TPTP Problem File: SEV615+1.p
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%------------------------------------------------------------------------------
% File : SEV615+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnAcyclic in pref union
% 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 : HahnAcyclic.in.pref.union.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2425 ( 593 unt; 0 def)
% Number of atoms : 10725 (1164 equ)
% Maximal formula atoms : 82 ( 4 avg)
% Number of connectives : 8586 ( 286 ~; 294 |; 877 &)
% ( 992 <=>;6137 =>; 0 <=; 0 <~>)
% Maximal formula depth : 55 ( 8 avg)
% Maximal term depth : 23 ( 1 avg)
% Number of predicates : 475 ( 474 usr; 0 prp; 1-23 aty)
% Number of functors : 1034 (1034 usr; 575 con; 0-22 aty)
% Number of variables : 10076 (9757 !; 319 ?)
% 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.prod$32394',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__0)
=> ( cType___24t(Vv__CANONICAL__2)
=> ( c_24__type__32407___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
=> ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> ? [Vvar__2___24Anonymous__32399] :
( t(Vvar__2___24Anonymous__32399,Vv__CANONICAL__2)
& ? [Vvar__3___24Anonymous__32400] :
( t(Vvar__3___24Anonymous__32400,Vv__CANONICAL__2)
& happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__32399,Vvar__3___24Anonymous__32400)
& ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432394___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
<=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__32399)),Vvar__3___24Anonymous__32400)))) ) ) ) ) ) ) ) ) ).
fof('$_case_Coq.Init.Specif.sumbool$1224',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ( ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& c_24__let__2__s__1217___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_241224___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1233___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) )
| ( p(cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& c_24__let__2__s__1217___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
& c_24__case__Coq_2eInit_2eSpecif_2esumbool_241224___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2eright___24a3(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1234___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eArith_2eGt_2egt__not__le___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_def_$_let_11_subst_l_28561',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__28561___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).
fof('$_def_$_let_2_s_1217',axiom,
! [V0__n,V1__m] : c_24__let__2__s__1217___24a2(V0__n,V1__m) = cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V0__n,V1__m) ).
fof('$_def_$_let_var_6_p_7702_7705',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7701] : c_24__let__var__6__p__7702__7705___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7701) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7701) ).
fof('$_def_$_let_var_6_p_7704_7706',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7703] : c_24__let__var__6__p__7704__7706___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7703) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7703) ).
fof('$_def_Coq.Arith.Between.in_int',axiom,
! [V0__p,V1__q,V2__r] :
( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
<=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r))
& p(cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q)) ) ) ).
fof('$_def_Coq.Arith.Compare_dec.le_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__dec___24a2(V0__n,V1__m) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_241224___24a2(V0__n,V1__m) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__3244___24a1(V0__A)) ).
fof('$_def_Coq.Arith.Wf_nat.has_unique_least_element',axiom,
! [V0__A,V1__R,V2__P] :
( cCoq_2eArith_2eWf__nat_2ehas__unique__least__element___24a3(V0__A,V1__R,V2__P)
<=> cCoq_2eInit_2eLogic_2eex___24a2(V0__A,cCoq_2eInit_2eLogic_2eunique___24a2(V0__A,c_24__lam__35041___24a3(V0__A,V1__R,V2__P))) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
! [V0__i,V1__t] :
( p(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('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__11891] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__11891)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__11891) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__11905] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__11905)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__11905) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__301] :
( t(Vvar__1___24Anonymous__301,V0__A)
& ? [Vvar__2___24Anonymous__302] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__302)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__301,Vvar__2___24Anonymous__302)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__301,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__302,V3__m)) ) ) ) ) ) ).
fof('$_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__13065] :
( t(Vvar__2___24Anonymous__13065,V0__A)
& ? [Vvar__3___24Anonymous__13066] :
( t(Vvar__3___24Anonymous__13066,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__13065,Vvar__3___24Anonymous__13066)
& cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__13065 ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__291] :
( t(Vvar__1___24Anonymous__291,V0__A)
& ? [Vvar__2___24Anonymous__292] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__292)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__291,Vvar__2___24Anonymous__292)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__292)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.list_rec',axiom,
! [V0__A,V1__P] : cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V0__A,V1__P) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V0__A,V1__P) ).
