)) ) ) ).
fof('$_type_30435',axiom,
! [Vv__CANONICAL__0,Vvar__30436] :
( c_24__type__30435___24t(Vv__CANONICAL__0,Vvar__30436)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__30436,Vv__CANONICAL__1)) ) ) ).
fof('$_type_3086',axiom,
! [Vvar__3087] :
( c_24__type__3086___24t(Vvar__3087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eSets_2eRelations__1_2eOrder___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3087,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ) ).
fof('$_type_3101',axiom,
! [Vvar__3102] :
( c_24__type__3101___24t(Vvar__3102)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__3102,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3119',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3120] :
( c_24__type__3119___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__3120)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3120,Vv__CANONICAL__3)) ) ) ).
fof('$_type_3131',axiom,
! [Vv__CANONICAL__0,Vvar__3132] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vvar__3132)
<=> ! [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__3132,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3134',axiom,
! [Vvar__3135] :
( c_24__type__3134___24t(Vvar__3135)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3135,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_314',axiom,
! [Vvar__315] :
( c_24__type__314___24t(Vvar__315)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__315,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3141',axiom,
! [Vvar__3142] :
( c_24__type__3141___24t(Vvar__3142)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__3142,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31484',axiom,
! [Vvar__31485] :
( c_24__type__31484___24t(Vvar__31485)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__31485,Vv__CANONICAL__0)) ) ) ).
fof('$_type_317',axiom,
! [Vvar__318] :
( c_24__type__317___24t(Vvar__318)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2ePartial__Order_2eRel___24t(Vv__CANONICAL__0,happ(happ(Vvar__318,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31812',axiom,
! [Vvar__31813] :
( c_24__type__31812___24t(Vvar__31813)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31813,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3183',axiom,
! [Vvar__3184] :
( c_24__type__3183___24t(Vvar__3184)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3184,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31865',axiom,
! [Vvar__31866] :
( c_24__type__31865___24t(Vvar__31866)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__31866,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31884',axiom,
! [Vvar__31885] :
( c_24__type__31884___24t(Vvar__31885)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eVectors_2eFin_2et___24t(cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__0),happ(Vvar__31885,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31908',axiom,
! [Vvar__31909] :
( c_24__type__31908___24t(Vvar__31909)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__108___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__31909,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3196',axiom,
! [Vvar__3197] :
( c_24__type__3196___24t(Vvar__3197)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__3197,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3198',axiom,
! [Vvar__3199] :
( c_24__type__3198___24t(Vvar__3199)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3199,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3209',axiom,
! [Vvar__3210] :
( c_24__type__3209___24t(Vvar__3210)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3210,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3222',axiom,
! [Vvar__3223] :
( c_24__type__3222___24t(Vvar__3223)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3223,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3225',axiom,
! [Vvar__3226] :
( c_24__type__3225___24t(Vvar__3226)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3226,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3246',axiom,
! [Vvar__3247] :
( c_24__type__3246___24t(Vvar__3247)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3247,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3258',axiom,
! [Vvar__3259] :
( c_24__type__3258___24t(Vvar__3259)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3259,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3277',axiom,
! [Vvar__3278] :
( c_24__type__3277___24t(Vvar__3278)
<=> ! [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__3278,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32787',axiom,
! [Vvar__32788] :
( c_24__type__32787___24t(Vvar__32788)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__1)
=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(happ(Vvar__32788,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3279',axiom,
! [Vvar__3280] :
( c_24__type__3279___24t(Vvar__3280)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__3280,Vv__CANONICAL__0)) ) ) ).
fof('$_type_32816',axiom,
! [Vvar__32817] :
( c_24__type__32816___24t(Vvar__32817)
<=> ! [Vv__CANONICAL__0] :
( cY___24t(Vv__CANONICAL__0)
=> cX___24t(happ(Vvar__32817,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3289',axiom,
! [Vvar__3290] :
( c_24__type__3289___24t(Vvar__3290)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3290,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3305',axiom,
! [Vvar__3306] :
( c_24__type__3305___24t(Vvar__3306)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__3306,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3317',axiom,
! [Vvar__3318] :
( c_24__type__3317___24t(Vvar__3318)
<=> ! [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__3318,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_3329',axiom,
! [Vvar__3330] :
( c_24__type__3329___24t(Vvar__3330)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__3330,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_3349',axiom,
! [Vvar__3350] :
( c_24__type__3349___24t(Vvar__3350)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__3350,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3354',axiom,
! [Vvar__3355] :
( c_24__type__3354___24t(Vvar__3355)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3355,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33563',axiom,
! [Vvar__33564] :
( c_24__type__33563___24t(Vvar__33564)
<=> ! [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__33564,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33568',axiom,
! [Vvar__33569] :
( c_24__type__33568___24t(Vvar__33569)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__33569,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33609',axiom,
! [Vvar__33610] :
( c_24__type__33609___24t(Vvar__33610)
<=> ! [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__33610,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3366',axiom,
! [Vvar__3367] :
( c_24__type__3366___24t(Vvar__3367)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3367,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_33691',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33692] :
( c_24__type__33691___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33692)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__33692,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_33867',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33868] :
( c_24__type__33867___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33868)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ( Vv__CANONICAL__1 = Vv__CANONICAL__2
=> cProp___24t(happ(Vvar__33868,Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33908',axiom,
! [Vvar__33909] :
( c_24__type__33908___24t(Vvar__33909)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33909,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3392',axiom,
! [Vvar__3393] :
( c_24__type__3392___24t(Vvar__3393)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__3393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_342',axiom,
! [Vvar__343] :
( c_24__type__342___24t(Vvar__343)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2ePartial__Order_2ePO___24t(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(Vv__CANONICAL__0),happ(happ(Vvar__343,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3465',axiom,
! [Vvar__3466] :
( c_24__type__3465___24t(Vvar__3466)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__5)
=> cType___24t(happ(happ(happ(happ(happ(happ(Vvar__3466,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_35368',axiom,
! [Vvar__35369] :
( c_24__type__35368___24t(Vvar__35369)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3131___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)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__35369,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_3537',axiom,
! [Vvar__3538] :
( c_24__type__3537___24t(Vvar__3538)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3538,Vv__CANONICAL__0)) ) ) ).
fof('$_type_35399',axiom,
! [Vvar__35400] :
( c_24__type__35399___24t(Vvar__35400)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3131___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)
=> ( p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__35400,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_35430',axiom,
! [Vvar__35431] :
( c_24__type__35430___24t(Vvar__35431)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__3))
=> cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(happ(happ(happ(happ(Vvar__35431,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ) ).
fof('$_type_35439',axiom,
! [Vv__CANONICAL__0,Vvar__35440] :
( c_24__type__35439___24t(Vv__CANONICAL__0,Vvar__35440)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__35440,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_3544',axiom,
! [Vv__CANONICAL__0,Vvar__3545] :
( c_24__type__3544___24t(Vv__CANONICAL__0,Vvar__3545)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__3545,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_3552',axiom,
! [Vvar__3553] :
( c_24__type__3552___24t(Vvar__3553)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__3553,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_3557',axiom,
! [Vvar__3558] :
( c_24__type__3557___24t(Vvar__3558)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__3558,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_3582',axiom,
! [Vv__CANONICAL__0,Vvar__3583] :
( c_24__type__3582___24t(Vv__CANONICAL__0,Vvar__3583)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__3584___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__3585___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(Vvar__3583,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3588',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3589] :
( c_24__type__3588___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__3589)
<=> ( Vv__CANONICAL__1 = Vv__CANONICAL__1
=> cProp___24t(Vvar__3589) ) ) ).
fof('$_type_3926',axiom,
! [Vvar__3927] :
( c_24__type__3926___24t(Vvar__3927)
<=> ! [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__3927,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3931',axiom,
! [Vvar__3932] :
( c_24__type__3931___24t(Vvar__3932)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3932,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3934',axiom,
! [Vvar__3935] :
( c_24__type__3934___24t(Vvar__3935)
<=> ! [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__3935,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4198',axiom,
! [Vv__CANONICAL__0,Vvar__4199] :
( c_24__type__4198___24t(Vv__CANONICAL__0,Vvar__4199)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4199,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4207',axiom,
! [Vv__CANONICAL__0,Vvar__4208] :
( c_24__type__4207___24t(Vv__CANONICAL__0,Vvar__4208)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__4208,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_4215',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4216] :
( c_24__type__4215___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__4216)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__4216,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_4251',axiom,
! [Vvar__4252] :
( c_24__type__4251___24t(Vvar__4252)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__4252,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4262',axiom,
! [Vvar__4263] :
( c_24__type__4262___24t(Vvar__4263)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__4263,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4282',axiom,
! [Vvar__4283] :
( c_24__type__4282___24t(Vvar__4283)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__4283,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_4744',axiom,
! [Vv__CANONICAL__0,Vvar__4745] :
( c_24__type__4744___24t(Vv__CANONICAL__0,Vvar__4745)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__4745,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_4762',axiom,
! [Vvar__4763] :
( c_24__type__4762___24t(Vvar__4763)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4767___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(happ(happ(Vvar__4763,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_4767',axiom,
! [Vv__CANONICAL__0,Vvar__4768] :
( c_24__type__4767___24t(Vv__CANONICAL__0,Vvar__4768)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__4768,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_4991',axiom,
! [Vvar__4992] :
( c_24__type__4991___24t(Vvar__4992)
<=> ! [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__4198___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4198___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__4207___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__4992,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('$_type_5',axiom,
! [Vv__CANONICAL__0,Vvar__6] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vvar__6)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__6,Vv__CANONICAL__1)) ) ) ).
fof('$_type_5009',axiom,
! [Vvar__5010] :
( c_24__type__5009___24t(Vvar__5010)
<=> ! [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__5010,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5027',axiom,
! [Vvar__5028] :
( c_24__type__5027___24t(Vvar__5028)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__5028,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5036',axiom,
! [Vvar__5037] :
( c_24__type__5036___24t(Vvar__5037)
<=> ! [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__5037,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5066',axiom,
! [Vvar__5067] :
( c_24__type__5066___24t(Vvar__5067)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5067,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5077',axiom,
! [Vvar__5078] :
( c_24__type__5077___24t(Vvar__5078)
<=> ! [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__5078,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5080',axiom,
! [Vvar__5081] :
( c_24__type__5080___24t(Vvar__5081)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__5081,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5095',axiom,
! [Vvar__5096] :
( c_24__type__5095___24t(Vvar__5096)
<=> ! [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__5096,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5099',axiom,
! [Vvar__5100] :
( c_24__type__5099___24t(Vvar__5100)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__5100,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_51',axiom,
! [Vvar__52] :
( c_24__type__51___24t(Vvar__52)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__52,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5108',axiom,
! [Vvar__5109] :
( c_24__type__5108___24t(Vvar__5109)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__5109,Vv__CANONICAL__0)) ) ) ).
fof('$_type_513',axiom,
! [Vvar__514] :
( c_24__type__513___24t(Vvar__514)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(happ(happ(Vvar__514,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__4) ) ) ) ) ) ) ) ) ).
fof('$_type_5289',axiom,
! [Vvar__5290] :
( c_24__type__5289___24t(Vvar__5290)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4744___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(Vvar__5290,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_539',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__540] :
( c_24__type__539___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__540)
<=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3)
=> ( ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__3) ) )
=> t(Vvar__540,Vv__CANONICAL__4) ) ) ) ).
fof('$_type_55284',axiom,
! [Vvar__55285] :
( c_24__type__55284___24t(Vvar__55285)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__55285,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5538',axiom,
! [Vvar__5539] :
( c_24__type__5538___24t(Vvar__5539)
<=> ! [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__5539,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5541',axiom,
! [Vvar__5542] :
( c_24__type__5541___24t(Vvar__5542)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__5542,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5546',axiom,
! [Vvar__5547] :
( c_24__type__5546___24t(Vvar__5547)
<=> ! [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__5547,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_56057',axiom,
! [Vvar__56058] :
( c_24__type__56057___24t(Vvar__56058)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eEnvRing_2eMon___24t(happ(happ(Vvar__56058,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_56075',axiom,
! [Vvar__56076] :
( c_24__type__56075___24t(Vvar__56076)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9219___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__1))
=> cProp___24t(happ(happ(happ(happ(Vvar__56076,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_56079',axiom,
! [Vvar__56080] :
( c_24__type__56079___24t(Vvar__56080)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__56080,Vv__CANONICAL__0)) ) ) ).
fof('$_type_56086',axiom,
! [Vvar__56087] :
( c_24__type__56086___24t(Vvar__56087)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3588___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__56087,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_56129',axiom,
! [Vvar__56130] :
( c_24__type__56129___24t(Vvar__56130)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__4198___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4198___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__5)
=> t(happ(happ(happ(happ(happ(happ(Vvar__56130,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_56162',axiom,
! [Vvar__56163] :
( c_24__type__56162___24t(Vvar__56163)
<=> ! [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__4744___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__56163,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_56189',axiom,
! [Vvar__56190] :
( c_24__type__56189___24t(Vvar__56190)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(happ(Vvar__56190,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_56199',axiom,
! [Vv__CANONICAL__0,Vvar__56200] :
( c_24__type__56199___24t(Vv__CANONICAL__0,Vvar__56200)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__56200,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_56332',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__56333] :
( c_24__type__56332___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__56333)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__56333,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_56351',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__56352] :
( c_24__type__56351___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__56352)
<=> ! [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__56352,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_56365',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__56366] :
( c_24__type__56365___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__56366)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__56366,Vv__CANONICAL__4)) ) ) ).
fof('$_type_56428',axiom,
! [Vvar__56429] :
( c_24__type__56428___24t(Vvar__56429)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4744___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)
=> ( happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) )
=> cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(happ(happ(happ(Vvar__56429,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_56448',axiom,
! [Vvar__56449] :
( c_24__type__56448___24t(Vvar__56449)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__30435___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__56449,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_56457',axiom,
! [Vvar__56458] :
( c_24__type__56457___24t(Vvar__56458)
<=> ! [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__56458,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_56462',axiom,
! [Vvar__56463] :
( c_24__type__56462___24t(Vvar__56463)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumor___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__56463,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_56465',axiom,
! [Vvar__56466] :
( c_24__type__56465___24t(Vvar__56466)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(c_24__prop__56467___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__56468___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__56466,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_56481',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56482] :
( c_24__type__56481___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__56482)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__56482,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_6444',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6445] :
( c_24__type__6444___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6445)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__6445,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_6458',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6459] :
( c_24__type__6458___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6459)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__6459,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_6465',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6466] :
( c_24__type__6465___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__6466)
<=> ! [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__6466,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_65',axiom,
! [Vvar__66] :
( c_24__type__65___24t(Vvar__66)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,happ(happ(Vvar__66,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_6886',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__6887] :
( c_24__type__6886___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__6887)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6887,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7',axiom,
! [Vvar__8] :
( c_24__type__7___24t(Vvar__8)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__8,Vv__CANONICAL__0)) ) ) ).
fof('$_type_7099',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7100] :
( c_24__type__7099___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7100)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7100,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7313] :
( c_24__type__7312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7313)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7313,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7508] :
( c_24__type__7507___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7508)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__7508,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_7720',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7721] :
( c_24__type__7720___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__7721)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__7721,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_7933',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7934] :
( c_24__type__7933___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__7934)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__7934,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_795',axiom,
! [Vvar__796] :
( c_24__type__795___24t(Vvar__796)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cType___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(happ(happ(Vvar__796,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__4) ) ) ) ) ) ) ) ) ).
fof('$_type_8146',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8147] :
( c_24__type__8146___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8147)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__8147,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_821',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__822] :
( c_24__type__821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__822)
<=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__3)
=> ( ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__6) ) )
=> t(Vvar__822,Vv__CANONICAL__4) ) ) ) ).
fof('$_type_8359',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8360] :
( c_24__type__8359___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8360)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__8360,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_8554',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8555] :
( c_24__type__8554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8555)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__8555,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_86',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__87] :
( c_24__type__86___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__87)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__87,Vv__CANONICAL__3)) ) ) ).
fof('$_type_8767',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8768] :
( c_24__type__8767___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__8768)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__8768,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_8962',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__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,Vv__CANONICAL__7,Vv__CANONICAL__8,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__8963)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__8963,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_9022',axiom,
! [Vvar__9023] :
( c_24__type__9022___24t(Vvar__9023)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9023,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9060',axiom,
! [Vvar__9061] :
( c_24__type__9060___24t(Vvar__9061)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4198___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__9061,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_9096',axiom,
! [Vvar__9097] :
( c_24__type__9096___24t(Vvar__9097)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eReals_2eRdefinitions_2eR___24t(happ(happ(Vvar__9097,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_9122',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9123] :
( c_24__type__9122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9123)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9123,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9130',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9131] :
( c_24__type__9130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9131)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9131,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9138',axiom,
! [Vvar__9139] :
( c_24__type__9138___24t(Vvar__9139)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__9139,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9172',axiom,
! [Vvar__9173] :
( c_24__type__9172___24t(Vvar__9173)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
=> cCoq_2eInit_2eSpecif_2esig2___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,happ(happ(happ(happ(Vvar__9173,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ) ) ).
fof('$_type_9200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9201] :
( c_24__type__9200___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9201)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9201,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9208',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9209] :
( c_24__type__9208___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__9209)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9209,Vv__CANONICAL__3)) ) ) ).
fof('$_type_9216',axiom,
! [Vvar__9217] :
( c_24__type__9216___24t(Vvar__9217)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9219___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__9217,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9219',axiom,
! [Vv__CANONICAL__0,Vvar__9220] :
( c_24__type__9219___24t(Vv__CANONICAL__0,Vvar__9220)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9220,Vv__CANONICAL__1)) ) ) ).
fof('$_type_9252',axiom,
! [Vvar__9253] :
( c_24__type__9252___24t(Vvar__9253)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__9219___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__9253,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_9270',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9271] :
( c_24__type__9270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9271)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__9271,Vv__CANONICAL__2)) ) ) ).
fof('$_type_9276',axiom,
! [Vvar__9277] :
( c_24__type__9276___24t(Vvar__9277)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5___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__9277,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_9450',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9451] :
( c_24__type__9450___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9451)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9451,Vv__CANONICAL__2)) ) ) ).
fof('$_type_9456',axiom,
! [Vvar__9457] :
( c_24__type__9456___24t(Vvar__9457)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___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__9457,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_9473',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9474] :
( c_24__type__9473___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9474)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__9474,Vv__CANONICAL__2)) ) ) ).
fof('$_type_9479',axiom,
! [Vvar__9480] :
( c_24__type__9479___24t(Vvar__9480)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__9219___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__9480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__1,cCoq_2eInit_2eSpecif_2eprojT1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))) ) ) ) ) ).
fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
c_24__type__5077___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
c_24__type__12599___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
c_24__type__5077___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
c_24__type__12603___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).
fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
c_24__type__14224___24t(cCoq_2eBool_2eBool_2eIs__true) ).
fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
c_24__type__3225___24t(cCoq_2eBool_2eBool_2eeqb) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__14234___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
c_24__type__12593___24t(cCoq_2eBool_2eZerob_2ezerob) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
c_24__type__29531___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__29528___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__12886___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.empty',axiom,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
c_24__type__29531___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
c_24__type__12935___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev_append',axiom,
c_24__type__32787___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
c_24__type__14501___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).
fof('$_typeof_Coq.Init.Datatypes.CompSpecT',axiom,
c_24__type__3465___24t(cCoq_2eInit_2eDatatypes_2eCompSpecT) ).
fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
c_24__type__3392___24t(cCoq_2eInit_2eDatatypes_2eCompareSpecT) ).
fof('$_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.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__3279___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__2908___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__3277___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__3225___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__3366___24t(cCoq_2eInit_2eDatatypes_2eapp) ).
fof('$_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__3354___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__3317___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__14499___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__7___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__3246___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__3349___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__7___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
c_24__type__3225___24t(cCoq_2eInit_2eDatatypes_2eorb) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__3305___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__3289___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__3329___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__3289___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_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('$_typeof_Coq.Init.Datatypes.xorb',axiom,
c_24__type__3225___24t(cCoq_2eInit_2eDatatypes_2exorb) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.compare',axiom,
c_24__type__5036___24t(cCoq_2eInit_2eNat_2ecompare) ).
fof('$_typeof_Coq.Init.Nat.div',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2ediv) ).
fof('$_typeof_Coq.Init.Nat.div2',axiom,
c_24__type__2908___24t(cCoq_2eInit_2eNat_2ediv2) ).
fof('$_typeof_Coq.Init.Nat.double',axiom,
c_24__type__2908___24t(cCoq_2eInit_2eNat_2edouble) ).
fof('$_typeof_Coq.Init.Nat.eqb',axiom,
c_24__type__5027___24t(cCoq_2eInit_2eNat_2eeqb) ).
fof('$_typeof_Coq.Init.Nat.even',axiom,
c_24__type__12593___24t(cCoq_2eInit_2eNat_2eeven) ).
fof('$_typeof_Coq.Init.Nat.gcd',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2egcd) ).
fof('$_typeof_Coq.Init.Nat.max',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2emax) ).
fof('$_typeof_Coq.Init.Nat.min',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2emin) ).
fof('$_typeof_Coq.Init.Nat.mul',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2emul) ).
fof('$_typeof_Coq.Init.Nat.odd',axiom,
c_24__type__12593___24t(cCoq_2eInit_2eNat_2eodd) ).
fof('$_typeof_Coq.Init.Nat.pow',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2epow) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__2908___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.shiftl',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2eshiftl) ).
fof('$_typeof_Coq.Init.Nat.sqrt',axiom,
c_24__type__2908___24t(cCoq_2eInit_2eNat_2esqrt) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__5009___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Nat.testbit',axiom,
c_24__type__5027___24t(cCoq_2eInit_2eNat_2etestbit) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__5077___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__5077___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__28493___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.exist2',axiom,
c_24__type__9172___24t(cCoq_2eInit_2eSpecif_2eexist2) ).
fof('$_typeof_Coq.Init.Specif.existT',axiom,
c_24__type__28532___24t(cCoq_2eInit_2eSpecif_2eexistT) ).
fof('$_typeof_Coq.Init.Specif.existT2',axiom,
c_24__type__9252___24t(cCoq_2eInit_2eSpecif_2eexistT2) ).
fof('$_typeof_Coq.Init.Specif.inleft',axiom,
c_24__type__56457___24t(cCoq_2eInit_2eSpecif_2einleft) ).
fof('$_typeof_Coq.Init.Specif.inright',axiom,
c_24__type__56462___24t(cCoq_2eInit_2eSpecif_2einright) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__28538___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
c_24__type__9276___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).
fof('$_typeof_Coq.Init.Specif.projT1',axiom,
c_24__type__9456___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).
fof('$_typeof_Coq.Init.Specif.projT2',axiom,
c_24__type__9479___24t(cCoq_2eInit_2eSpecif_2eprojT2) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__28543___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__28475___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__9138___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__28514___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__9216___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__11497___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__28555___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__29099___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__17014___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.fold_left',axiom,
c_24__type__17063___24t(cCoq_2eLists_2eList_2efold__left) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__17094___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.List.last',axiom,
c_24__type__56189___24t(cCoq_2eLists_2eList_2elast) ).
fof('$_typeof_Coq.Lists.List.map',axiom,
c_24__type__31908___24t(cCoq_2eLists_2eList_2emap) ).
fof('$_typeof_Coq.Lists.List.nth',axiom,
c_24__type__17039___24t(cCoq_2eLists_2eList_2enth) ).
fof('$_typeof_Coq.Lists.SetoidList.compat_bool',axiom,
c_24__type__56448___24t(cCoq_2eLists_2eSetoidList_2ecompat__bool) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__28257___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.proof_irrelevance',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.prop_extensionality',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__3537___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_dep_eq_on',axiom,
c_24__type__15009___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq',axiom,
c_24__type__56079___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Eq_rect_eq_on',axiom,
c_24__type__56075___24t(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq__on) ).
fof('$_typeof_Coq.Logic.EqdepFacts.Streicher_K_on_',axiom,
c_24__type__56086___24t(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_',axiom,
c_24__type__56079___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
c_24__type__15018___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).
fof('$_typeof_Coq.Logic.EqdepFacts.UIP_refl_on_',axiom,
c_24__type__33908___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__) ).
fof('$_typeof_Coq.NArith.BinNat.N.b2n',axiom,
c_24__type__31484___24t(cCoq_2eNArith_2eBinNat_2eN_2eb2n) ).
fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
c_24__type__12495___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).
fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
c_24__type__12582___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__12495___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__12495___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.compare',axiom,
c_24__type__12426___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
c_24__type__12391___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__12486___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
c_24__type__12435___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.gcd',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2egcd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.log2',axiom,
c_24__type__12391___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elog2) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.modulo',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.odd',axiom,
c_24__type__12435___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eodd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pow',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epow) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
c_24__type__12391___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sqrt',axiom,
c_24__type__12391___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
c_24__type__12403___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__12391___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
c_24__type__12391___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
c_24__type__12486___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
c_24__type__12489___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).
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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__3209___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__3222___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__3222___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__3196___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__3196___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
c_24__type__12835___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__12835___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
c_24__type__12844___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('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
c_24__type__12650___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__12640___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
c_24__type__12725___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
c_24__type__12701___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
c_24__type__12820___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
c_24__type__12640___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
c_24__type__12640___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
c_24__type__12640___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
c_24__type__12832___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
c_24__type__12832___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.pred',axiom,
c_24__type__3196___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2epred) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__12640___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
c_24__type__3196___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
c_24__type__12825___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
c_24__type__18547___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).
fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
c_24__type__5080___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).
fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).
fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
c_24__type__5108___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('$_typeof_Coq.Reals.Rdefinitions.Rdiv',axiom,
c_24__type__5095___24t(cCoq_2eReals_2eRdefinitions_2eRdiv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
c_24__type__5099___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
c_24__type__5099___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
c_24__type__5080___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
c_24__type__5099___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__5099___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rminus',axiom,
c_24__type__5095___24t(cCoq_2eReals_2eRdefinitions_2eRminus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
c_24__type__5095___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
c_24__type__5080___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
c_24__type__5095___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).
fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
c_24__type__18727___24t(cCoq_2eReals_2eRdefinitions_2eup) ).
fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
c_24__type__18841___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).
fof('$_typeof_Coq.Reals.Rpow_def.pow',axiom,
c_24__type__9096___24t(cCoq_2eReals_2eRpow__def_2epow) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__7___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__28120___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Cpo.Complete_rec',axiom,
c_24__type__2542___24t(cCoq_2eSets_2eCpo_2eComplete__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Complete_rect',axiom,
c_24__type__2542___24t(cCoq_2eSets_2eCpo_2eComplete__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Conditionally_complete_rec',axiom,
c_24__type__2801___24t(cCoq_2eSets_2eCpo_2eConditionally__complete__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Conditionally_complete_rect',axiom,
c_24__type__2801___24t(cCoq_2eSets_2eCpo_2eConditionally__complete__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Glb_rec',axiom,
c_24__type__1359___24t(cCoq_2eSets_2eCpo_2eGlb__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Glb_rect',axiom,
c_24__type__1359___24t(cCoq_2eSets_2eCpo_2eGlb__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Lower_Bound_rec',axiom,
c_24__type__795___24t(cCoq_2eSets_2eCpo_2eLower__Bound__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Lower_Bound_rect',axiom,
c_24__type__795___24t(cCoq_2eSets_2eCpo_2eLower__Bound__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Lub_rec',axiom,
c_24__type__1077___24t(cCoq_2eSets_2eCpo_2eLub__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Lub_rect',axiom,
c_24__type__1077___24t(cCoq_2eSets_2eCpo_2eLub__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Totally_ordered_rec',axiom,
c_24__type__1868___24t(cCoq_2eSets_2eCpo_2eTotally__ordered__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Totally_ordered_rect',axiom,
c_24__type__1868___24t(cCoq_2eSets_2eCpo_2eTotally__ordered__rect) ).
fof('$_typeof_Coq.Sets.Cpo.Upper_Bound_rec',axiom,
c_24__type__513___24t(cCoq_2eSets_2eCpo_2eUpper__Bound__rec) ).
fof('$_typeof_Coq.Sets.Cpo.Upper_Bound_rect',axiom,
c_24__type__513___24t(cCoq_2eSets_2eCpo_2eUpper__Bound__rect) ).
fof('$_typeof_Coq.Sets.Ensembles.Add',axiom,
c_24__type__51___24t(cCoq_2eSets_2eEnsembles_2eAdd) ).
fof('$_typeof_Coq.Sets.Ensembles.Complement',axiom,
c_24__type__65___24t(cCoq_2eSets_2eEnsembles_2eComplement) ).
fof('$_typeof_Coq.Sets.Ensembles.Disjoint_rec',axiom,
c_24__type__2944___24t(cCoq_2eSets_2eEnsembles_2eDisjoint__rec) ).
fof('$_typeof_Coq.Sets.Ensembles.Disjoint_rect',axiom,
c_24__type__2944___24t(cCoq_2eSets_2eEnsembles_2eDisjoint__rect) ).
fof('$_typeof_Coq.Sets.Ensembles.Ensemble',axiom,
c_24__type__7___24t(cCoq_2eSets_2eEnsembles_2eEnsemble) ).
fof('$_typeof_Coq.Sets.Ensembles.In',axiom,
c_24__type__12___24t(cCoq_2eSets_2eEnsembles_2eIn) ).
fof('$_typeof_Coq.Sets.Ensembles.Included',axiom,
c_24__type__17___24t(cCoq_2eSets_2eEnsembles_2eIncluded) ).
fof('$_typeof_Coq.Sets.Ensembles.Same_set',axiom,
c_24__type__17___24t(cCoq_2eSets_2eEnsembles_2eSame__set) ).
fof('$_typeof_Coq.Sets.Ensembles.Setminus',axiom,
c_24__type__159___24t(cCoq_2eSets_2eEnsembles_2eSetminus) ).
fof('$_typeof_Coq.Sets.Ensembles.Strict_Included',axiom,
c_24__type__17___24t(cCoq_2eSets_2eEnsembles_2eStrict__Included) ).
fof('$_typeof_Coq.Sets.Ensembles.Subtract',axiom,
c_24__type__51___24t(cCoq_2eSets_2eEnsembles_2eSubtract) ).
fof('$_typeof_Coq.Sets.Partial_Order.Carrier',axiom,
c_24__type__7___24t(cCoq_2eSets_2ePartial__Order_2eCarrier) ).
fof('$_typeof_Coq.Sets.Partial_Order.Carrier_of',axiom,
c_24__type__3101___24t(cCoq_2eSets_2ePartial__Order_2eCarrier__of) ).
fof('$_typeof_Coq.Sets.Partial_Order.Definition_of_PO',axiom,
c_24__type__3086___24t(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO) ).
fof('$_typeof_Coq.Sets.Partial_Order.PO',axiom,
c_24__type__7___24t(cCoq_2eSets_2ePartial__Order_2ePO) ).
fof('$_typeof_Coq.Sets.Partial_Order.Rel_of',axiom,
c_24__type__314___24t(cCoq_2eSets_2ePartial__Order_2eRel__of) ).
fof('$_typeof_Coq.Sets.Partial_Order.Strict_Rel_of',axiom,
c_24__type__317___24t(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of) ).
fof('$_typeof_Coq.Sets.Powerset.Power_set_PO',axiom,
c_24__type__342___24t(cCoq_2eSets_2ePowerset_2ePower__set__PO) ).
fof('$_typeof_Coq.Sets.Relations_1.Antisymmetric',axiom,
c_24__type__3134___24t(cCoq_2eSets_2eRelations__1_2eAntisymmetric) ).
fof('$_typeof_Coq.Sets.Relations_1.Reflexive',axiom,
c_24__type__3134___24t(cCoq_2eSets_2eRelations__1_2eReflexive) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__7___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Sets.Relations_1.Transitive',axiom,
c_24__type__3134___24t(cCoq_2eSets_2eRelations__1_2eTransitive) ).
fof('$_typeof_Coq.Sets.Relations_1.contains',axiom,
c_24__type__3141___24t(cCoq_2eSets_2eRelations__1_2econtains) ).
fof('$_typeof_Coq.Sets.Relations_1.same_relation',axiom,
c_24__type__3141___24t(cCoq_2eSets_2eRelations__1_2esame__relation) ).
fof('$_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__11527___24t(cCoq_2eStrings_2eString_2eString) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__18439___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedType.EQ',axiom,
c_24__type__35399___24t(cCoq_2eStructures_2eOrderedType_2eEQ) ).
fof('$_typeof_Coq.Structures.OrderedType.GT',axiom,
c_24__type__35430___24t(cCoq_2eStructures_2eOrderedType_2eGT) ).
fof('$_typeof_Coq.Structures.OrderedType.LT',axiom,
c_24__type__35368___24t(cCoq_2eStructures_2eOrderedType_2eLT) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
c_24__type__12495___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).
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__5077___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
c_24__type__5077___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
c_24__type__12835___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_dec',axiom,
c_24__type__56465___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq__dec) ).
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__12835___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.eq',axiom,
c_24__type__55284___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2eeq) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
c_24__type__55284___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
c_24__type__3183___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).
fof('$_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('$_typeof_Coq.Vectors.Fin.F1',axiom,
c_24__type__31884___24t(cCoq_2eVectors_2eFin_2eF1) ).
fof('$_typeof_Coq.Vectors.Fin.t',axiom,
c_24__type__14248___24t(cCoq_2eVectors_2eFin_2et) ).
fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
c_24__type__11600___24t(cCoq_2eVectors_2eVectorDef_2econs) ).
fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
c_24__type__11592___24t(cCoq_2eVectors_2eVectorDef_2enil) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__11575___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.Bezout',axiom,
c_24__type__29189___24t(cCoq_2eZArith_2eBinInt_2eZ_2eBezout) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.b2z',axiom,
c_24__type__31865___24t(cCoq_2eZArith_2eBinInt_2eZ_2eb2z) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
c_24__type__29591___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__13567___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.eqb',axiom,
c_24__type__12354___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
c_24__type__12354___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.log2',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
c_24__type__29557___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__31812___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.quot',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equot) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.rem',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2erem) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sqrt',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__13531___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__12388___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
c_24__type__29561___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__12354___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.ZArith.Zdiv.Remainder',axiom,
c_24__type__3183___24t(cCoq_2eZArith_2eZdiv_2eRemainder) ).
fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
c_24__type__18841___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).
fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
c_24__type__29305___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__7___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.Env.jump',axiom,
c_24__type__3552___24t(cCoq_2emicromega_2eEnv_2ejump) ).
fof('$_typeof_Coq.micromega.Env.nth',axiom,
c_24__type__3557___24t(cCoq_2emicromega_2eEnv_2enth) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
c_24__type__33563___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).
fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
c_24__type__14862___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).
fof('$_typeof_Coq.micromega.EnvRing.PEsub',axiom,
c_24__type__33568___24t(cCoq_2emicromega_2eEnvRing_2ePEsub) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__7___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
c_24__type__14920___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).
fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
c_24__type__14912___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).
fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
c_24__type__33609___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__7___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__56057___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).
fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
c_24__type__56057___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__18772___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__7___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_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.PolEnv',axiom,
c_24__type__7___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__28629___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__3926___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__3934___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__3931___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__7___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__4762___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.condition',axiom,
c_24__type__4282___24t(cCoq_2esetoid__ring_2eField__theory_2econdition) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.denum',axiom,
c_24__type__4262___24t(cCoq_2esetoid__ring_2eField__theory_2edenum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
c_24__type__7___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.mk_linear',axiom,
c_24__type__4251___24t(cCoq_2esetoid__ring_2eField__theory_2emk__linear) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.num',axiom,
c_24__type__4262___24t(cCoq_2esetoid__ring_2eField__theory_2enum) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
c_24__type__7___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__56129___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__4991___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
c_24__type__56162___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).
fof('$_typeof_Coq.setoid_ring.Ring.bool_eq',axiom,
c_24__type__3225___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.PEO',axiom,
c_24__type__24330___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__5541___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__5546___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__5538___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__5546___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__24339___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__5546___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__7___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__5289___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__7___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_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.Computational',axiom,
c_24__type__56428___24t(cCoq_2esetoid__ring_2eRing__theory_2eComputational) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
c_24__type__9022___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
c_24__type__9022___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
c_24__type__9060___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
c_24__type__12391___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
c_24__type__24378___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__24357___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_X',axiom,
cType___24t(cX) ).
fof('$_typeof_Y',axiom,
cType___24t(cY) ).
fof('$_typeof_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble',axiom,
c_24__type__2990___24t(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble) ).
fof('$_typeof_ZornsLemma.Families.Family',axiom,
c_24__type__7___24t(cZornsLemma_2eFamilies_2eFamily) ).
fof('$_typeof_ZornsLemma.InverseImage.inverse_image',axiom,
c_24__type__104___24t(cZornsLemma_2eInverseImage_2einverse__image) ).
fof('$_typeof_f',axiom,
c_24__type__2___24t(cf) ).
fof('$_typeof_g',axiom,
c_24__type__32816___24t(cg) ).
fof('Coq.Arith.Compare_dec.not_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.EqNat.eq_nat_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V0__n,V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Arith.Gt.gt_0_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO)
| cCoq_2eInit_2eDatatypes_2eO = V0__n ) ) ).
fof('Coq.Arith.Gt.gt_le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V1__m,V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m) ) ) ) ).
fof('Coq.Arith.Gt.gt_n_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2egt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Arith.Le.le_S_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.Lt.S_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)
=> V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) ) ) ) ).
fof('Coq.Arith.Lt.le_lt_or_eq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.nat_total_order',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V2__z)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_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.eq_trans',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.add_assoc',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_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V0__n),cCoq_2eInit_2eNat_2eadd___24a2(V2__p,V1__m)) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_sub_eq_l',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_2eNat_2eadd___24a2(V1__m,V2__p) = V0__n
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m) = V2__p ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5009,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__2908,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2eadd) ).
fof('Coq.Arith.PeanoNat.Nat.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__32774___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_stepl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( V0__x = V1__y
=> ( V0__x = V2__z
=> V2__z = V1__y ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2egcd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2egcd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.le_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)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eInit_2ePeano_2ele___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_stepr',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)
<=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5077,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3258,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2ele) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.Arith.PeanoNat.Nat.lt_0_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).
fof('Coq.Arith.PeanoNat.Nat.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
<=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_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)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__z)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_total',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5077,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3258,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cProp,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3c_3d_3e)),cCoq_2eInit_2ePeano_2elt) ).
fof('Coq.Arith.PeanoNat.Nat.max_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.max_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.max_spec',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
& cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
& cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.max_unicity',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)
& V2__p = V1__m )
| ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
& V2__p = V0__n ) )
=> V2__p = cCoq_2eInit_2eNat_2emax___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.max_unicity_ext',axiom,
! [V0__f] :
( c_24__type__5009___24t(V0__f)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( cCoq_2eInit_2ePeano_2elt___24a2(V1__n,V2__m)
& happ(happ(V0__f,V1__n),V2__m) = V2__m )
| ( cCoq_2eInit_2ePeano_2ele___24a2(V2__m,V1__n)
& happ(happ(V0__f,V1__n),V2__m) = V1__n ) ) ) )
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> happ(happ(V0__f,V2__n),V3__m) = cCoq_2eInit_2eNat_2emax___24a2(V2__n,V3__m) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.min_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.min_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
=> cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.min_spec',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
& cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
& cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.min_unicity',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)
& V2__p = V0__n )
| ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)
& V2__p = V1__m ) )
=> V2__p = cCoq_2eInit_2eNat_2emin___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.min_unicity_ext',axiom,
! [V0__f] :
( c_24__type__5009___24t(V0__f)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( ( cCoq_2eInit_2ePeano_2elt___24a2(V1__n,V2__m)
& happ(happ(V0__f,V1__n),V2__m) = V1__n )
| ( cCoq_2eInit_2ePeano_2ele___24a2(V2__m,V1__n)
& happ(happ(V0__f,V1__n),V2__m) = V2__m ) ) ) )
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
=> happ(happ(V0__f,V2__n),V3__m) = cCoq_2eInit_2eNat_2emin___24a2(V2__n,V3__m) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mod_small',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( cCoq_2eInit_2ePeano_2elt___24a2(V0__a,V1__b)
=> cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,V1__b) = V0__a ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eO ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__n) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_assoc',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_2eNat_2emul___24a2(V0__n,cCoq_2eInit_2eNat_2emul___24a2(V1__m,V2__p)) = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_cancel_l',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)
=> ( V2__p != cCoq_2eInit_2eDatatypes_2eO
=> ( cCoq_2eInit_2eNat_2emul___24a2(V2__p,V0__n) = cCoq_2eInit_2eNat_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mul_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5009,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__2908,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat))),cCoq_2eInit_2eNat_2emul) ).