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.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__13077] :
( t(Vvar__2___24Anonymous__13077,V0__A)
& ? [Vvar__3___24Anonymous__13078] :
( t(Vvar__3___24Anonymous__13078,V1__B)
& V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__13077,Vvar__3___24Anonymous__13078)
& cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__13078 ) ) ) ) ) ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
| ? [Vvar__0___24Anonymous__372] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__372)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__372)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__372,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.modulo',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emodulo___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__1058] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1058)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1058)
& cCoq_2eInit_2eNat_2emodulo___24a2(V0__x,V1__y) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__1058,cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__1058,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__1058))) ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__1053] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1053)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1053)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__1056] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1056)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1056)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__1053,Vvar__0___24Anonymous__1056) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Init.Peano.ge',axiom,
! [V0__n,V1__m] :
( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.gt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n)) ) ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [V0__n,V1__m] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m)) ) ).
fof('$_def_Coq.Init.Specif.absurd_set',axiom,
! [V0__A,V1__C] : cCoq_2eInit_2eSpecif_2eabsurd__set___24a2(V0__A,V1__C) = cCoq_2eInit_2eLogic_2eFalse__rec___24a1(V1__C) ).
fof('$_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('$_def_Coq.Lists.List.In',axiom,
! [V0__A,V2__a,V3__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> p(c_24False) ) )
| ? [Vvar__1___24Anonymous__363] :
( t(Vvar__1___24Anonymous__363,V0__A)
& ? [Vvar__2___24Anonymous__364] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__364)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__363,Vvar__2___24Anonymous__364)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__363 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__364)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.filter',axiom,
! [V0__A,V1__f,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_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__13469] :
( t(Vvar__1___24Anonymous__13469,V0__A)
& ? [Vvar__2___24Anonymous__13470] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__13470)
& ( cType___24t(V0__A)
=> ( c_24__type__13399___24t(V0__A,V1__f)
=> ( t(Vvar__1___24Anonymous__13469,V0__A)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13469,Vvar__2___24Anonymous__13470)
& ( ( happ(V1__f,Vvar__1___24Anonymous__13469) = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__13469,cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__13470)) )
| ( happ(V1__f,Vvar__1___24Anonymous__13469) = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,V3__l) = cCoq_2eLists_2eList_2efilter___24a3(V0__A,V1__f,Vvar__2___24Anonymous__13470) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.List.fold_right',axiom,
! [V0__A,V1__B,V2__f,V3__a0,V5__l] :
( cType___24t(V0__A)
=> ( cType___24t(V1__B)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = V3__a0 )
| ? [Vvar__1___24Anonymous__22003] :
( t(Vvar__1___24Anonymous__22003,V1__B)
& ? [Vvar__2___24Anonymous__22004] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__22004)
& V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__22003,Vvar__2___24Anonymous__22004)
& cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__22003),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__22004)) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.equivlistA',axiom,
! [V0__A,V1__eqA,V2__l,V3__l_27] :
( cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V0__A,V1__eqA,V2__l,V3__l_27)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V2__l)
<=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l_27) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.removeA',axiom,
! [V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l] :
( cType___24t(V0__A)
=> ( c_24__type__14144___24t(V0__A,V1__eqA,V1__eqA)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l)
=> ( ( V5__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A) )
| ? [Vvar__1___24Anonymous__14120] :
( t(Vvar__1___24Anonymous__14120,V0__A)
& ? [Vvar__2___24Anonymous__14121] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__14121)
& ( cType___24t(V0__A)
=> ( c_24__type__14153___24t(V0__A,V1__eqA,V1__eqA)
=> ( c_24__type__14162___24t(V0__A,V1__eqA,V2__eqA__dec)
=> ( t(V4__x,V0__A)
=> ( t(Vvar__1___24Anonymous__14120,V0__A)
=> ( V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14120,Vvar__2___24Anonymous__14121)
& ( ( p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__14120))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__14120) = cCoq_2eInit_2eSpecif_2eleft___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__14120),c_24__prop__14165___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__14120))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__14121) )
| ( ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__14120))
& happ(happ(V2__eqA__dec,V4__x),Vvar__1___24Anonymous__14120) = cCoq_2eInit_2eSpecif_2eright___24a2(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__14120),c_24__prop__14166___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__14120))
& cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,V5__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__14120,cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V0__A,V1__eqA,V2__eqA__dec,V4__x,Vvar__2___24Anonymous__14121)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.ConstructiveDefiniteDescription_on',axiom,
! [V0__A] : cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on___24a1(V0__A) = c_24__type__15952___24a1(V0__A) ).