fof('Coq.Arith.PeanoNat.Nat.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.neq_sym',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).
fof('Coq.Arith.PeanoNat.Nat.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2epow___24a2(V0__a,V1__b) != cCoq_2eInit_2eDatatypes_2eO ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.pred_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2epred___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2eNat_2esub___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) = V0__n ) ).
fof('Coq.Arith.PeanoNat.Nat.sub_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2esub___24a2(V1__m,V0__n),V0__n) = V1__m ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
=> ( cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( V0__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.Arith.PeanoNat.Nat.succ_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__2908,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)),cCoq_2eInit_2eDatatypes_2eS) ).
fof('Coq.Arith.PeanoNat.Nat.two_succ',axiom,
cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).
fof('Coq.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.andb_true_r',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b,cCoq_2eInit_2eDatatypes_2etrue) = V0__b ) ).
fof('Coq.Bool.Bool.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Bool.Bool.eq_iff_eq_true',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( V0__b1 = V1__b2
<=> ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Bool.Bool.eq_true_iff_eq',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
<=> V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> V0__b1 = V1__b2 ) ) ) ).
fof('Coq.Bool.Bool.negb_sym',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ! [V1__b_27] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
=> ( V1__b_27 = cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b)
=> V0__b = cCoq_2eInit_2eDatatypes_2enegb___24a1(V1__b_27) ) ) ) ).
fof('Coq.Bool.Bool.negb_true_iff',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( cCoq_2eInit_2eDatatypes_2enegb___24a1(V0__b) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.not_false_is_true',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2efalse
=> V0__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ).
fof('Coq.Bool.Bool.not_true_is_false',axiom,
! [V0__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
=> ( V0__b != cCoq_2eInit_2eDatatypes_2etrue
=> V0__b = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('Coq.Bool.Bool.orb_true_intro',axiom,
! [V0__b1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ! [V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
| V1__b2 = cCoq_2eInit_2eDatatypes_2etrue )
=> cCoq_2eInit_2eDatatypes_2eorb___24a2(V0__b1,V1__b2) = 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.andb_prop',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b)
=> ( cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2etrue
=> ( V0__a = cCoq_2eInit_2eDatatypes_2etrue
& V1__b = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).
fof('Coq.Init.Datatypes.comparison_eq_stable',axiom,
! [V0__c] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V0__c)
=> ! [V1__c_27] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V1__c_27)
=> ( ~ ( V0__c != V1__c_27 )
=> V0__c = V1__c_27 ) ) ) ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__30323___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__3258___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal2_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__56199___24t(V0__B,V1__f)
=> ! [V2__x1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x1)
=> ! [V3__y1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y1)
=> ! [V4__x2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x2)
=> ! [V5__y2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__y2)
=> ( V2__x1 = V3__y1
=> ( V4__x2 = V5__y2
=> happ(happ(V1__f,V2__x1),V4__x2) = happ(happ(V1__f,V3__y1),V5__y2) ) ) ) ) ) ) ) ) ).
fof('Coq.Init.Peano.f_equal_nat',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__18520___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ) ).
fof('Coq.Init.Peano.le_n',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).
fof('Coq.Init.Peano.not_eq_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n != V1__m
=> cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n) != cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m) ) ) ) ).
fof('Coq.Init.Specif.proj2_sig',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__5___24t(V0__A,V1__P)
=> ! [V2__e] :
( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
=> p(happ(V1__P,cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e))) ) ) ) ).
fof('Coq.Lists.List.map_ext',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__108___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__108___24t(V0__A,V1__B,V3__g)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> happ(V2__f,V4__a) = happ(V3__g,V4__a) )
=> ! [V5__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V5__l) = cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V3__g,V5__l) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.Build_has_fixpoint',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( ( ( p(V0__A)
=> p(V0__A) )
=> p(V0__A) )
=> ( ( ( p(V0__A)
=> p(V0__A) )
=> c_24Proof = c_24Proof )
=> cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(V0__A) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.Build_retract',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ( p(V1__B)
=> p(V0__A) )
=> ( ( p(V1__B)
=> c_24Proof = c_24Proof )
=> cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(V0__A,V1__B) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.aux',axiom,
! [V0__bool] :
( cProp___24t(V0__bool)
=> ( p(V0__bool)
=> ( p(V0__bool)
=> ( ! [V3__C] :
( cProp___24t(V3__C)
=> ( p(V3__C)
=> ( p(V3__C)
=> ( p(V0__bool)
=> p(V3__C) ) ) ) )
=> ( ! [V4__C] :
( cProp___24t(V4__C)
=> ( p(V4__C)
=> ( p(V4__C)
=> c_24Proof = c_24Proof ) ) )
=> ( ! [V5__C] :
( cProp___24t(V5__C)
=> ( p(V5__C)
=> ( p(V5__C)
=> c_24Proof = c_24Proof ) ) )
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
=> ( ! [V7__P] :
( c_24__type__14322___24t(V0__bool,V7__P)
=> ( p(V7__P)
=> ( p(V7__P)
=> ( p(V0__bool)
=> p(V7__P) ) ) ) )
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.ext_prop_dep_proof_irrel_gen',axiom,
! [V0__bool] :
( cProp___24t(V0__bool)
=> ( p(V0__bool)
=> ( p(V0__bool)
=> ( ! [V3__C] :
( cProp___24t(V3__C)
=> ( p(V3__C)
=> ( p(V3__C)
=> ( p(V0__bool)
=> p(V3__C) ) ) ) )
=> ( ! [V4__C] :
( cProp___24t(V4__C)
=> ( p(V4__C)
=> ( p(V4__C)
=> c_24Proof = c_24Proof ) ) )
=> ( ! [V5__C] :
( cProp___24t(V5__C)
=> ( p(V5__C)
=> ( p(V5__C)
=> c_24Proof = c_24Proof ) ) )
=> ( p(cCoq_2eLogic_2eClassicalFacts_2eprop__extensionality)
=> ( ! [V7__P] :
( c_24__type__14322___24t(V0__bool,V7__P)
=> ( p(V7__P)
=> ( p(V7__P)
=> ( p(V0__bool)
=> p(V7__P) ) ) ) )
=> p(cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.p2p1',axiom,
! [V0__or] :
( c_24__type__14331___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__P] :
( c_24__type__14394___24t(V0__or,V5__A,V6__B,V7__P)
=> ( ( p(V5__A)
=> p(V7__P) )
=> ( ( p(V6__B)
=> p(V7__P) )
=> ( p(happ(happ(V0__or,V5__A),V6__B))
=> p(V7__P) ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> p(happ(happ(V0__or,V6__A),c_24__prop__55887___24a1(V6__A))) )
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ( p(V7__B)
=> ( p(V7__B)
=> ! [V10__A] :
( cProp___24t(V10__A)
=> ( p(V10__A)
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.p2p2',axiom,
! [V0__or] :
( c_24__type__14331___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V5__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__P] :
( c_24__type__14394___24t(V0__or,V5__A,V6__B,V7__P)
=> ( ( p(V5__A)
=> p(V7__P) )
=> ( ( p(V6__B)
=> p(V7__P) )
=> ( p(happ(happ(V0__or,V5__A),V6__B))
=> p(V7__P) ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> p(happ(happ(V0__or,V6__A),c_24__prop__55955___24a1(V6__A))) )
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ( p(V7__B)
=> ( p(V7__B)
=> ( c_24Proof != c_24Proof
=> ! [V11__A] :
( cProp___24t(V11__A)
=> ( c_24Proof = c_24Proof
=> p(V11__A) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__14331___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__C] :
( cProp___24t(V7__C)
=> ( ( p(V5__A)
=> p(V7__C) )
=> ( ( p(V6__B)
=> p(V7__C) )
=> ( p(V6__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ! [V8__P] :
( c_24__type__14394___24t(V0__or,V6__A,V7__B,V8__P)
=> ( ( p(V6__A)
=> p(V8__P) )
=> ( ( p(V7__B)
=> p(V8__P) )
=> ( p(happ(happ(V0__or,V6__A),V7__B))
=> p(V8__P) ) ) ) ) ) )
=> ( ! [V7__A] :
( cProp___24t(V7__A)
=> p(happ(happ(V0__or,V7__A),c_24__prop__14419___24a1(V7__A))) )
=> ! [V8__B] :
( cProp___24t(V8__B)
=> ( p(V8__B)
=> ( p(V8__B)
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wproof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__14331___24t(V0__or)
=> ( ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( p(V1__A)
=> p(happ(happ(V0__or,V1__A),V2__B)) ) ) )
=> ( ! [V2__A] :
( cProp___24t(V2__A)
=> ! [V3__B] :
( cProp___24t(V3__B)
=> ( p(V3__B)
=> p(happ(happ(V0__or,V2__A),V3__B)) ) ) )
=> ( ! [V3__A] :
( cProp___24t(V3__A)
=> ! [V4__B] :
( cProp___24t(V4__B)
=> ! [V5__C] :
( cProp___24t(V5__C)
=> ( ( p(V3__A)
=> p(V5__C) )
=> ( ( p(V4__B)
=> p(V5__C) )
=> ( p(happ(happ(V0__or,V3__A),V4__B))
=> p(V5__C) ) ) ) ) ) )
=> ( ! [V4__A] :
( cProp___24t(V4__A)
=> ! [V5__B] :
( cProp___24t(V5__B)
=> ! [V6__C] :
( cProp___24t(V6__C)
=> ( ( p(V4__A)
=> p(V6__C) )
=> ( ( p(V5__B)
=> p(V6__C) )
=> ( p(V4__A)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V5__A] :
( cProp___24t(V5__A)
=> ! [V6__B] :
( cProp___24t(V6__B)
=> ! [V7__C] :
( cProp___24t(V7__C)
=> ( ( p(V5__A)
=> p(V7__C) )
=> ( ( p(V6__B)
=> p(V7__C) )
=> ( p(V6__B)
=> c_24Proof = c_24Proof ) ) ) ) ) )
=> ( ! [V6__A] :
( cProp___24t(V6__A)
=> ! [V7__B] :
( cProp___24t(V7__B)
=> ! [V8__P] :
( c_24__type__14394___24t(V0__or,V6__A,V7__B,V8__P)
=> ( ( p(V6__A)
=> p(V8__P) )
=> ( ( p(V7__B)
=> p(V8__P) )
=> ( p(happ(happ(V0__or,V6__A),V7__B))
=> p(V8__P) ) ) ) ) ) )
=> ( ! [V7__A] :
( cProp___24t(V7__A)
=> p(happ(happ(V0__or,c_24__prop__56053___24a1(V7__A)),c_24__prop__56054___24a1(V7__A))) )
=> ! [V8__B] :
( cProp___24t(V8__B)
=> ( p(V8__B)
=> ( p(V8__B)
=> ~ ( c_24Proof != c_24Proof ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__5___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.Eq_rect_eq.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__9219___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.Streicher_K',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__3588___24t(V0__U,V1__x,V2__P)
=> ( p(happ(V2__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x)))
=> ( V1__x = V1__x
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.UIP',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> ( V1__x = V2__y
=> c_24Proof = c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.UIP_refl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ( V1__x = V1__x
=> c_24Proof = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__U,V1__x) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.eq_dep_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9219___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> ! [V4__y] :
( t(V4__y,happ(V1__P,V2__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V4__y)
=> V3__x = V4__y ) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.eq_rec_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__9219___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.EqdepTheory.eq_rect_eq',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( t(V1__p,V0__U)
=> ! [V2__Q] :
( c_24__type__9219___24t(V0__U,V2__Q)
=> ! [V3__x] :
( t(V3__x,happ(V2__Q,V1__p))
=> ( V1__p = V1__p
=> V3__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__U,V1__p,V2__Q,V3__x,V1__p) ) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Classical_Prop.proof_irrelevance',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
=> ( p(V0__P)
=> c_24Proof = c_24Proof ) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.EqdepFacts.UIP_shift_on',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( t(V1__x,V0__X)
=> ( cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V0__X,V1__x)
=> ( V1__x = V1__x
=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a1(c_24__prop__33910___24a2(V0__X,V1__x)) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__9219___24t(V0__U,V1__P)
=> ! [V2__p] :
( t(V2__p,V0__U)
=> ! [V3__x] :
( t(V3__x,happ(V1__P,V2__p))
=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.eq_indd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__P] :
( c_24__type__33867___24t(V0__A,V1__x,V2__P)
=> ( p(happ(happ(V2__P,V1__x),cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( V1__x = V4__y
=> p(happ(V2__P,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Logic.EqdepFacts.internal_eq_sym_internal',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
=> V2__y = V1__x ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__3588___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__P] :
( c_24__type__3588___24t(V0__A,V1__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V1__x)))
=> ( V1__x = V1__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_set',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__3582___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__3588___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.K_dec_type',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__3582___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__3588___24t(V0__A,V2__x,V3__P)
=> ( p(happ(V3__P,cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__x)))
=> ( V2__x = V2__x
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.UIP_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__3582___24t(V0__A,V1___24Anonymous)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_dep_eq_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__3582___24t(V0__A,V1___24Anonymous)
=> ! [V2__P] :
( c_24__type__9219___24t(V0__A,V2__P)
=> ! [V3__p] :
( t(V3__p,V0__A)
=> ! [V4__x] :
( t(V4__x,happ(V2__P,V3__p))
=> ! [V5__y] :
( t(V5__y,happ(V2__P,V3__p))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__A,V2__P,V3__p,V4__x,V3__p,V5__y)
=> V4__x = V5__y ) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ( ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) ) )
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V2__x = V3__y
=> ( V2__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_proofs_unicity_on',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ( ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
| V1__x != V2__y ) )
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( V1__x = V3__y
=> ( V1__x = V3__y
=> c_24Proof = c_24Proof ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.eq_rect_eq_dec',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1___24Anonymous] :
( c_24__type__3582___24t(V0__A,V1___24Anonymous)
=> ! [V2__p] :
( t(V2__p,V0__A)
=> ! [V3__Q] :
( c_24__type__9219___24t(V0__A,V3__Q)
=> ! [V4__x] :
( t(V4__x,happ(V3__Q,V2__p))
=> ( V2__p = V2__p
=> V4__x = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V0__A,V2__p,V3__Q,V4__x,V2__p) ) ) ) ) ) ) ).
fof('Coq.Logic.Eqdep_dec.trans_sym_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__y] :
( t(V2__y,V0__A)
=> ( V1__x = V2__y
=> cCoq_2eInit_2eLogic_2eeq__ind___24a4(V0__A,V1__x,c_24__lam__33928___24a2(V0__A,V2__y),V2__y) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V0__A,V2__y) ) ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PredExt_imp_PropExt',axiom,
( ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__5___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__5___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
<=> p(happ(V2__Q,V3__x)) ) )
=> V1__P = V2__Q ) ) ) )
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ! [V2__B] :
( cProp___24t(V2__B)
=> ( ( p(V1__A)
<=> p(V2__B) )
=> V1__A = V2__B ) ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PredExt_imp_PropFunExt',axiom,
( ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__5___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__5___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
<=> p(happ(V2__Q,V3__x)) ) )
=> V1__P = V2__Q ) ) ) )
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__P] :
( c_24__type__5___24t(V1__A,V2__P)
=> ! [V3__Q] :
( c_24__type__5___24t(V1__A,V3__Q)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> happ(V2__P,V4__x) = happ(V3__Q,V4__x) )
=> V2__P = V3__Q ) ) ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PropExt_and_PropFunExt_iff_PredExt',axiom,
( ( ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) )
& ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__5___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__5___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> happ(V1__P,V3__x) = happ(V2__Q,V3__x) )
=> V1__P = V2__Q ) ) ) ) )
<=> ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__5___24t(V0__A,V1__P)
=> ! [V2__Q] :
( c_24__type__5___24t(V0__A,V2__Q)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
<=> p(happ(V2__Q,V3__x)) ) )
=> V1__P = V2__Q ) ) ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PropExt_and_PropFunExt_imp_PredExt',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) )
=> ( ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__P] :
( c_24__type__5___24t(V1__A,V2__P)
=> ! [V3__Q] :
( c_24__type__5___24t(V1__A,V3__Q)
=> ( ! [V4__x] :
( t(V4__x,V1__A)
=> happ(V2__P,V4__x) = happ(V3__Q,V4__x) )
=> V2__P = V3__Q ) ) ) )
=> ! [V2__A] :
( cType___24t(V2__A)
=> ! [V3__P] :
( c_24__type__5___24t(V2__A,V3__P)
=> ! [V4__Q] :
( c_24__type__5___24t(V2__A,V4__Q)
=> ( ! [V5__x] :
( t(V5__x,V2__A)
=> ( p(happ(V3__P,V5__x))
<=> p(happ(V4__Q,V5__x)) ) )
=> V3__P = V4__Q ) ) ) ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PropExt_imp_ProvPropExt',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) )
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ( p(V1__A)
=> V1__A = c_24True ) ) ) ).
fof('Coq.Logic.PropExtensionalityFacts.PropExt_imp_RefutPropExt',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( p(V0__A)
<=> p(V1__B) )
=> V0__A = V1__B ) ) )
=> ! [V1__A] :
( cProp___24t(V1__A)
=> ( ~ p(V1__A)
=> V1__A = c_24False ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.IsTotal.lt_total',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.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V2__z)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.eq_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.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.NArith.BinNat.N.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.NArith.BinNat.N.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eN0) = V0__n ) ).
fof('Coq.NArith.BinNat.N.add_assoc',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_2eBinNatDef_2eN_2eadd___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
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.eq_decidable',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__32772___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.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.eqb_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
<=> V0__n = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.le_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).
fof('Coq.NArith.BinNat.N.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_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_preorder',axiom,
cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.le_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)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12495,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__12499,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,cProp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),c_3c_3d_3e)),cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('Coq.NArith.BinNat.N.lt_0_1',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).
fof('Coq.NArith.BinNat.N.lt_1_2',axiom,
cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).
fof('Coq.NArith.BinNat.N.lt_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
<=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_le_trans',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_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)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__z)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_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.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.max_r',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_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.max_spec',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_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V1__m )
| ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
& cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.NArith.BinNat.N.min_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.min_r',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(V1__m,V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.NArith.BinNat.N.min_spec',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_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V0__n )
| ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n)
& cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mod_small',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__a,V1__b)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V0__a,V1__b) = V0__a ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ).
fof('Coq.NArith.BinNat.N.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.NArith.BinNat.N.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.mul_assoc',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_2eBinNatDef_2eN_2emul___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V2__p)) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_cancel_l',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)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eN0
=> ( cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V0__n) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_0_lt_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ) ).
fof('Coq.NArith.BinNat.N.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.NArith.BinNat.N.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eN0) ).
fof('Coq.NArith.BinNat.N.pow_nonzero',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V0__a,V1__b) != cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).
fof('Coq.NArith.BinNat.N.pred_succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) = V0__n ) ).
fof('Coq.NArith.BinNat.N.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eN0
=> cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n)) = V0__n ) ) ).
fof('Coq.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__3198___24t(V0__P)
=> ( ! [V1__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
=> ( p(happ(V0__P,V1__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exI___24a1(V1__p))) ) )
=> ( ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__p)
=> ( p(happ(V0__P,V2__p))
=> p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exO___24a1(V2__p))) ) )
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2exH))
=> ! [V4__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__p)
=> p(happ(V0__P,V4__p)) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_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.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V1__y,V0__x)
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V1__y)
=> ( V0__x != V1__y
=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.PArith.BinPos.Pos.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.PArith.BinPos.Pos.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.PArith.BinPos.Pos.iter_swap_gen',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__108___24t(V0__A,V1__B,V2__f)
=> ! [V3__g] :
( c_24__type__56481___24t(V0__A,V1__B,V3__g)
=> ! [V4__h] :
( c_24__type__6458___24t(V0__A,V1__B,V4__h)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> happ(V2__f,happ(V3__g,V5__a)) = happ(V4__h,happ(V2__f,V5__a)) )
=> ! [V6__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> happ(V2__f,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V0__A,V3__g,V7__a,V6__p)) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__B,V4__h,happ(V2__f,V7__a),V6__p) ) ) ) ) ) ) ) ) ).
fof('Coq.PArith.BinPos.Pos.lt_total',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__p,V1__q)
| V0__p = V1__q
| cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p) ) ) ) ).
fof('Coq.PArith.Pnat.Pos2Nat.inj',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__p) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V1__q)
=> V0__p = V1__q ) ) ) ).
fof('Coq.QArith.QArith_base.Q_Setoid',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eQArith_2eQArith__base_2eQ,cCoq_2eQArith_2eQArith__base_2eQeq) ).
fof('Coq.Reals.RIneq.IZR_neq',axiom,
! [V0__z1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z1)
=> ! [V1__z2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__z2)
=> ( V0__z1 != V1__z2
=> cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z1) != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__z2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_dec',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
| V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_ge_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V0__r1 = V1__r2
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Req_le_sym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( V1__r2 = V0__r1
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Rge_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRge___24a2(V0__r1,V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1) ) ) ) ).
fof('Coq.Reals.RIneq.Rgt_not_eq',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2)
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rle_antisym',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRle___24a2(V1__r2,V0__r1)
=> V0__r1 = V1__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_dichotomy_converse',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2) )
=> V0__r1 != V1__r2 ) ) ) ).
fof('Coq.Reals.RIneq.Rlt_irrefl',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ~ cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r,V0__r) ) ).
fof('Coq.Reals.RIneq.Rlt_le',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.Ropp_involutive',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V0__r)) = V0__r ) ).
fof('Coq.Reals.RIneq.Rplus_eq_compat_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( V1__r1 = V2__r2
=> cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2) ) ) ) ) ).
fof('Coq.Reals.RIneq.Rplus_eq_reg_l',axiom,
! [V0__r] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r)
=> ! [V1__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r1)
=> ! [V2__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V1__r1) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V0__r,V2__r2)
=> V1__r1 = V2__r2 ) ) ) ) ).
fof('Coq.Reals.RIneq.Rtotal_order',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> ( cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V0__r1,V1__r2)
| V0__r1 = V1__r2
| cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V0__r1,V1__r2) ) ) ) ).
fof('Coq.Reals.RIneq.eq_IZR',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__n) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.Reals.RIneq.f_equal_R',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__f] :
( c_24__type__35439___24t(V0__B,V1__f)
=> ! [V2__x] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V3__y)
=> ( V2__x = V3__y
=> happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).
fof('Coq.Reals.Raxioms.Rmult_comm',axiom,
! [V0__r1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V0__r1)
=> ! [V1__r2] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V1__r2)
=> cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V0__r1,V1__r2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V1__r2,V0__r1) ) ) ).
fof('Coq.Sets.Classical_sets.Complement_Complement',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__U,V1__A)) = V1__A ) ) ).
fof('Coq.Sets.Classical_sets.Included_Strict_Included',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y)
| V1__X = V2__Y ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Inhabited_Setminus',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__Y,V1__X)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Strict_Included_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
& cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Strict_super_set_contains_new_element',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> ( V1__X != V2__Y
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V2__Y,V1__X)) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Subtract_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
=> ( V2__x != V3__y
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__A,V2__x),V3__y) ) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.Subtract_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__A,V2__x),V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
& V2__x != V3__y ) ) ) ) ) ) ).
fof('Coq.Sets.Classical_sets.not_SIncl_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ~ cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) ) ) ).
fof('Coq.Sets.Classical_sets.not_empty_Inhabited',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( V1__A != cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__A) ) ) ) ).
fof('Coq.Sets.Classical_sets.not_included_empty_Inhabited',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__A) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_intro1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_intro2',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V2__x) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__y)
| V2__x = V3__y ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Add_not_Empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x) != cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Extension',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ( V1__B = V2__C
=> cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__B,V2__C) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Included_Empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__A) ) ) ).
fof('Coq.Sets.Constructive_sets.Inhabited_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x)) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Inhabited_not_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__X)
=> V1__X != cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Intersection_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Noone_in_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Constructive_sets.Setminus_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__U,V1__A,V2__B),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Singleton_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( V1__x = V2__y
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V2__y) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Singleton_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V2__y)
=> V1__x = V2__y ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Strict_Included_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
& V1__X != V2__Y )
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V2__Y) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.Strict_Included_strict',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ~ cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V1__X) ) ) ).
fof('Coq.Sets.Constructive_sets.Union_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
| cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Constructive_sets.not_Empty_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) != cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x) ) ) ) ).
fof('Coq.Sets.Cpo.Bottom_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__bot] :
( t(V2__bot,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V2__bot)
=> ( ! [V4__y] :
( t(V4__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V4__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V2__bot,V4__y) ) )
=> cCoq_2eSets_2eCpo_2eBottom___24a3(V0__U,V1__D,V2__bot) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Complete_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ( ? [V3__bot] :
( t(V3__bot,V0__U)
& cCoq_2eSets_2eCpo_2eBottom___24a3(V0__U,V1__D,V3__bot) )
=> ( ! [V4__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__X)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(V0__U,V1__D,V4__X)
=> ? [V6__bsup] :
( t(V6__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V4__X,V6__bsup) ) ) )
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eCpo_2eComplete___24a2(V0__U,V1__D)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Complete_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ( ? [V3__bot] :
( t(V3__bot,V0__U)
& cCoq_2eSets_2eCpo_2eBottom___24a3(V0__U,V1__D,V3__bot) )
=> ( ! [V4__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__X)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(V0__U,V1__D,V4__X)
=> ? [V6__bsup] :
( t(V6__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V4__X,V6__bsup) ) ) )
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eCpo_2eComplete___24a2(V0__U,V1__D)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Conditionally_complete_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( ? [V5__maj] :
( t(V5__maj,V0__U)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V3__X,V5__maj) )
=> ? [V6__bsup] :
( t(V6__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V3__X,V6__bsup) ) ) ) )
=> p(V2__P) )
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V0__U,V1__D)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Conditionally_complete_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( ? [V5__maj] :
( t(V5__maj,V0__U)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V3__X,V5__maj) )
=> ? [V6__bsup] :
( t(V6__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V3__X,V6__bsup) ) ) ) )
=> p(V2__P) )
=> ( cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V0__U,V1__D)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Definition_of_Complete',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ( ? [V2__bot] :
( t(V2__bot,V0__U)
& cCoq_2eSets_2eCpo_2eBottom___24a3(V0__U,V1__D,V2__bot) )
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eCpo_2eDirected___24a3(V0__U,V1__D,V3__X)
=> ? [V5__bsup] :
( t(V5__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V3__X,V5__bsup) ) ) )
=> cCoq_2eSets_2eCpo_2eComplete___24a2(V0__U,V1__D) ) ) ) ) ).
fof('Coq.Sets.Cpo.Definition_of_Conditionally_complete',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ( ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ( ? [V4__maj] :
( t(V4__maj,V0__U)
& cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__X,V4__maj) )
=> ? [V5__bsup] :
( t(V5__bsup,V0__U)
& cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V2__X,V5__bsup) ) ) ) )
=> cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V0__U,V1__D) ) ) ) ).
fof('Coq.Sets.Cpo.Glb_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__y,V3__x) ) )
=> cCoq_2eSets_2eCpo_2eGlb___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Glb_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V3__x) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eGlb___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Glb_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V3__x) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eGlb___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lower_Bound_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V5__y) ) )
=> cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lower_Bound_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V6__y) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lower_Bound_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V6__y) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lub_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V5__y) ) )
=> cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lub_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V6__y) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Lub_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__x,V6__y) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eLub___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Totally_ordered_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ! [V5__x] :
( t(V5__x,V0__U)
=> ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V5__x,V6__y),V2__B)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__x,V6__y)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V5__x) ) ) ) ) )
=> p(V3__P) )
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V0__U,V1__D,V2__B)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Totally_ordered_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D))
=> ! [V5__x] :
( t(V5__x,V0__U)
=> ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V5__x,V6__y),V2__B)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__x,V6__y)
| cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V5__x) ) ) ) ) )
=> p(V3__P) )
=> ( cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V0__U,V1__D,V2__B)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Upper_Bound_definition',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V5__y] :
( t(V5__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V5__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V5__y,V3__x) ) )
=> cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Upper_Bound_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V3__x) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Cpo.Upper_Bound_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__D),V3__x)
=> ( ! [V6__y] :
( t(V6__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__B,V6__y)
=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V6__y,V3__x) ) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V0__U,V1__D,V2__B,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__P] :
( c_24__type__5___24t(V0__U,V3__P)
=> ( p(happ(V3__P,V1__x))
=> ( p(happ(V3__P,V2__y))
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eCouple___24a4(V0__U,V1__x,V2__y,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),V1__x) ) ) ) ).
fof('Coq.Sets.Ensembles.Couple_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),V2__y) ) ) ) ).
fof('Coq.Sets.Ensembles.Disjoint_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( ! [V4__x] :
( t(V4__x,V0__U)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V4__x) )
=> p(V3__P) )
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(V0__U,V1__B,V2__C)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Disjoint_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ( ! [V3__x] :
( t(V3__x,V0__U)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V3__x) )
=> cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(V0__U,V1__B,V2__C) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Disjoint_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( cProp___24t(V3__P)
=> ( ( ! [V4__x] :
( t(V4__x,V0__U)
=> ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V4__x) )
=> p(V3__P) )
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(V0__U,V1__B,V2__C)
=> p(V3__P) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Empty_set_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__5___24t(V0__U,V1__P)
=> ! [V2__u] :
( t(V2__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eEmpty__set___24a2(V0__U,V2__u)
=> p(happ(V1__P,V2__u)) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Extensionality_Ensembles',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V0__U,V1__A,V2__B)
=> V1__A = V2__B ) ) ) ) ).
fof('Coq.Sets.Ensembles.Full_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__U),V1__x) ) ) ).
fof('Coq.Sets.Ensembles.In_singleton',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),V1__x) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V2__x)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Inhabited_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__P] :
( cProp___24t(V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> p(V2__P) ) )
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__B)
=> p(V2__P) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__5___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V4__x)
=> p(happ(V3__P,V4__x)) ) ) )
=> ! [V5__u] :
( t(V5__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V0__U,V1__B,V2__C,V5__u)
=> p(happ(V3__P,V5__u)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Intersection_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__5___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V4__x)
=> p(happ(V3__P,V4__x)) ) ) )
=> ! [V5__u] :
( t(V5__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V0__U,V1__B,V2__C,V5__u)
=> p(happ(V3__P,V5__u)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Singleton_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__P] :
( c_24__type__5___24t(V0__U,V2__P)
=> ( p(happ(V2__P,V1__x))
=> ! [V4__u] :
( t(V4__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V0__U,V1__x,V4__u)
=> p(happ(V2__P,V4__u)) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> ! [V4__P] :
( c_24__type__5___24t(V0__U,V4__P)
=> ( p(happ(V4__P,V1__x))
=> ( p(happ(V4__P,V2__y))
=> ( p(happ(V4__P,V3__z))
=> ! [V8__u] :
( t(V8__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eTriple___24a5(V0__U,V1__x,V2__y,V3__z,V8__u)
=> p(happ(V4__P,V8__u)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z),V1__x) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_m',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z),V2__y) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Triple_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z),V3__z) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__5___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> p(happ(V3__P,V4__x)) ) )
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V5__x)
=> p(happ(V3__P,V5__x)) ) )
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(V0__U,V1__B,V2__C,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_introl',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_intror',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__B,V2__C),V3__x) ) ) ) ) ) ).
fof('Coq.Sets.Ensembles.Union_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__B)
=> ! [V2__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__C)
=> ! [V3__P] :
( c_24__type__5___24t(V0__U,V3__P)
=> ( ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__B,V4__x)
=> p(happ(V3__P,V4__x)) ) )
=> ( ! [V5__x] :
( t(V5__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__C,V5__x)
=> p(happ(V3__P,V5__x)) ) )
=> ! [V6__u] :
( t(V6__u,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eUnion___24a4(V0__U,V1__B,V2__C,V6__u)
=> p(happ(V3__P,V6__u)) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.Empty_is_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) ) ).
fof('Coq.Sets.Finite_sets.Finite_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__3020___24t(V0__U,V1__P)
=> ( p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__A)
=> ( p(happ(V1__P,V3__A))
=> ! [V6__x] :
( t(V6__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V6__x)
=> p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V6__x))) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V4__e)
=> p(happ(V1__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.Finite_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__3020___24t(V0__U,V1__P)
=> ( p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__A)
=> ( p(happ(V1__P,V3__A))
=> ! [V6__x] :
( t(V6__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V6__x)
=> p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V6__x))) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V4__e)
=> p(happ(V1__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.Union_is_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.card_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__A,V2__n)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V4__x)
=> cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V4__x),cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_elim',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__p)
=> c_24__case__Coq_2eInit_2eDatatypes_2enat_24235___24a3(V0__U,V1__X,V2__p) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__202___24t(V0__U,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)),cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V3__A,V4__n)
=> ( p(happ(happ(V1__P,V3__A),V4__n))
=> ! [V7__x] :
( t(V7__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V7__x)
=> p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V7__x)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n))) ) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__e,V5__n)
=> p(happ(happ(V1__P,V4__e),V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_invert',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__p)
=> c_24__case__Coq_2eInit_2eDatatypes_2enat_24225___24a3(V0__U,V1__X,V2__p) ) ) ) ) ).
fof('Coq.Sets.Finite_sets.cardinal_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__202___24t(V0__U,V1__P)
=> ( p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)),cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V3__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__A)
=> ! [V4__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V3__A,V4__n)
=> ( p(happ(happ(V1__P,V3__A),V4__n))
=> ! [V7__x] :
( t(V7__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V3__A,V7__x)
=> p(happ(happ(V1__P,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V3__A,V7__x)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n))) ) ) ) ) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__e,V5__n)
=> p(happ(happ(V1__P,V4__e),V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Add_preserves_Finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__X)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x)) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Finite_downward_closed',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__X) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.G_aux',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__3020___24t(V0__U,V1__P)
=> ( ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V2__X)
=> ( ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V4__Y,V2__X)
=> p(happ(V1__P,V4__Y)) ) )
=> p(happ(V1__P,V2__X)) ) ) )
=> p(happ(V1__P,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Generalized_induction_on_finite_sets',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__3020___24t(V0__U,V1__P)
=> ( ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V2__X)
=> ( ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V4__Y,V2__X)
=> p(happ(V1__P,V4__Y)) ) )
=> p(happ(V1__P,V2__X)) ) ) )
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V3__X)
=> p(happ(V1__P,V3__X)) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Intersection_preserves_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__A)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V3__X,V1__A)) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.Union_preserves_Finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V2__Y)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__X,V2__Y)) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.card_Add_gen',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__n_27] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n_27)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__A,V3__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V4__n_27)
=> cCoq_2eInit_2ePeano_2ele___24a2(V4__n_27,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.card_soustr_1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__n)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V4__x)
=> cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V4__x),cCoq_2eInit_2eNat_2epred___24a1(V2__n)) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinalO_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,cCoq_2eInit_2eDatatypes_2eO)
=> V1__X = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_finite',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__n)
=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__X) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_is_functional',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__c1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__c1)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__c1)
=> ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ! [V5__c2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__c2)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__Y,V5__c2)
=> ( V1__X = V4__Y
=> V2__c1 = V5__c2 ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.cardinal_unicity',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V4__m)
=> V2__n = V4__m ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.finite_cardinal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V0__U,V1__X)
=> ? [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
& cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V3__n) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.incl_card_le',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ! [V4__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V3__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V2__Y,V4__m)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> cCoq_2eInit_2ePeano_2ele___24a2(V3__n,V4__m) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.incl_st_card_lt',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__c1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__c1)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V2__c1)
=> ! [V4__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__Y)
=> ! [V5__c2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__c2)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V4__Y,V5__c2)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,V4__Y)
=> cCoq_2eInit_2ePeano_2egt___24a2(V5__c2,V2__c1) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Finite_sets_facts.inh_card_gt_O',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,V1__X)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V0__U,V1__X,V3__n)
=> cCoq_2eInit_2ePeano_2egt___24a2(V3__n,cCoq_2eInit_2eDatatypes_2eO) ) ) ) ) ) ).
fof('Coq.Sets.Partial_Order.Definition_of_covers',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V3__x,V2__y)
=> ( ~ ? [V5__z] :
( t(V5__z,V0__U)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V3__x,V5__z)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V5__z,V2__y) )
=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(V0__U,V1__p,V2__y,V3__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Partial_Order.PO_cond1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V0__U,cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V0__U,V1__p)) ) ) ).
fof('Coq.Sets.Partial_Order.PO_cond2',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(V0__U,cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V0__U,V1__p)) ) ) ).
fof('Coq.Sets.Partial_Order.Strict_Rel_Transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a2(V0__U,V1__D)) ) ) ).
fof('Coq.Sets.Partial_Order.Strict_Rel_Transitive_with_Rel',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__D,V2__x,V3__y)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V3__y,V4__z)
=> cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__D,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Partial_Order.Strict_Rel_Transitive_with_Rel_left',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__D] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__D)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> ( cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V0__U,V1__D,V2__x,V3__y)
=> ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__D,V3__y,V4__z)
=> cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__D,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Partial_Order.covers_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__p] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V0__U,V1__p)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__P] :
( cProp___24t(V4__P)
=> ( ( cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V3__x,V2__y)
=> ( ~ ? [V6__z] :
( t(V6__z,V0__U)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V3__x,V6__z)
& cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V0__U,V1__p,V6__z,V2__y) )
=> p(V4__P) ) )
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(V0__U,V1__p,V2__y,V3__x)
=> p(V4__P) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Definition_of_Power_set',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__X,V1__A)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__A),V2__X) ) ) ) ) ).
fof('Coq.Sets.Powerset.Empty_set_is_Bottom',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eCpo_2eBottom___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) ) ) ).
fof('Coq.Sets.Powerset.Empty_set_minimal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__X) ) ) ).
fof('Coq.Sets.Powerset.Inclusion_is_an_order',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Inclusion_is_transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V1__a) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_decreases_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b),V2__b) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_is_Glb',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__b)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__b,V1__A)
=> cCoq_2eSets_2eCpo_2eGlb___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eCouple___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),V2__a,V3__b),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__a,V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Intersection_maximal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__a)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__a,V2__b)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Power_set_Inhabited',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set___24a2(V0__U,V1__X)) ) ) ).
fof('Coq.Sets.Powerset.Power_set_ind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__P] :
( c_24__type__3020___24t(V0__U,V2__P)
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> p(happ(V2__P,V3__X)) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(V0__U,V1__A,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Power_set_sind',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__P] :
( c_24__type__3020___24t(V0__U,V2__P)
=> ( ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__X,V1__A)
=> p(happ(V2__P,V3__X)) ) )
=> ! [V4__e] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V4__e)
=> ( cCoq_2eSets_2ePowerset_2ePower__set___24a3(V0__U,V1__A,V4__e)
=> p(happ(V2__P,V4__e)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Strict_Rel_is_Strict_Included',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2esame__relation___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eStrict__Included___24a1(V0__U),cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__U)))) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2eEnsembles_2eStrict__Included___24a1(V0__U)) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive_with_inclusion',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__x)
=> ! [V2__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__y)
=> ! [V3__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__z)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V2__y)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__y,V3__z)
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V3__z) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Strict_inclusion_is_transitive_with_inclusion_left',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__x)
=> ! [V2__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__y)
=> ! [V3__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__z)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__x,V2__y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__y,V3__z)
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__x,V3__z) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Union_increases_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__a,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b)) ) ) ) ).
fof('Coq.Sets.Powerset.Union_increases_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__b,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b)) ) ) ) ).
fof('Coq.Sets.Powerset.Union_is_Lub',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__b)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__b,V1__A)
=> cCoq_2eSets_2eCpo_2eLub___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eCouple___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),V2__a,V3__b),cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__a,V3__b)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset.Union_minimal',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__a)
=> ! [V2__b] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__b)
=> ! [V3__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__a,V3__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__b,V3__X)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__a,V2__b),V3__X) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Add_covers',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ! [V4__x] :
( t(V4__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V4__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__a,V4__x)
=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__a,V4__x),V2__a) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Included_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__A)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__A,V3__x))
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__A)
| ? [V5__A_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__A_27)
& V1__X = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V5__A_27,V3__x)
& cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V5__A_27,V2__A) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Simplify_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__X0] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__X0)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V3__x)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__X0,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V3__x) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__X0,V3__x)
=> V1__X = V2__X0 ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Singleton_atomic',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__A)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__A,V1__x)
=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V2__A),cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.Sub_Add_new',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> V1__X = cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V2__x) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.add_soustr_1',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x),V2__x),V1__X) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.add_soustr_2',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x),V2__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.add_soustr_xy',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ( V2__x != V3__y
=> cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V3__y) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V3__y),V2__x) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.covers_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__a_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__a_27)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__a_27,V1__A)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__a_27,V2__a)
=> ? [V7__x] :
( t(V7__x,V0__U)
& V3__a_27 = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__a,V7__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V7__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__a,V7__x) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.covers_is_Add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__a] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__a)
=> ! [V3__a_27] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__a_27)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__a,V1__A)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V3__a_27,V1__A)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__a_27,V2__a)
<=> ? [V6__x] :
( t(V6__x,V0__U)
& V3__a_27 = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__a,V6__x)
& cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V6__x)
& ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V2__a,V6__x) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,V2__Y)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V3__x),cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V2__Y,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_add_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V2__x),V1__X) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_add_r',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x),V2__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_soustr_in',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x),V1__X) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.incl_st_add_soustr',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__Y)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V3__x),V2__Y)
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V2__Y,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.less_than_singleton',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__x))
=> V1__X = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.setcover_inv',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__x)
=> ! [V3__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__y)
=> ( cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__y,V2__x)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__x,V3__y)
& ! [V5__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__z)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__x,V5__z)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V5__z,V3__y)
=> ( V2__x = V5__z
| V5__z = V3__y ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_Classical_facts.sincl_add_x',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x))
=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V1__A,V2__B) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Add_commutative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__y),V2__x) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Add_commutative\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ! [V3__y] :
( t(V3__y,V0__U)
=> ! [V4__z] :
( t(V4__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V2__x),V3__y),V4__z) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V4__z),V2__x),V3__y) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Add_distributes',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ! [V4__y] :
( t(V4__y,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,V1__A)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),V4__y) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V4__y)) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Couple_as_union',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__y)) = cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Disjoint_Intersection',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ( cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(V0__A,V1__s1,V2__s2)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__A,V1__s1,V2__s2) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Distributivity',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__C)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V3__C)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__A,V2__B),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__A,V3__C)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Distributivity\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__C)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__B,V3__C)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V3__C)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Distributivity_l',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__C)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__C) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__A,V3__C),cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__B,V3__C)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Empty_set_zero',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__X) = V1__X ) ) ).
fof('Coq.Sets.Powerset_facts.Empty_set_zero\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U),V1__x) = cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x) ) ) ).
fof('Coq.Sets.Powerset_facts.Empty_set_zero_right',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U)) = V1__X ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_Empty_set_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A),V1__s) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_Empty_set_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__A,V1__s,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A)) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ).
fof('Coq.Sets.Powerset_facts.Intersection_commutative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V1__A,V2__B) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__U,V2__B,V1__A) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Non_disjoint_union',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__X,V2__x) = V1__X ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Non_disjoint_union\'',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ! [V2__x] :
( t(V2__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__X,V2__x)
=> cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V0__U,V1__X,V2__x) = V1__X ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Seminus_Empty_set_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A),V1__s) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ).
fof('Coq.Sets.Powerset_facts.Seminus_Empty_set_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A)) = V1__s ) ) ).
fof('Coq.Sets.Powerset_facts.Setminus_Disjoint_noop',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ( cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__A,V1__s1,V2__s2) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,V2__s2) = V1__s1 ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Setminus_Included_empty',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__A,V1__s1,V2__s2)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,V2__s2) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__A) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Setminus_Union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ! [V3__s3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V3__s3)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__A,V1__s1,V2__s2),V3__s3) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,V3__s3),cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V2__s2,V3__s3)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Setminus_Union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V1__s1)
=> ! [V2__s2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V2__s2)
=> ! [V3__s3] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__A,V3__s3)
=> cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__A,V2__s2,V3__s3)) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V0__A,V1__s1,V2__s2),V3__s3) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Triple_as_Couple',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y) = cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V1__x,V2__y) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Triple_as_Couple_Singleton',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eCouple___24a3(V0__U,V1__x,V2__y),cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V3__z)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Triple_as_union',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__x] :
( t(V1__x,V0__U)
=> ! [V2__y] :
( t(V2__y,V0__U)
=> ! [V3__z] :
( t(V3__z,V0__U)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V1__x),cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V2__y)),cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V0__U,V3__z)) = cCoq_2eSets_2eEnsembles_2eTriple___24a4(V0__U,V1__x,V2__y,V3__z) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_absorbs',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V2__B,V1__A)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B) = V1__A ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__x) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_associative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__C] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__C)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B),V3__C) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V3__C)) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_commutative',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V2__B) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V2__B,V1__A) ) ) ) ).
fof('Coq.Sets.Powerset_facts.Union_idempotent',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__U,V1__A,V1__A) = V1__A ) ) ).
fof('Coq.Sets.Powerset_facts.incl_add',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,V2__B)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x)) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.incl_add_x',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__B] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__B)
=> ! [V3__x] :
( t(V3__x,V0__U)
=> ( ~ cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__U,V1__A,V3__x)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V1__A,V3__x),cCoq_2eSets_2eEnsembles_2eAdd___24a3(V0__U,V2__B,V3__x))
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__A,V2__B) ) ) ) ) ) ) ).
fof('Coq.Sets.Powerset_facts.less_than_empty',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__X] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__X)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__U,V1__X,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U))
=> V1__X = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__U) ) ) ) ).
fof('Coq.Sets.Powerset_facts.setcover_intro',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__A] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V1__A)
=> ! [V2__x] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V2__x)
=> ! [V3__y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V3__y)
=> ( cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__x,V3__y)
=> ( ~ ? [V5__z] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__U,V5__z)
& cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V2__x,V5__z)
& cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V0__U,V5__z,V3__y) )
=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__U),cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V0__U,V1__A),V3__y,V2__x) ) ) ) ) ) ) ).
fof('Coq.Sets.Relations_1_facts.cong_transitive_same_relation',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__R] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,V1__R)
=> ! [V2__R_27] :
( cCoq_2eSets_2eRelations__1_2eRelation___24t(V0__U,V2__R_27)
=> ( cCoq_2eSets_2eRelations__1_2esame__relation___24a3(V0__U,V1__R,V2__R_27)
=> ( cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V1__R)
=> cCoq_2eSets_2eRelations__1_2eTransitive___24a2(V0__U,V2__R_27) ) ) ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_sym',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq_trans',axiom,
! [V0__x] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_BootStrap.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.IsTotal.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> V0__x = V0__x ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = V1__y
=> V1__y = V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_lt_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V2__z)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x)
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_neq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y != V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_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.eq_trans',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = V1__y
=> ( V1__y = V2__z
=> V0__x = V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_antisym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
=> V0__x = V1__y ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.le_neq_lt',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x != V1__y
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ~ cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x != V1__y
=> ( V1__y = V2__z
=> V0__x != V2__z ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.neq_sym',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x != V1__y
=> V1__y != V0__x ) ) ) ).
fof('Coq.ZArith.BinInt.Z.Private_Tac.not_neq_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ~ ( V0__x != V1__y )
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.BinInt.Z.abs_eq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__n) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.add_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.add_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.add_le_mono_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__p,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.bits_inj\'',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V2__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V0__a,V2__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V1__b,V2__n) ) )
=> V0__a = V1__b ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mod',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__a = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b)),cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.div_mul',axiom,
! [V0__a] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
=> ( V1__b != cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V1__b),V1__b) = V0__a ) ) ) ).
fof('Coq.ZArith.BinInt.Z.divide_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n)
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.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__14155___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_mul_0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
| V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__m != cCoq_2eNumbers_2eBinNums_2eZ0
=> V0__n = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = V1__m
<=> V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.eq_opp_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(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.gcd_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V1__m,V0__n) ) ) ).
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))
| 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))
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p)
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_lteq',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_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
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_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)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V0__x = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__z,V1__y)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_stepr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
=> ( V1__y = V2__z
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V2__z)) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n),V1__m))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3183,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eZ,c_24__type__5066,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,
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,
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_eq_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
<=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_gt_cases',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
<=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> 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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_neq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> V0__n != V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V0__x = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V2__z,V1__y) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_stepr',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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)
=> ( V1__y = V2__z
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V2__z) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_succ_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m))
<=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_total',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| V0__n = V1__m
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_unicity',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
& V2__p = V1__m )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& V2__p = V0__n ) )
=> V2__p = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.max_unicity_ext',axiom,
! [V0__f] :
( c_24__type__13531___24t(V0__f)
=> ( ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m)
& happ(happ(V0__f,V1__n),V2__m) = V2__m )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__m,V1__n))
& happ(happ(V0__f,V1__n),V2__m) = V1__n ) ) ) )
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__m)
=> happ(happ(V0__f,V2__n),V3__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V2__n,V3__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_spec',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_unicity',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
& V2__p = V0__n )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n))
& V2__p = V1__m ) )
=> V2__p = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.min_unicity_ext',axiom,
! [V0__f] :
( c_24__type__13531___24t(V0__f)
=> ( ! [V1__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__m)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__n,V2__m)
& happ(happ(V0__f,V1__n),V2__m) = V1__n )
| ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V2__m,V1__n))
& happ(happ(V0__f,V1__n),V2__m) = V2__m ) ) ) )
=> ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
=> ! [V3__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__m)
=> happ(happ(V0__f,V2__n),V3__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V2__n,V3__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__n) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_1_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_cancel_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
<=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_nonneg_nonneg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m))) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_opp_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n),V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__p,V1__m)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_reg_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ( V2__p != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)
=> V0__n = V1__m ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.mul_shuffle0',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),V1__m) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.neq_sym',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> V1__m != V0__n ) ) ) ).
fof('Coq.ZArith.BinInt.Z.one_succ',axiom,
cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) ).
fof('Coq.ZArith.BinInt.Z.opp_0',axiom,
cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eNumbers_2eBinNums_2eZ0) = cCoq_2eNumbers_2eBinNums_2eZ0 ).
fof('Coq.ZArith.BinInt.Z.opp_inj',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_inj_wd',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.opp_involutive',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.opp_pos_neg',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ).
fof('Coq.ZArith.BinInt.Z.sgn_null',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZ0) = V0__n ) ).
fof('Coq.ZArith.BinInt.Z.sub_diag',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ).
fof('Coq.ZArith.BinInt.Z.sub_move_0_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eZ0
<=> V0__n = V1__m ) ) ) ).
fof('Coq.ZArith.BinInt.Z.sub_simpl_r',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(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),V1__m) = V0__n ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_inj',axiom,
! [V0__n1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n1)
=> ! [V1__n2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__n2)
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__n2)
=> V0__n1 = V1__n2 ) ) ) ).
fof('Coq.ZArith.BinInt.Z.succ_pred',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V0__n)) = V0__n ) ).
fof('Coq.ZArith.BinInt.Zmult_integral_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != cCoq_2eNumbers_2eBinNums_2eZ0
=> ( cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0
=> V1__m = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zplus_eq_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ! [V2__p] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
=> ! [V3__q] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__q)
=> ( V0__n = V1__m
=> ( V2__p = V3__q
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V3__q) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zplus_minus_eq',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)
=> ( V0__n = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)
=> V2__p = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Zpos_eq',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( V0__p = V1__q
=> cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V1__q) ) ) ) ).
fof('Coq.ZArith.BinInt.Zsucc_eq_compat',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V1__m) ) ) ) ).
fof('Coq.ZArith.Zbool.Zeq_bool_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue
=> V0__x = V1__y ) ) ) ).
fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.ZArith.Zorder.not_Zeq',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n != V1__m
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
| cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n) ) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
fof('Coq.micromega.EnvRing.Mphi_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__4198___24t(V0__R,V2__rmul)
=> ! [V3__M] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V3__M)
=> ! [V4__e1] :
( c_24__type__3544___24t(V0__R,V4__e1)
=> ! [V5__e2] :
( c_24__type__3544___24t(V0__R,V5__e2)
=> ( ! [V6__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__x)
=> happ(V4__e1,V6__x) = happ(V5__e2,V6__x) )
=> cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V0__R,V1__rI,V2__rmul,V4__e1,V3__M) = cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V0__R,V1__rI,V2__rmul,V5__e2,V3__M) ) ) ) ) ) ) ) ).
fof('Coq.micromega.EnvRing.env_morph',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__4198___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__4198___24t(V0__R,V2__rmul)
=> ! [V3__C] :
( cType___24t(V3__C)
=> ! [V4__phi] :
( c_24__type__4215___24t(V0__R,V3__C,V4__phi)
=> ! [V5__p] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V3__C,V5__p)
=> ! [V6__e1] :
( c_24__type__33691___24t(V0__R,V3__C,V6__e1)
=> ! [V7__e2] :
( c_24__type__33691___24t(V0__R,V3__C,V7__e2)
=> ( ! [V8__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V8__x)
=> happ(V6__e1,V8__x) = happ(V7__e2,V8__x) )
=> cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V6__e1,V5__p) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V0__R,V1__radd,V2__rmul,V3__C,V4__phi,V7__e2,V5__p) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.F.E_ST',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2epositive,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2epositive)) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.dec_eq',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__29371___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.eq_refl_iff',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ( V0__x = V0__x
<=> p(c_24True) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = 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)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
=> ( V0__x = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y)
=> V0__x = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.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.omega.PreOmega.Z.rem_0_r_ext',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V0__x,V1__y) = V0__x ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___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__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___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__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_zero',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> p(happ(happ(V7__req,happ(V6__ropp,V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__4198___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__4198___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__4207___24t(V0__R,V3__ropp)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,c_3d___24a1(V0__R)) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eq_s_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__4198___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__4198___24t(V0__R,V2__rmul)
=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V0__R,V1__radd,V2__rmul,c_3d___24a1(V0__R)) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Eqsth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,c_3d___24a1(V0__R)) ) ).
fof('Coq.setoid_ring.Ring_theory.Rth_ARth',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__6444___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__6444___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__6444___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__6458___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__6465___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__4215___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.morph1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__4198___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__4198___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__4198___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__4207___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__3131___24t(V0__R,V7__req)
=> ! [V8__C] :
( cType___24t(V8__C)
=> ! [V9__cO] :
( t(V9__cO,V8__C)
=> ! [V10__cI] :
( t(V10__cI,V8__C)
=> ! [V11__cadd] :
( c_24__type__6444___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__6444___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__6444___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__6458___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__6465___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__4215___24t(V0__R,V8__C,V16__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
=> p(happ(happ(V7__req,happ(V16__phi,V10__cI)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('InverseImageLemmas.in_inverse_image',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T)
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V1__Y,V3__T,happ(V2__f,V4__x))
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T),V4__x) ) ) ) ) ) ) ).
fof('InverseImageLemmas.inverse_image_fun',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T) = c_24__lam__29604___24a4(V0__X,V1__Y,V2__f,V3__T) ) ) ) ) ).
fof('ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble_is_identity',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( c_24__type__5___24t(V0__X,V1__P)
=> cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V0__X,c_24__lam__2997___24a2(V0__X,V1__P)) = V1__P ) ) ).
fof('ZornsLemma.EnsemblesSpec.intro_characteristic_sat',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__P] :
( c_24__type__5___24t(V0__X,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__X)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__X,cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V0__X,V1__P),V2__x) ) ) ) ) ).
fof('ZornsLemma.Families.FamilyIntersection_ind',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__P] :
( c_24__type__5___24t(V0__T,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__T)
=> ( ! [V4__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V4__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V4__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V4__S,V3__x) ) )
=> p(happ(V2__P,V3__x)) ) )
=> ! [V4__t] :
( t(V4__t,V0__T)
=> ( cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(V0__T,V1__F,V4__t)
=> p(happ(V2__P,V4__t)) ) ) ) ) ) ) ).
fof('ZornsLemma.Families.FamilyUnion_ind',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__P] :
( c_24__type__5___24t(V0__T,V2__P)
=> ( ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V3__S)
=> ! [V4__x] :
( t(V4__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V3__S,V4__x)
=> p(happ(V2__P,V4__x)) ) ) ) )
=> ! [V4__t] :
( t(V4__t,V0__T)
=> ( cZornsLemma_2eFamilies_2eFamilyUnion___24a3(V0__T,V1__F,V4__t)
=> p(happ(V2__P,V4__t)) ) ) ) ) ) ) ).
fof('ZornsLemma.Families.empty_family_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T))) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__T) ) ).
fof('ZornsLemma.Families.empty_family_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T))) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__T) ) ).
fof('ZornsLemma.Families.family_intersection_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__x] :
( t(V2__x,V0__T)
=> ( ! [V3__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V3__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V3__S)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V3__S,V2__x) ) )
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V1__F),V2__x) ) ) ) ) ).
fof('ZornsLemma.Families.family_union_intro',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V0__T,V2__S)
=> ! [V3__x] :
( t(V3__x,V0__T)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__S)
=> ( cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,V2__S,V3__x)
=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V1__F),V3__x) ) ) ) ) ) ) ).
fof('ZornsLemma.Families.subfamily_intersection',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__G] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V2__G)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__G)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V2__G),cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V0__T,V1__F)) ) ) ) ) ).
fof('ZornsLemma.Families.subfamily_union',axiom,
! [V0__T] :
( cType___24t(V0__T)
=> ! [V1__F] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V1__F)
=> ! [V2__G] :
( cZornsLemma_2eFamilies_2eFamily___24t(V0__T,V2__G)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V0__T),V1__F,V2__G)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__T,cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V1__F),cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V0__T,V2__G)) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_complement',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eComplement___24a2(V1__Y,V3__T)) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T)) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_composition',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__Z] :
( cType___24t(V2__Z)
=> ! [V3__f] :
( c_24__type__108___24t(V1__Y,V2__Z,V3__f)
=> ! [V4__g] :
( c_24__type__127___24t(V0__X,V1__Y,V2__Z,V4__g)
=> ! [V5__U] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V2__Z,V5__U)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V2__Z,c_24__lam__141___24a5(V0__X,V1__Y,V2__Z,V3__f,V4__g),V5__U) = cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V4__g,cZornsLemma_2eInverseImage_2einverse__image___24a4(V1__Y,V2__Z,V3__f,V5__U)) ) ) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_empty',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V1__Y)) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V0__X) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_full',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V1__Y)) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V0__X) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_increasing',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T1)
=> ! [V4__T2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V4__T2)
=> ( cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V1__Y,V3__T1,V4__T2)
=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T1),cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V4__T2)) ) ) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_intersection',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T1)
=> ! [V4__T2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V4__T2)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V1__Y,V3__T1,V4__T2)) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T1),cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V4__T2)) ) ) ) ) ) ).
fof('ZornsLemma.InverseImage.inverse_image_union',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__Y] :
( cType___24t(V1__Y)
=> ! [V2__f] :
( c_24__type__108___24t(V0__X,V1__Y,V2__f)
=> ! [V3__T1] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V3__T1)
=> ! [V4__T2] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V1__Y,V4__T2)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,cCoq_2eSets_2eEnsembles_2eUnion___24a3(V1__Y,V3__T1,V4__T2)) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V0__X,cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V3__T1),cZornsLemma_2eInverseImage_2einverse__image___24a4(V0__X,V1__Y,V2__f,V4__T2)) ) ) ) ) ) ).
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('$adef_$_prop_55887_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55887,V_24X1) = c_24__prop__55887___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Singleton_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSingleton___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ZornsLemma.Families.FamilyUnion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyUnion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Empty_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eEmpty__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_14419_$a1',axiom,
! [V_24X1] : happ(c_24__prop__14419,V_24X1) = c_24__prop__14419___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Reals.Rfunctions.ZintPos_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintPos,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2elog2,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Upper_Bound_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eUpper__Bound,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eUpper__Bound___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_3_R_564_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__564,V_24X1),V_24X2) = c_24__let__3__R__564___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_3_R_846_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__846,V_24X1),V_24X2) = c_24__let__3__R__846___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Relations_1.same_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eRelations__1_2esame__relation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eRelations__1_2esame__relation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_ZornsLemma.Families.FamilyIntersection_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2) = cZornsLemma_2eFamilies_2eFamilyIntersection___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$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('$adef_Coq.Reals.Rdefinitions.IPR_$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('$adef_Coq.Init.Datatypes.CompareSpecT_$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('$adef_$_let_2_C_845_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__845,V_24X1),V_24X2) = c_24__let__2__C__845___24a2(V_24X1,V_24X2) ).
fof('$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.setoid_ring.Field_theory.FEdiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_2_C_2591_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__2591,V_24X1),V_24X2) = c_24__let__2__C__2591___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIn,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_29348_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__29348,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__29348___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__rect__eq___24a1(V_24X1) ) ).
fof('$adef_Coq.Init.Specif.projT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.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.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_32772_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__32772,V_24X1),V_24X2) = c_24__prop__32772___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2859_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2859,V_24X1),V_24X2),V_24X3) = c_24__lam__2859___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esqrt,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esqrt___24a1(V_24X1) ).
fof('$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_$_let_2_C_1409_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__1409,V_24X1),V_24X2) = c_24__let__2__C__1409___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_2_C_1777_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__1777,V_24X1),V_24X2) = c_24__let__2__C__1777___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__double___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.Fapp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFapp,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Partial_Order.Definition_of_PO_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.ZArith.BinIntDef.Z.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Cpo.Directed_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eDirected,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eDirected___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Partial_Order.Carrier_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eCarrier__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eCarrier__of___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_574_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__574,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__574___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Sets.Ensembles.Subtract_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSubtract,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eSubtract___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Couple_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eCouple,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eCouple___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Powerset.Inclusion_is_an_order_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePowerset_2eInclusion__is__an__order,V_24X1) = cCoq_2eSets_2ePowerset_2eInclusion__is__an__order___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('$adef_Coq.Sets.Ensembles.Empty_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEmpty__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eEmpty__set___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eComplement___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.eq_rec_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rec,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rec___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Sets.Powerset.Power_set_Inhabited_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set__Inhabited,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set__Inhabited___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Sets.Cpo.Lub_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eLub__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eLub__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.InverseImage.inverse_image_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cZornsLemma_2eInverseImage_2einverse__image,V_24X1),V_24X2),V_24X3),V_24X4) = cZornsLemma_2eInverseImage_2einverse__image___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_3_R_2722_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__2722,V_24X1),V_24X2) = c_24__let__3__R__2722___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Nat.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ediv,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_29350_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29350,V_24X1),V_24X2),V_24X3) = c_24__prop__29350___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$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('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Singleton_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eEnsembles_2eSingleton,V_24X1),V_24X2) = cCoq_2eSets_2eEnsembles_2eSingleton___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_3585_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__3585,V_24X1),V_24X2),V_24X3) = c_24__prop__3585___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Complement_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eComplement,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eComplement___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
<=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).
fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).
fof('$adef_$_prop_56054_$a1',axiom,
! [V_24X1] : happ(c_24__prop__56054,V_24X1) = c_24__prop__56054___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('$adef_Coq.Sets.Partial_Order.Rel_of_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eRel__of,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2eRel__of___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Strict_Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eStrict__Included,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eStrict__Included___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2eb2n,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP__$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP_____24a1(V_24X1) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rle_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRle,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRle___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_fix_12610_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__12610__1__add__carry,V_24X1),V_24X2) = c_24__fix__12610__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2997_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2997,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2997___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Cpo.Complete_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eComplete__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eComplete__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_2595_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2595,V_24X1),V_24X2),V_24X3) = c_24__lam__2595___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Union_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eUnion,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eUnion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_2595_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2595,V_24X1),V_24X2) = c_24__lam__2595___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Conditionally_complete_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Streicher_K_on__$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on__,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLogic_2eEqdepFacts_2eStreicher__K__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_dep_eq_on_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLogic_2eEqdepFacts_2eEq__dep__eq__on___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring.bool_eq_$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('$adef_$_lam_856_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__856,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__856___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_$_let_2_C_1921_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__1921,V_24X1),V_24X2) = c_24__let__2__C__1921___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rdiv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRdiv,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRdiv___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.Families.FamilyUnion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyUnion,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyUnion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.max_$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('$adef_Coq.Reals.Rdefinitions.Rge_$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('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Couple_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eCouple,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eCouple___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).
fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Env.jump_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnv_2ejump___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_56468_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56468,V_24X1),V_24X2) = c_24__prop__56468___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_refl_on__$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__,V_24X1))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a1(V_24X1) ) ).
fof('$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.Sets.Ensembles.Setminus_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSetminus,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eSetminus___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Finite_sets.cardinal_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eFinite__sets_2ecardinal,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eFinite__sets_2ecardinal___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Complete_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eComplete__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eComplete__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_3_R_1128_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__1128,V_24X1),V_24X2) = c_24__let__3__R__1128___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.condition_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2econdition,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2econdition___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Complete_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eCpo_2eComplete,V_24X1),V_24X2))
<=> cCoq_2eSets_2eCpo_2eComplete___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).
fof('$adef_$_prop_56053_$a1',axiom,
! [V_24X1] : happ(c_24__prop__56053,V_24X1) = c_24__prop__56053___24a1(V_24X1) ).
fof('$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.Reals.Rdefinitions.Ropp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).
fof('$adef_$_prop_29349_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29349,V_24X1),V_24X2),V_24X3) = c_24__prop__29349___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Partial_Order.covers_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2ecovers,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2ecovers___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2enat__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1420_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1420,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1420___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Inhabited_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eInhabited,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eInhabited___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Cpo.Lower_Bound_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLower__Bound,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eLower__Bound___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rminus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRminus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRminus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Init.Logic.eq_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eeq__refl,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eeq__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Logic.ClassicalFacts.retract_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eClassicalFacts_2eretract,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eClassicalFacts_2eretract___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rplus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRplus,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRplus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_3_R_414_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__414,V_24X1),V_24X2) = c_24__let__3__R__414___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('$adef_Coq.setoid_ring.Field_theory.FEadd_$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('$adef_Coq.PArith.BinPosDef.Pos.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).
fof('$adef_$_let_2_C_563_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__563,V_24X1),V_24X2) = c_24__let__2__C__563___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1928_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1928,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1928___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_2_C_977_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__977,V_24X1),V_24X2) = c_24__let__2__C__977___24a2(V_24X1,V_24X2) ).
fof('$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.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_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Lower_Bound_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eLower__Bound__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eLower__Bound__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.num_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2enum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2enum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
<=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_3_R_1260_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__1260,V_24X1),V_24X2) = c_24__let__3__R__1260___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('$adef_$_let_2_C_413_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__413,V_24X1),V_24X2) = c_24__let__2__C__413___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_3_R_2856_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__2856,V_24X1),V_24X2) = c_24__let__3__R__2856___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Included_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eIncluded___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Nat.modulo_$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('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$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('$adef_Coq.Sets.Cpo.Conditionally_complete_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eConditionally__complete__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
<=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.gt_$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('$adef_Coq.Sets.Cpo.Upper_Bound_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eUpper__Bound__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eUpper__Bound__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_29352_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29352,V_24X1),V_24X2),V_24X3) = c_24__prop__29352___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Init.Logic.eq_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Zdiv.Remainder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZdiv_2eRemainder,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZdiv_2eRemainder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rdefinitions.Rinv_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRinv,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRinv___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Glb_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eGlb__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eSets_2eCpo_2eGlb__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Cpo.Complete_rect_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eCpo_2eComplete__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eCpo_2eComplete__rect___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_3584_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__3584,V_24X1),V_24X2),V_24X3) = c_24__prop__3584___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$235_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24235,V_24X1),V_24X2),V_24X3))
<=> c_24__case__Coq_2eInit_2eDatatypes_2enat_24235___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_ZornsLemma.Families.Family_$a1',axiom,
! [V_24X1] : happ(cZornsLemma_2eFamilies_2eFamily,V_24X1) = cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Relations_1.Order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eOrder,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_Coq.Init.Nat.sqrt_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2esqrt,V_24X1) = cCoq_2eInit_2eNat_2esqrt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.size_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eEnsembles_2eIntersection___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.CompSpecT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompSpecT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eCompSpecT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Cpo.Lub_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLub,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eLub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_let_2_C_1259_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__1259,V_24X1),V_24X2) = c_24__let__2__C__1259___24a2(V_24X1,V_24X2) ).
fof('$adef_g_$a1',axiom,
! [V_24X1] : happ(cg,V_24X1) = cg___24a1(V_24X1) ).
fof('$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_$_let_2_C_1127_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__1127,V_24X1),V_24X2) = c_24__let__2__C__1127___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('$adef_Coq.Sets.Ensembles.Disjoint_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eDisjoint__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eEnsembles_2eDisjoint__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_prop_29354_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__29354,V_24X1),V_24X2) = c_24__prop__29354___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Partial_Order.Strict_Rel_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a2(V_24X1,V_24X2) ).
fof('$adef_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.PArith.BinPos.Pos.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
<=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.setoid_ring.Field_theory.rsplit_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Intersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eIntersection,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eIntersection___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.nat$225_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24225,V_24X1),V_24X2),V_24X3))
<=> c_24__case__Coq_2eInit_2eDatatypes_2enat_24225___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$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('$adef_Coq.ZArith.BinIntDef.Z.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Partial_Order.Carrier_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePartial__Order_2eCarrier,V_24X1) = cCoq_2eSets_2ePartial__Order_2eCarrier___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).
fof('$adef_$_lam_29604_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__29604,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__29604___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Cpo.Bottom_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eBottom,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eBottom___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_33910_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__33910,V_24X1),V_24X2) = c_24__prop__33910___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Lists.List.nth_$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('$adef_Coq.micromega.EnvRing.Pphi_$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_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eEnvRing_2ePphi___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_574_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__574,V_24X1),V_24X2) = c_24__lam__574___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Setminus_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSetminus,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eSetminus___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1),V_24X2))
<=> cCoq_2eSets_2eEnsembles_2eFull__set___24a2(V_24X1,V_24X2) ) ).
fof('$adef_f_$a1',axiom,
! [V_24X1] : happ(cf,V_24X1) = cf___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Glb_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eGlb__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eGlb__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_55955_$a1',axiom,
! [V_24X1] : happ(c_24__prop__55955,V_24X1) = c_24__prop__55955___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Upper_Bound_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eUpper__Bound__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eSets_2eCpo_2eUpper__Bound__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Relations_1.contains_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eRelations__1_2econtains,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eRelations__1_2econtains___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_856_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__856,V_24X1),V_24X2) = c_24__lam__856___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).
fof('$adef_$_lam_33928_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33928,V_24X1),V_24X2) = c_24__lam__33928___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('$adef_Coq.Sets.Cpo.Lub_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eLub__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eLub__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31939_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31939,V_24X1) = c_24__lam__31939___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Ensembles.Triple_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eTriple,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eSets_2eEnsembles_2eTriple___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Sets.Partial_Order.Strict_Rel_of_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2ePartial__Order_2eStrict__Rel__of___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_let_var_6_p_24343_24346_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__24343__24346,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__24343__24346___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_Coq.Init.Nat.shiftl_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eshiftl,V_24X1) = cCoq_2eInit_2eNat_2eshiftl___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNatDef.N.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2egcd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Powerset.Power_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Env.nth_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2enth,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2enth___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.gcd_$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('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.eqb_$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_1138_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1138,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1138___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
<=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_$_lam_141_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__141,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__141___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_Coq.Sets.Partial_Order.Definition_of_PO_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2ePartial__Order_2eDefinition__of__PO___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Cpo.Upper_Bound_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eUpper__Bound__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eUpper__Bound__rec___24a2(V_24X1,V_24X2) ).
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('$adef_$_let_3_R_696_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__696,V_24X1),V_24X2) = c_24__let__3__R__696___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Mphi_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2eMphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2eMphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Cpo.Conditionally_complete_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eConditionally__complete__rec___24a2(V_24X1,V_24X2) ).
fof('$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.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.NArith.BinNatDef.N.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epow,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_let_3_R_1778_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__1778,V_24X1),V_24X2) = c_24__let__3__R__1778___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Finite_sets.Finite_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eFinite__sets_2eFinite,V_24X1),V_24X2))
<=> cCoq_2eSets_2eFinite__sets_2eFinite___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Sets.Cpo.Lower_Bound_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eLower__Bound__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eLower__Bound__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_32774_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__32774,V_24X1),V_24X2) = c_24__prop__32774___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_56467_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__56467,V_24X1),V_24X2) = c_24__prop__56467___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_95_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__95,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__95___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Logic.EqdepFacts.UIP_refl_on__$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on__,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eEqdepFacts_2eUIP__refl__on_____24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Logic.eq_ind_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__ind,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eLogic_2eeq__ind___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Powerset.Power_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2ePowerset_2ePower__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2ePowerset_2ePower__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_case_Coq.Numbers.BinNums.Z$18829_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2418829,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2418829___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_2_C_2855_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__2855,V_24X1),V_24X2) = c_24__let__2__C__2855___24a2(V_24X1,V_24X2) ).
fof('$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.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.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_abstraction_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__abstraction___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1138_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1138,V_24X1),V_24X2) = c_24__lam__1138___24a2(V_24X1,V_24X2) ).
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('$adef_$_let_var_6_p_24345_24347_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__24345__24347,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__24345__24347___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.modulo_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emodulo,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emodulo___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.Sets.Ensembles.Triple_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eTriple,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eEnsembles_2eTriple___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.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.NArith.BinNatDef.N.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eodd,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).
fof('$adef_ZornsLemma.Families.FamilyIntersection_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cZornsLemma_2eFamilies_2eFamilyIntersection,V_24X1),V_24X2),V_24X3))
<=> cZornsLemma_2eFamilies_2eFamilyIntersection___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_29351_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29351,V_24X1),V_24X2),V_24X3) = c_24__prop__29351___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Structures.OrderedType.GT_$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('$adef_$_lam_33928_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__33928,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__33928___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Vectors.Fin.FS_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Lower_Bound_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLower__Bound__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eSets_2eCpo_2eLower__Bound__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_3_R_2465_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__2465,V_24X1),V_24X2) = c_24__let__3__R__2465___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_95_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__95,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__95___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_2859_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2859,V_24X1),V_24X2) = c_24__lam__2859___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eBinInt_2eZ_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_14155_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__14155,V_24X1),V_24X2) = c_24__prop__14155___24a2(V_24X1,V_24X2) ).
fof('$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_$_let_2_C_695_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__695,V_24X1),V_24X2) = c_24__let__2__C__695___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$27660_$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_2427660,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_2427660___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
<=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Powerset.Power_set_PO_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePowerset_2ePower__set__PO,V_24X1),V_24X2) = cCoq_2eSets_2ePowerset_2ePower__set__PO___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Sets.Ensembles.Union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eUnion,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eUnion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.sumor_$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('$adef_$_let_3_R_2592_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__2592,V_24X1),V_24X2) = c_24__let__3__R__2592___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.rem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2erem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2erem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Relations_1.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eRelations__1_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eSets_2eRelations__1_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emul,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1928_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1928,V_24X1),V_24X2) = c_24__lam__1928___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Lub_rect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eLub__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eSets_2eCpo_2eLub__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Same_set_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eSame__set,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eSame__set___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.exist_$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('$adef_Coq.Reals.Rpow_def.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRpow__def_2epow,V_24X1),V_24X2) = cCoq_2eReals_2eRpow__def_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_cont_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare__cont___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quot_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equot,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equot___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.log2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2elog2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2elog2___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.cons_$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('$adef_$_lam_1420_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1420,V_24X1),V_24X2) = c_24__lam__1420___24a2(V_24X1,V_24X2) ).
fof('$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.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Sets.Ensembles.Disjoint_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eDisjoint,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eEnsembles_2eDisjoint___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSets_2eCpo_2eTotally__ordered___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Glb_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eSets_2eCpo_2eGlb,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eSets_2eCpo_2eGlb___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Sets.Ensembles.Full_set_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eFull__set,V_24X1) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Add_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eSets_2eEnsembles_2eAdd,V_24X1),V_24X2),V_24X3) = cCoq_2eSets_2eEnsembles_2eAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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_$_case_Coq.Init.Datatypes.nat$18812_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2418812,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2418812___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$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('$adef_Coq.micromega.EnvRing.Pc_$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('$adef_$_let_2_C_2464_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__2464,V_24X1),V_24X2) = c_24__let__2__C__2464___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Partial_Order.Rel_of_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2ePartial__Order_2eRel__of,V_24X1),V_24X2) = cCoq_2eSets_2ePartial__Order_2eRel__of___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2edouble,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.gcd_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Cpo.Conditionally_complete_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSets_2eCpo_2eConditionally__complete,V_24X1),V_24X2))
<=> cCoq_2eSets_2eCpo_2eConditionally__complete___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).
fof('$adef_$_let_3_R_978_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__978,V_24X1),V_24X2) = c_24__let__3__R__978___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eTotally__ordered__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2997_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2997,V_24X1),V_24X2) = c_24__lam__2997___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Sets.Cpo.Totally_ordered_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eTotally__ordered__rect,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eTotally__ordered__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_ZornsLemma.EnsemblesSpec.characteristic_function_to_ensemble_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble,V_24X1),V_24X2) = cZornsLemma_2eEnsemblesSpec_2echaracteristic__function__to__ensemble___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_$_case_Coq.Init.Datatypes.nat$18834_$a1',axiom,
! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2418834___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Strict_Included_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eStrict__Included,V_24X1) = cCoq_2eSets_2eEnsembles_2eStrict__Included___24a1(V_24X1) ).
fof('$adef_$_let_3_R_1410_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__1410,V_24X1),V_24X2) = c_24__let__3__R__1410___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.ClassicalFacts.has_fixpoint_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint,V_24X1))
<=> cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1(V_24X1) ) ).
fof('$adef_Coq.Sets.Ensembles.Included_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eIncluded,V_24X1) = cCoq_2eSets_2eEnsembles_2eIncluded___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_31940_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31940,V_24X1) = c_24__lam__31940___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$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('$adef_Coq.Init.Nat.min_$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('$adef_$_let_2_C_2721_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__C__2721,V_24X1),V_24X2) = c_24__let__2__C__2721___24a2(V_24X1,V_24X2) ).
fof('$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.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_29371_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__29371,V_24X1),V_24X2) = c_24__prop__29371___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.pow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epow,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2epow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
<=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).
fof('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).
fof('$adef_Coq.Sets.Ensembles.Disjoint_rec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eSets_2eEnsembles_2eDisjoint__rec,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eSets_2eEnsembles_2eDisjoint__rec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.Sets.Cpo.Glb_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eSets_2eCpo_2eGlb__rec,V_24X1),V_24X2) = cCoq_2eSets_2eCpo_2eGlb__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
<=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.EqdepFacts.Eq_rect_eq_on_$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('$adef_Coq.Lists.SetoidList.compat_bool_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2ecompat__bool,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2ecompat__bool___24a3(V_24X1,V_24X2,V_24X3) ) ).
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_3_R_1922_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__3__R__1922,V_24X1),V_24X2) = c_24__let__3__R__1922___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_141_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__141,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__141___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
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('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_29604_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__29604,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__29604___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Sets.Partial_Order.PO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2ePartial__Order_2ePO,V_24X1) = cCoq_2eSets_2ePartial__Order_2ePO___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.setoid_ring.Field_theory.denum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2edenum,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2edenum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_$_prop_29353_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29353,V_24X1),V_24X2),V_24X3) = c_24__prop__29353___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sets.Ensembles.Ensemble_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eEnsembles_2eEnsemble,V_24X1) = cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.divmod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.double_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).
fof('$tdef_$_type_12593',axiom,
! [V_24Y] :
( c_24__type__12593___24t(V_24Y)
<=> t(V_24Y,c_24__type__12593) ) ).
fof('$tdef_$_type_3557',axiom,
! [V_24Y] :
( c_24__type__3557___24t(V_24Y)
<=> t(V_24Y,c_24__type__3557) ) ).
fof('$tdef_Coq.micromega.Env.Env',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnv_2eEnv___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12701',axiom,
! [V_24Y] :
( c_24__type__12701___24t(V_24Y)
<=> t(V_24Y,c_24__type__12701) ) ).
fof('$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('$tdef_$_type_9096',axiom,
! [V_24Y] :
( c_24__type__9096___24t(V_24Y)
<=> t(V_24Y,c_24__type__9096) ) ).
fof('$tdef_$_type_5108',axiom,
! [V_24Y] :
( c_24__type__5108___24t(V_24Y)
<=> t(V_24Y,c_24__type__5108) ) ).
fof('$tdef_$_type_29557',axiom,
! [V_24Y] :
( c_24__type__29557___24t(V_24Y)
<=> t(V_24Y,c_24__type__29557) ) ).
fof('$tdef_$_type_29184',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29184___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29184___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15408',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__15408___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__15408___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_317',axiom,
! [V_24Y] :
( c_24__type__317___24t(V_24Y)
<=> t(V_24Y,c_24__type__317) ) ).
fof('$tdef_$_type_2542',axiom,
! [V_24Y] :
( c_24__type__2542___24t(V_24Y)
<=> t(V_24Y,c_24__type__2542) ) ).
fof('$tdef_$_type_3279',axiom,
! [V_24Y] :
( c_24__type__3279___24t(V_24Y)
<=> t(V_24Y,c_24__type__3279) ) ).
fof('$tdef_$_type_26180',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26180___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26180___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_27256',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__27256___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__27256___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_27782',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27782___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_3086',axiom,
! [V_24Y] :
( c_24__type__3086___24t(V_24Y)
<=> t(V_24Y,c_24__type__3086) ) ).
fof('$tdef_$_type_26895',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26895___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26895___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_25139',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__25139___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__25139___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_21115',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__21115___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__21115___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_18175',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__18175___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__18175___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_56428',axiom,
! [V_24Y] :
( c_24__type__56428___24t(V_24Y)
<=> t(V_24Y,c_24__type__56428) ) ).
fof('$tdef_$_type_12',axiom,
! [V_24Y] :
( c_24__type__12___24t(V_24Y)
<=> t(V_24Y,c_24__type__12) ) ).
fof('$tdef_$_type_18520',axiom,
! [V_24X1,V_24Y] :
( c_24__type__18520___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__18520___24a1(V_24X1)) ) ).
fof('$tdef_$_type_22476',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__22476___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__22476___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_30323',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30323___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30323___24a1(V_24X1)) ) ).
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_$_type_9456',axiom,
! [V_24Y] :
( c_24__type__9456___24t(V_24Y)
<=> t(V_24Y,c_24__type__9456) ) ).
fof('$tdef_$_type_3131',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3131___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3131___24a1(V_24X1)) ) ).
fof('$tdef_$_type_9122',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9122___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9122___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_5289',axiom,
! [V_24Y] :
( c_24__type__5289___24t(V_24Y)
<=> t(V_24Y,c_24__type__5289) ) ).
fof('$tdef_$_type_29189',axiom,
! [V_24Y] :
( c_24__type__29189___24t(V_24Y)
<=> t(V_24Y,c_24__type__29189) ) ).
fof('$tdef_$_type_8359',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8359___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8359___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_3931',axiom,
! [V_24Y] :
( c_24__type__3931___24t(V_24Y)
<=> t(V_24Y,c_24__type__3931) ) ).
fof('$tdef_$_type_9022',axiom,
! [V_24Y] :
( c_24__type__9022___24t(V_24Y)
<=> t(V_24Y,c_24__type__9022) ) ).
fof('$tdef_$_type_56481',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__56481___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__56481___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_23814',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__23814___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__23814___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_33609',axiom,
! [V_24Y] :
( c_24__type__33609___24t(V_24Y)
<=> t(V_24Y,c_24__type__33609) ) ).
fof('$tdef_$_type_11592',axiom,
! [V_24Y] :
( c_24__type__11592___24t(V_24Y)
<=> t(V_24Y,c_24__type__11592) ) ).
fof('$tdef_$_type_104',axiom,
! [V_24Y] :
( c_24__type__104___24t(V_24Y)
<=> t(V_24Y,c_24__type__104) ) ).
fof('$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_$_type_18772',axiom,
! [V_24Y] :
( c_24__type__18772___24t(V_24Y)
<=> t(V_24Y,c_24__type__18772) ) ).
fof('$tdef_$_type_1103',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1103___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1103___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_56057',axiom,
! [V_24Y] :
( c_24__type__56057___24t(V_24Y)
<=> t(V_24Y,c_24__type__56057) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26213',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26213___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26213___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15009',axiom,
! [V_24Y] :
( c_24__type__15009___24t(V_24Y)
<=> t(V_24Y,c_24__type__15009) ) ).
fof('$tdef_$_type_26072',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26072___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26072___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2954',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__2954___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__2954___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3020',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3020___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3020___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8554',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8554___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8554___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_28267',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28267___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28267___24a2(V_24X1,V_24X2)) ) ).
fof('$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_4991',axiom,
! [V_24Y] :
( c_24__type__4991___24t(V_24Y)
<=> t(V_24Y,c_24__type__4991) ) ).
fof('$tdef_$_type_9270',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9270___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9270___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_108',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__108___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__108___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6444',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6444___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6444___24a2(V_24X1,V_24X2)) ) ).
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_$_type_17039',axiom,
! [V_24Y] :
( c_24__type__17039___24t(V_24Y)
<=> t(V_24Y,c_24__type__17039) ) ).
fof('$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_65',axiom,
! [V_24Y] :
( c_24__type__65___24t(V_24Y)
<=> t(V_24Y,c_24__type__65) ) ).
fof('$tdef_$_type_31484',axiom,
! [V_24Y] :
( c_24__type__31484___24t(V_24Y)
<=> t(V_24Y,c_24__type__31484) ) ).
fof('$tdef_$_type_9130',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9130___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9130___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Y',axiom,
! [V_24Y] :
( cY___24t(V_24Y)
<=> t(V_24Y,cY) ) ).
fof('$tdef_$_type_14234',axiom,
! [V_24Y] :
( c_24__type__14234___24t(V_24Y)
<=> t(V_24Y,c_24__type__14234) ) ).
fof('$tdef_$_type_28555',axiom,
! [V_24Y] :
( c_24__type__28555___24t(V_24Y)
<=> t(V_24Y,c_24__type__28555) ) ).
fof('$tdef_$_type_9219',axiom,
! [V_24X1,V_24Y] :
( c_24__type__9219___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__9219___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35439',axiom,
! [V_24X1,V_24Y] :
( c_24__type__35439___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__35439___24a1(V_24X1)) ) ).
fof('$tdef_$_type_27020',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__27020___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__27020___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_Coq.setoid_ring.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_$_type_12486',axiom,
! [V_24Y] :
( c_24__type__12486___24t(V_24Y)
<=> t(V_24Y,c_24__type__12486) ) ).
fof('$tdef_$_type_3544',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3544___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3544___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3277',axiom,
! [V_24Y] :
( c_24__type__3277___24t(V_24Y)
<=> t(V_24Y,c_24__type__3277) ) ).
fof('$tdef_$_type_30435',axiom,
! [V_24X1,V_24Y] :
( c_24__type__30435___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__30435___24a1(V_24X1)) ) ).
fof('$tdef_$_type_86',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__86___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__86___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_56365',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__56365___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__56365___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27826',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27826___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27826___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_18276',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18276___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18276___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Sets.Ensembles.Ensemble',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2eEnsembles_2eEnsemble___24a1(V_24X1)) ) ).
fof('$tdef_$_type_56075',axiom,
! [V_24Y] :
( c_24__type__56075___24t(V_24Y)
<=> t(V_24Y,c_24__type__56075) ) ).
fof('$tdef_$_type_29591',axiom,
! [V_24Y] :
( c_24__type__29591___24t(V_24Y)
<=> t(V_24Y,c_24__type__29591) ) ).
fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Numbers.BinNums.N',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).
fof('$tdef_$_type_56465',axiom,
! [V_24Y] :
( c_24__type__56465___24t(V_24Y)
<=> t(V_24Y,c_24__type__56465) ) ).
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_$_type_27405',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27405___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27405___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_539',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__539___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__539___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3537',axiom,
! [V_24Y] :
( c_24__type__3537___24t(V_24Y)
<=> t(V_24Y,c_24__type__3537) ) ).
fof('$tdef_$_type_31908',axiom,
! [V_24Y] :
( c_24__type__31908___24t(V_24Y)
<=> t(V_24Y,c_24__type__31908) ) ).
fof('$tdef_$_type_14501',axiom,
! [V_24Y] :
( c_24__type__14501___24t(V_24Y)
<=> t(V_24Y,c_24__type__14501) ) ).
fof('$tdef_$_type_4215',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__4215___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__4215___24a2(V_24X1,V_24X2)) ) ).
fof('$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_4251',axiom,
! [V_24Y] :
( c_24__type__4251___24t(V_24Y)
<=> t(V_24Y,c_24__type__4251) ) ).
fof('$tdef_$_type_14322',axiom,
! [V_24X1,V_24Y] :
( c_24__type__14322___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__14322___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23491',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__23491___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__23491___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_35368',axiom,
! [V_24Y] :
( c_24__type__35368___24t(V_24Y)
<=> t(V_24Y,c_24__type__35368) ) ).
fof('$tdef_$_type_314',axiom,
! [V_24Y] :
( c_24__type__314___24t(V_24Y)
<=> t(V_24Y,c_24__type__314) ) ).
fof('$tdef_$_type_3183',axiom,
! [V_24Y] :
( c_24__type__3183___24t(V_24Y)
<=> t(V_24Y,c_24__type__3183) ) ).
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_$_type_25847',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25847___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25847___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_24896',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24896___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__24896___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4198',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4198___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4198___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26156',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26156___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26156___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5077',axiom,
! [V_24Y] :
( c_24__type__5077___24t(V_24Y)
<=> t(V_24Y,c_24__type__5077) ) ).
fof('$tdef_$_type_3289',axiom,
! [V_24Y] :
( c_24__type__3289___24t(V_24Y)
<=> t(V_24Y,c_24__type__3289) ) ).
fof('$tdef_$_type_17094',axiom,
! [V_24Y] :
( c_24__type__17094___24t(V_24Y)
<=> t(V_24Y,c_24__type__17094) ) ).
fof('$tdef_$_type_12435',axiom,
! [V_24Y] :
( c_24__type__12435___24t(V_24Y)
<=> t(V_24Y,c_24__type__12435) ) ).
fof('$tdef_$_type_12426',axiom,
! [V_24Y] :
( c_24__type__12426___24t(V_24Y)
<=> t(V_24Y,c_24__type__12426) ) ).
fof('$tdef_$_type_513',axiom,
! [V_24Y] :
( c_24__type__513___24t(V_24Y)
<=> t(V_24Y,c_24__type__513) ) ).
fof('$tdef_$_type_28475',axiom,
! [V_24Y] :
( c_24__type__28475___24t(V_24Y)
<=> t(V_24Y,c_24__type__28475) ) ).
fof('$tdef_$_type_4207',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4207___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4207___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17148',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__17148___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__17148___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_28257',axiom,
! [V_24Y] :
( c_24__type__28257___24t(V_24Y)
<=> t(V_24Y,c_24__type__28257) ) ).
fof('$tdef_$_type_2908',axiom,
! [V_24Y] :
( c_24__type__2908___24t(V_24Y)
<=> t(V_24Y,c_24__type__2908) ) ).
fof('$tdef_$_type_202',axiom,
! [V_24X1,V_24Y] :
( c_24__type__202___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__202___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12825',axiom,
! [V_24Y] :
( c_24__type__12825___24t(V_24Y)
<=> t(V_24Y,c_24__type__12825) ) ).
fof('$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('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_$_type_19754',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__19754___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__19754___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Init.Datatypes.unit',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eunit) ) ).
fof('$tdef_$_type_3305',axiom,
! [V_24Y] :
( c_24__type__3305___24t(V_24Y)
<=> t(V_24Y,c_24__type__3305) ) ).
fof('$tdef_$_type_12844',axiom,
! [V_24Y] :
( c_24__type__12844___24t(V_24Y)
<=> t(V_24Y,c_24__type__12844) ) ).
fof('$tdef_$_type_11600',axiom,
! [V_24Y] :
( c_24__type__11600___24t(V_24Y)
<=> t(V_24Y,c_24__type__11600) ) ).
fof('$tdef_$_type_5009',axiom,
! [V_24Y] :
( c_24__type__5009___24t(V_24Y)
<=> t(V_24Y,c_24__type__5009) ) ).
fof('$tdef_$_type_3465',axiom,
! [V_24Y] :
( c_24__type__3465___24t(V_24Y)
<=> t(V_24Y,c_24__type__3465) ) ).
fof('$tdef_$_type_8962',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__8962___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__8962___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('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Sets.Partial_Order.PO',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2ePartial__Order_2ePO___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2ePartial__Order_2ePO___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12935',axiom,
! [V_24Y] :
( c_24__type__12935___24t(V_24Y)
<=> t(V_24Y,c_24__type__12935) ) ).
fof('$tdef_$_type_33867',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33867___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33867___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12495',axiom,
! [V_24Y] :
( c_24__type__12495___24t(V_24Y)
<=> t(V_24Y,c_24__type__12495) ) ).
fof('$tdef_$_type_12391',axiom,
! [V_24Y] :
( c_24__type__12391___24t(V_24Y)
<=> t(V_24Y,c_24__type__12391) ) ).
fof('$tdef_$_type_18841',axiom,
! [V_24Y] :
( c_24__type__18841___24t(V_24Y)
<=> t(V_24Y,c_24__type__18841) ) ).
fof('$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_29531',axiom,
! [V_24Y] :
( c_24__type__29531___24t(V_24Y)
<=> t(V_24Y,c_24__type__29531) ) ).
fof('$tdef_$_type_5',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1077',axiom,
! [V_24Y] :
( c_24__type__1077___24t(V_24Y)
<=> t(V_24Y,c_24__type__1077) ) ).
fof('$tdef_$_type_17101',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__17101___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__17101___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_26520',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26520___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26520___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_25076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__25076___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__25076___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_56162',axiom,
! [V_24Y] :
( c_24__type__56162___24t(V_24Y)
<=> t(V_24Y,c_24__type__56162) ) ).
fof('$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_3134',axiom,
! [V_24Y] :
( c_24__type__3134___24t(V_24Y)
<=> t(V_24Y,c_24__type__3134) ) ).
fof('$tdef_$_type_25888',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25888___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25888___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3349',axiom,
! [V_24Y] :
( c_24__type__3349___24t(V_24Y)
<=> t(V_24Y,c_24__type__3349) ) ).
fof('$tdef_$_type_18439',axiom,
! [V_24Y] :
( c_24__type__18439___24t(V_24Y)
<=> t(V_24Y,c_24__type__18439) ) ).
fof('$tdef_$_type_28471',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28471___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28471___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_35430',axiom,
! [V_24Y] :
( c_24__type__35430___24t(V_24Y)
<=> t(V_24Y,c_24__type__35430) ) ).
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_$_type_5546',axiom,
! [V_24Y] :
( c_24__type__5546___24t(V_24Y)
<=> t(V_24Y,c_24__type__5546) ) ).
fof('$tdef_$_type_4762',axiom,
! [V_24Y] :
( c_24__type__4762___24t(V_24Y)
<=> t(V_24Y,c_24__type__4762) ) ).
fof('$tdef_$_type_24959',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__24959___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__24959___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_56462',axiom,
! [V_24Y] :
( c_24__type__56462___24t(V_24Y)
<=> t(V_24Y,c_24__type__56462) ) ).
fof('$tdef_$_type_2829',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2829___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2829___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_24357',axiom,
! [V_24Y] :
( c_24__type__24357___24t(V_24Y)
<=> t(V_24Y,c_24__type__24357) ) ).
fof('$tdef_$_type_17883',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__17883___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__17883___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9252',axiom,
! [V_24Y] :
( c_24__type__9252___24t(V_24Y)
<=> t(V_24Y,c_24__type__9252) ) ).
fof('$tdef_$_type_56351',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__56351___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__56351___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15222',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__15222___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__15222___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15583',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__15583___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__15583___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15018',axiom,
! [V_24Y] :
( c_24__type__15018___24t(V_24Y)
<=> t(V_24Y,c_24__type__15018) ) ).
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_$_type_11575',axiom,
! [V_24Y] :
( c_24__type__11575___24t(V_24Y)
<=> t(V_24Y,c_24__type__11575) ) ).
fof('$tdef_$_type_26126',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26126___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26126___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35399',axiom,
! [V_24Y] :
( c_24__type__35399___24t(V_24Y)
<=> t(V_24Y,c_24__type__35399) ) ).
fof('$tdef_$_type_3246',axiom,
! [V_24Y] :
( c_24__type__3246___24t(V_24Y)
<=> t(V_24Y,c_24__type__3246) ) ).
fof('$tdef_$_type_18400',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18400___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18400___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2944',axiom,
! [V_24Y] :
( c_24__type__2944___24t(V_24Y)
<=> t(V_24Y,c_24__type__2944) ) ).
fof('$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_11527',axiom,
! [V_24Y] :
( c_24__type__11527___24t(V_24Y)
<=> t(V_24Y,c_24__type__11527) ) ).
fof('$tdef_$_type_15315',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__15315___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__15315___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12499',axiom,
! [V_24Y] :
( c_24__type__12499___24t(V_24Y)
<=> t(V_24Y,c_24__type__12499) ) ).
fof('$tdef_$_type_24160',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__24160___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__24160___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_3119',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__3119___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__3119___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_$_type_1385',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__1385___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__1385___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_342',axiom,
! [V_24Y] :
( c_24__type__342___24t(V_24Y)
<=> t(V_24Y,c_24__type__342) ) ).
fof('$tdef_$_type_33691',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33691___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33691___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8767',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__8767___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__8767___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_3366',axiom,
! [V_24Y] :
( c_24__type__3366___24t(V_24Y)
<=> t(V_24Y,c_24__type__3366) ) ).
fof('$tdef_$_type_17',axiom,
! [V_24Y] :
( c_24__type__17___24t(V_24Y)
<=> t(V_24Y,c_24__type__17) ) ).
fof('$tdef_$_type_24339',axiom,
! [V_24Y] :
( c_24__type__24339___24t(V_24Y)
<=> t(V_24Y,c_24__type__24339) ) ).
fof('$tdef_$_type_27862',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27862___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27862___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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('$tdef_$_type_15000',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__15000___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__15000___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_28510',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__28510___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__28510___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_$_type_5036',axiom,
! [V_24Y] :
( c_24__type__5036___24t(V_24Y)
<=> t(V_24Y,c_24__type__5036) ) ).
fof('$tdef_$_type_20423',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__20423___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__20423___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_29561',axiom,
! [V_24Y] :
( c_24__type__29561___24t(V_24Y)
<=> t(V_24Y,c_24__type__29561) ) ).
fof('$tdef_$_type_14224',axiom,
! [V_24Y] :
( c_24__type__14224___24t(V_24Y)
<=> t(V_24Y,c_24__type__14224) ) ).
fof('$tdef_$_type_26042',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26042___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26042___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_14331',axiom,
! [V_24Y] :
( c_24__type__14331___24t(V_24Y)
<=> t(V_24Y,c_24__type__14331) ) ).
fof('$tdef_$_type_56448',axiom,
! [V_24Y] :
( c_24__type__56448___24t(V_24Y)
<=> t(V_24Y,c_24__type__56448) ) ).
fof('$tdef_$_type_4262',axiom,
! [V_24Y] :
( c_24__type__4262___24t(V_24Y)
<=> t(V_24Y,c_24__type__4262) ) ).
fof('$tdef_$_type_33908',axiom,
! [V_24Y] :
( c_24__type__33908___24t(V_24Y)
<=> t(V_24Y,c_24__type__33908) ) ).
fof('$tdef_$_type_127',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__127___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__127___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_28629',axiom,
! [V_24Y] :
( c_24__type__28629___24t(V_24Y)
<=> t(V_24Y,c_24__type__28629) ) ).
fof('$tdef_$_type_3354',axiom,
! [V_24Y] :
( c_24__type__3354___24t(V_24Y)
<=> t(V_24Y,c_24__type__3354) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27547',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27547___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27547___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_9200',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9200___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9200___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_3934',axiom,
! [V_24Y] :
( c_24__type__3934___24t(V_24Y)
<=> t(V_24Y,c_24__type__3934) ) ).
fof('$tdef_$_type_5099',axiom,
! [V_24Y] :
( c_24__type__5099___24t(V_24Y)
<=> t(V_24Y,c_24__type__5099) ) ).
fof('$tdef_$_type_5541',axiom,
! [V_24Y] :
( c_24__type__5541___24t(V_24Y)
<=> t(V_24Y,c_24__type__5541) ) ).
fof('$tdef_$_type_31865',axiom,
! [V_24Y] :
( c_24__type__31865___24t(V_24Y)
<=> t(V_24Y,c_24__type__31865) ) ).
fof('$tdef_$_type_6886',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__6886___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__6886___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_9479',axiom,
! [V_24Y] :
( c_24__type__9479___24t(V_24Y)
<=> t(V_24Y,c_24__type__9479) ) ).
fof('$tdef_$_type_56199',axiom,
! [V_24X1,V_24Y] :
( c_24__type__56199___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__56199___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32787',axiom,
! [V_24Y] :
( c_24__type__32787___24t(V_24Y)
<=> t(V_24Y,c_24__type__32787) ) ).
fof('$tdef_$_type_12489',axiom,
! [V_24Y] :
( c_24__type__12489___24t(V_24Y)
<=> t(V_24Y,c_24__type__12489) ) ).
fof('$tdef_$_type_12820',axiom,
! [V_24Y] :
( c_24__type__12820___24t(V_24Y)
<=> t(V_24Y,c_24__type__12820) ) ).
fof('$tdef_$_type_7933',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__7933___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__7933___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_19408',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__19408___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__19408___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_1868',axiom,
! [V_24Y] :
( c_24__type__1868___24t(V_24Y)
<=> t(V_24Y,c_24__type__1868) ) ).
fof('$tdef_$_type_9060',axiom,
! [V_24Y] :
( c_24__type__9060___24t(V_24Y)
<=> t(V_24Y,c_24__type__9060) ) ).
fof('$tdef_$_type_33563',axiom,
! [V_24Y] :
( c_24__type__33563___24t(V_24Y)
<=> t(V_24Y,c_24__type__33563) ) ).
fof('$tdef_$_type_29099',axiom,
! [V_24Y] :
( c_24__type__29099___24t(V_24Y)
<=> t(V_24Y,c_24__type__29099) ) ).
fof('$tdef_$_type_27597',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27597___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27597___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_17973',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__17973___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__17973___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.rsplit',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1)) ) ).
fof('$tdef_$_type_26096',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26096___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26096___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_28514',axiom,
! [V_24Y] :
( c_24__type__28514___24t(V_24Y)
<=> t(V_24Y,c_24__type__28514) ) ).
fof('$tdef_$_type_15758',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15758___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15758___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.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_3582',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3582___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3582___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8146',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__8146___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__8146___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_28493',axiom,
! [V_24Y] :
( c_24__type__28493___24t(V_24Y)
<=> t(V_24Y,c_24__type__28493) ) ).
fof('$tdef_$_type_29175',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__29175___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__29175___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_18419',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__18419___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__18419___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3588',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__3588___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__3588___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_28538',axiom,
! [V_24Y] :
( c_24__type__28538___24t(V_24Y)
<=> t(V_24Y,c_24__type__28538) ) ).
fof('$tdef_$_type_28455',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__28455___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__28455___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3209',axiom,
! [V_24Y] :
( c_24__type__3209___24t(V_24Y)
<=> t(V_24Y,c_24__type__3209) ) ).
fof('$tdef_$_type_3317',axiom,
! [V_24Y] :
( c_24__type__3317___24t(V_24Y)
<=> t(V_24Y,c_24__type__3317) ) ).
fof('$tdef_$_type_17070',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__17070___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__17070___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7312',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__7312___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__7312___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_29528',axiom,
! [V_24Y] :
( c_24__type__29528___24t(V_24Y)
<=> t(V_24Y,c_24__type__29528) ) ).
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_4767',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4767___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4767___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3101',axiom,
! [V_24Y] :
( c_24__type__3101___24t(V_24Y)
<=> t(V_24Y,c_24__type__3101) ) ).
fof('$tdef_$_type_4744',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4744___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4744___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23168',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__23168___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__23168___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_5080',axiom,
! [V_24Y] :
( c_24__type__5080___24t(V_24Y)
<=> t(V_24Y,c_24__type__5080) ) ).
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_$_type_5538',axiom,
! [V_24Y] :
( c_24__type__5538___24t(V_24Y)
<=> t(V_24Y,c_24__type__5538) ) ).
fof('$tdef_$_type_2990',axiom,
! [V_24Y] :
( c_24__type__2990___24t(V_24Y)
<=> t(V_24Y,c_24__type__2990) ) ).
fof('$tdef_$_type_821',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__821___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__821___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5066',axiom,
! [V_24Y] :
( c_24__type__5066___24t(V_24Y)
<=> t(V_24Y,c_24__type__5066) ) ).
fof('$tdef_$_type_25870',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25870___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25870___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_6465',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6465___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6465___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12582',axiom,
! [V_24Y] :
( c_24__type__12582___24t(V_24Y)
<=> t(V_24Y,c_24__type__12582) ) ).
fof('$tdef_$_type_29305',axiom,
! [V_24Y] :
( c_24__type__29305___24t(V_24Y)
<=> t(V_24Y,c_24__type__29305) ) ).
fof('$tdef_$_type_15490',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15490___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15490___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3222',axiom,
! [V_24Y] :
( c_24__type__3222___24t(V_24Y)
<=> t(V_24Y,c_24__type__3222) ) ).
fof('$tdef_ZornsLemma.Families.Family',axiom,
! [V_24X1,V_24Y] :
( cZornsLemma_2eFamilies_2eFamily___24t(V_24X1,V_24Y)
<=> t(V_24Y,cZornsLemma_2eFamilies_2eFamily___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Bool.Bool.reflect',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31884',axiom,
! [V_24Y] :
( c_24__type__31884___24t(V_24Y)
<=> t(V_24Y,c_24__type__31884) ) ).
fof('$tdef_$_type_27505',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27505___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27505___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_51',axiom,
! [V_24Y] :
( c_24__type__51___24t(V_24Y)
<=> t(V_24Y,c_24__type__51) ) ).
fof('$tdef_$_type_29091',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__29091___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__29091___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$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_795',axiom,
! [V_24Y] :
( c_24__type__795___24t(V_24Y)
<=> t(V_24Y,c_24__type__795) ) ).
fof('$tdef_$_type_56332',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__56332___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__56332___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_56079',axiom,
! [V_24Y] :
( c_24__type__56079___24t(V_24Y)
<=> t(V_24Y,c_24__type__56079) ) ).
fof('$tdef_$_type_27145',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__27145___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__27145___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('$tdef_Coq.Sets.Partial_Order.Rel',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eSets_2ePartial__Order_2eRel___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eSets_2ePartial__Order_2eRel___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18547',axiom,
! [V_24Y] :
( c_24__type__18547___24t(V_24Y)
<=> t(V_24Y,c_24__type__18547) ) ).
fof('$tdef_$_type_14394',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14394___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14394___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Numbers.BinNums.Z',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eZ) ) ).
fof('$tdef_$_type_31812',axiom,
! [V_24Y] :
( c_24__type__31812___24t(V_24Y)
<=> t(V_24Y,c_24__type__31812) ) ).
fof('$tdef_$_type_25824',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25824___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25824___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_28120',axiom,
! [V_24Y] :
( c_24__type__28120___24t(V_24Y)
<=> t(V_24Y,c_24__type__28120) ) ).
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_$_type_14920',axiom,
! [V_24Y] :
( c_24__type__14920___24t(V_24Y)
<=> t(V_24Y,c_24__type__14920) ) ).
fof('$tdef_$_type_12886',axiom,
! [V_24Y] :
( c_24__type__12886___24t(V_24Y)
<=> t(V_24Y,c_24__type__12886) ) ).
fof('$tdef_$_type_26770',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26770___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26770___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_7099',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__7099___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__7099___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_21807',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__21807___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__21807___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_12725',axiom,
! [V_24Y] :
( c_24__type__12725___24t(V_24Y)
<=> t(V_24Y,c_24__type__12725) ) ).
fof('$tdef_$_type_12650',axiom,
! [V_24Y] :
( c_24__type__12650___24t(V_24Y)
<=> t(V_24Y,c_24__type__12650) ) ).
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_$_type_13531',axiom,
! [V_24Y] :
( c_24__type__13531___24t(V_24Y)
<=> t(V_24Y,c_24__type__13531) ) ).
fof('$tdef_$_type_7507',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__7507___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__7507___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_9208',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__9208___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__9208___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33568',axiom,
! [V_24Y] :
( c_24__type__33568___24t(V_24Y)
<=> t(V_24Y,c_24__type__33568) ) ).
fof('$tdef_$_type_20769',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__20769___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__20769___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_14149',axiom,
! [V_24Y] :
( c_24__type__14149___24t(V_24Y)
<=> t(V_24Y,c_24__type__14149) ) ).
fof('$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_28532',axiom,
! [V_24Y] :
( c_24__type__28532___24t(V_24Y)
<=> t(V_24Y,c_24__type__28532) ) ).
fof('$tdef_$_type_25914',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25914___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25914___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_14499',axiom,
! [V_24Y] :
( c_24__type__14499___24t(V_24Y)
<=> t(V_24Y,c_24__type__14499) ) ).
fof('$tdef_$_type_12640',axiom,
! [V_24Y] :
( c_24__type__12640___24t(V_24Y)
<=> t(V_24Y,c_24__type__12640) ) ).
fof('$tdef_$_type_21461',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__21461___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__21461___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_3552',axiom,
! [V_24Y] :
( c_24__type__3552___24t(V_24Y)
<=> t(V_24Y,c_24__type__3552) ) ).
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_$_type_159',axiom,
! [V_24Y] :
( c_24__type__159___24t(V_24Y)
<=> t(V_24Y,c_24__type__159) ) ).
fof('$tdef_$_type_3329',axiom,
! [V_24Y] :
( c_24__type__3329___24t(V_24Y)
<=> t(V_24Y,c_24__type__3329) ) ).
fof('$tdef_$_type_20100',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__20100___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__20100___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.micromega.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_2801',axiom,
! [V_24Y] :
( c_24__type__2801___24t(V_24Y)
<=> t(V_24Y,c_24__type__2801) ) ).
fof('$tdef_$_type_2569',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2569___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2569___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_27455',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27455___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27455___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_56129',axiom,
! [V_24Y] :
( c_24__type__56129___24t(V_24Y)
<=> t(V_24Y,c_24__type__56129) ) ).
fof('$tdef_$_type_14972',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__14972___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__14972___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_18074',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__18074___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__18074___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12403',axiom,
! [V_24Y] :
( c_24__type__12403___24t(V_24Y)
<=> t(V_24Y,c_24__type__12403) ) ).
fof('$tdef_$_type_5027',axiom,
! [V_24Y] :
( c_24__type__5027___24t(V_24Y)
<=> t(V_24Y,c_24__type__5027) ) ).
fof('$tdef_$_type_14912',axiom,
! [V_24Y] :
( c_24__type__14912___24t(V_24Y)
<=> t(V_24Y,c_24__type__14912) ) ).
fof('$tdef_$_type_1896',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__1896___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__1896___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3198',axiom,
! [V_24Y] :
( c_24__type__3198___24t(V_24Y)
<=> t(V_24Y,c_24__type__3198) ) ).
fof('$tdef_$_type_12832',axiom,
! [V_24Y] :
( c_24__type__12832___24t(V_24Y)
<=> t(V_24Y,c_24__type__12832) ) ).
fof('$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_9216',axiom,
! [V_24Y] :
( c_24__type__9216___24t(V_24Y)
<=> t(V_24Y,c_24__type__9216) ) ).
fof('$tdef_$_type_25932',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25932___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25932___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_22153',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__22153___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__22153___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_13567',axiom,
! [V_24Y] :
( c_24__type__13567___24t(V_24Y)
<=> t(V_24Y,c_24__type__13567) ) ).
fof('$tdef_$_type_12354',axiom,
! [V_24Y] :
( c_24__type__12354___24t(V_24Y)
<=> t(V_24Y,c_24__type__12354) ) ).
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_$_type_28162',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__28162___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__28162___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_27673',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27673___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27673___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_9138',axiom,
! [V_24Y] :
( c_24__type__9138___24t(V_24Y)
<=> t(V_24Y,c_24__type__9138) ) ).
fof('$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_9172',axiom,
! [V_24Y] :
( c_24__type__9172___24t(V_24Y)
<=> t(V_24Y,c_24__type__9172) ) ).
fof('$tdef_$_type_27906',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__27906___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__27906___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_25022',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__25022___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__25022___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_22822',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__22822___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__22822___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_14248',axiom,
! [V_24Y] :
( c_24__type__14248___24t(V_24Y)
<=> t(V_24Y,c_24__type__14248) ) ).
fof('$tdef_$_type_12835',axiom,
! [V_24Y] :
( c_24__type__12835___24t(V_24Y)
<=> t(V_24Y,c_24__type__12835) ) ).
fof('$tdef_X',axiom,
! [V_24Y] :
( cX___24t(V_24Y)
<=> t(V_24Y,cX) ) ).
fof('$tdef_$_type_55284',axiom,
! [V_24Y] :
( c_24__type__55284___24t(V_24Y)
<=> t(V_24Y,c_24__type__55284) ) ).
fof('$tdef_$_type_9473',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9473___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9473___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_24378',axiom,
! [V_24Y] :
( c_24__type__24378___24t(V_24Y)
<=> t(V_24Y,c_24__type__24378) ) ).
fof('$tdef_$_type_7720',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__7720___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__7720___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_6458',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__6458___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__6458___24a2(V_24X1,V_24X2)) ) ).
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_$_type_9450',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__9450___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__9450___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3258',axiom,
! [V_24Y] :
( c_24__type__3258___24t(V_24Y)
<=> t(V_24Y,c_24__type__3258) ) ).
fof('$tdef_$_type_7',axiom,
! [V_24Y] :
( c_24__type__7___24t(V_24Y)
<=> t(V_24Y,c_24__type__7) ) ).
fof('$tdef_$_type_12388',axiom,
! [V_24Y] :
( c_24__type__12388___24t(V_24Y)
<=> t(V_24Y,c_24__type__12388) ) ).
fof('$tdef_$_type_18727',axiom,
! [V_24Y] :
( c_24__type__18727___24t(V_24Y)
<=> t(V_24Y,c_24__type__18727) ) ).
fof('$tdef_$_type_56189',axiom,
! [V_24Y] :
( c_24__type__56189___24t(V_24Y)
<=> t(V_24Y,c_24__type__56189) ) ).
fof('$tdef_$_type_17063',axiom,
! [V_24Y] :
( c_24__type__17063___24t(V_24Y)
<=> t(V_24Y,c_24__type__17063) ) ).
fof('$tdef_$_type_3141',axiom,
! [V_24Y] :
( c_24__type__3141___24t(V_24Y)
<=> t(V_24Y,c_24__type__3141) ) ).
fof('$tdef_$_type_11497',axiom,
! [V_24Y] :
( c_24__type__11497___24t(V_24Y)
<=> t(V_24Y,c_24__type__11497) ) ).
fof('$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_$_type_26264',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26264___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26264___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_2',axiom,
! [V_24Y] :
( c_24__type__2___24t(V_24Y)
<=> t(V_24Y,c_24__type__2) ) ).
fof('$tdef_$_type_56457',axiom,
! [V_24Y] :
( c_24__type__56457___24t(V_24Y)
<=> t(V_24Y,c_24__type__56457) ) ).
fof('$tdef_$_type_56086',axiom,
! [V_24Y] :
( c_24__type__56086___24t(V_24Y)
<=> t(V_24Y,c_24__type__56086) ) ).
fof('$tdef_$_type_3196',axiom,
! [V_24Y] :
( c_24__type__3196___24t(V_24Y)
<=> t(V_24Y,c_24__type__3196) ) ).
fof('$tdef_$_type_26237',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__26237___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__26237___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_26645',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y] :
( c_24__type__26645___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24Y)
<=> t(V_24Y,c_24__type__26645___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).
fof('$tdef_$_type_5095',axiom,
! [V_24Y] :
( c_24__type__5095___24t(V_24Y)
<=> t(V_24Y,c_24__type__5095) ) ).
fof('$tdef_$_type_32816',axiom,
! [V_24Y] :
( c_24__type__32816___24t(V_24Y)
<=> t(V_24Y,c_24__type__32816) ) ).
fof('$tdef_$_type_3225',axiom,
! [V_24Y] :
( c_24__type__3225___24t(V_24Y)
<=> t(V_24Y,c_24__type__3225) ) ).
fof('$tdef_$_type_17014',axiom,
! [V_24Y] :
( c_24__type__17014___24t(V_24Y)
<=> t(V_24Y,c_24__type__17014) ) ).
fof('$tdef_$_type_17681',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__17681___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__17681___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4282',axiom,
! [V_24Y] :
( c_24__type__4282___24t(V_24Y)
<=> t(V_24Y,c_24__type__4282) ) ).
fof('$tdef_$_type_9276',axiom,
! [V_24Y] :
( c_24__type__9276___24t(V_24Y)
<=> t(V_24Y,c_24__type__9276) ) ).
fof('$tdef_$_type_3926',axiom,
! [V_24Y] :
( c_24__type__3926___24t(V_24Y)
<=> t(V_24Y,c_24__type__3926) ) ).
fof('$tdef_$_type_28543',axiom,
! [V_24Y] :
( c_24__type__28543___24t(V_24Y)
<=> t(V_24Y,c_24__type__28543) ) ).
fof('$tdef_$_type_1359',axiom,
! [V_24Y] :
( c_24__type__1359___24t(V_24Y)
<=> t(V_24Y,c_24__type__1359) ) ).
fof('$tdef_$_type_3392',axiom,
! [V_24Y] :
( c_24__type__3392___24t(V_24Y)
<=> t(V_24Y,c_24__type__3392) ) ).
fof('$tdef_$_type_14862',axiom,
! [V_24Y] :
( c_24__type__14862___24t(V_24Y)
<=> t(V_24Y,c_24__type__14862) ) ).
fof('$tdef_$_type_25801',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__25801___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__25801___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_15665',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__15665___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__15665___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_17782',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__17782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__17782___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_24330',axiom,
! [V_24Y] :
( c_24__type__24330___24t(V_24Y)
<=> t(V_24Y,c_24__type__24330) ) ).
fof('$tdef_$_type_12603',axiom,
! [V_24Y] :
( c_24__type__12603___24t(V_24Y)
<=> t(V_24Y,c_24__type__12603) ) ).
fof('$tdef_$_type_12599',axiom,
! [V_24Y] :
( c_24__type__12599___24t(V_24Y)
<=> t(V_24Y,c_24__type__12599) ) ).
fof('_HAMMER_GOAL',conjecture,
( ! [V0__y] :
( cY___24t(V0__y)
=> cf___24a1(cg___24a1(V0__y)) = V0__y )
=> ! [V1__S] :
( cCoq_2eSets_2eEnsembles_2eEnsemble___24t(cY,V1__S)
=> cZornsLemma_2eInverseImage_2einverse__image___24a4(cY,cX,cg,cZornsLemma_2eInverseImage_2einverse__image___24a4(cX,cY,cf,V1__S)) = V1__S ) ) ).
%------------------------------------------------------------------------------