fof('$_def_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
( p(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle)
<=> ! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalRelReification_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalRelReification__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__1196___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> cCoq_2eInit_2eLogic_2eex___24a2(V1__B,cCoq_2eInit_2eLogic_2eunique___24a2(V1__B,c_24__lam__12917___24a4(V0__A,V1__B,V2__R,V3__x))) )
=> ? [V4__f] :
( c_24__type__315___24t(V0__A,V1__B,V4__f)
& ! [V5__x] :
( t(V5__x,V0__A)
=> p(happ(happ(V2__R,V5__x),happ(V4__f,V5__x))) ) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.Minimal',axiom,
! [V0__P,V1__n] :
( cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V0__P,V1__n)
<=> ( p(happ(V0__P,V1__n))
& ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( p(happ(V0__P,V2__k))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__n,V2__k)) ) ) ) ) ).
fof('$_def_Coq.Logic.ClassicalFacts.Minimization_Property',axiom,
! [V0__P] :
( cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V0__P)
<=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(happ(V0__P,V1__n))
=> ? [V3__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
& cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V0__P,V3__m) ) ) ) ) ).
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.weak_excluded_middle',axiom,
( p(cCoq_2eLogic_2eClassicalFacts_2eweak__excluded__middle)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( ~ ~ p(V0__A)
| ~ p(V0__A) ) ) ) ).
fof('$_def_Coq.Logic.Decidable.decidable',axiom,
! [V0__P] :
( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
<=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_def_Coq.NArith.BinNat.N.lt',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__3160___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
! [V0__n,V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
| ? [Vvar__0___24Anonymous__12815] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12815)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12815)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
| ? [Vvar__0___24Anonymous__12818] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12818)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12818)
& cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__12815,Vvar__0___24Anonymous__12818)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
! [V0__a,V1__b] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
=> ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
| ? [Vvar__0___24Anonymous__35218] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35218)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
=> ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35218)
& ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
| ? [Vvar__0___24Anonymous__35221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35221)
& V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__35221)
& cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__35218,V1__b) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.eqb',axiom,
! [V1__n,V2__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__n)
=> ( ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eN0
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
| ? [Vvar__0___24Anonymous__14220] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14220)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14220)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
| ? [Vvar__0___24Anonymous__14221] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14221)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__m)
=> ( V1__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14221)
& ( ( V2__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__0___24Anonymous__14224] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__14224)
& V2__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__14224)
& cCoq_2eNArith_2eBinNatDef_2eN_2eeqb___24a2(V1__n,V2__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__14221,Vvar__0___24Anonymous__14224) ) ) ) ) ) ) ) ).
fof('$_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__12822] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12822)
& ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12822)
& ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
| ? [Vvar__0___24Anonymous__12825] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12825)
& V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__12825)
& cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__12822,Vvar__0___24Anonymous__12825)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__3088] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3088)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3088)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__3088)) ) ) ) ).
fof('$_def_Coq.PArith.BinPos.Pos.lt',axiom,
! [V0__x,V1__y] :
( p(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.BinPosDef.Pos.add',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__15286] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15286)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15286)
& ( ? [Vvar__0___24Anonymous__15290] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15290)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15290)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__15285__1__add__carry___24a2(Vvar__0___24Anonymous__15286,Vvar__0___24Anonymous__15290)) )
| ? [Vvar__0___24Anonymous__15291] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15291)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15291)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__15286,Vvar__0___24Anonymous__15291)) )
| ( 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__15286)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__15292] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15292)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15292)
& ( ? [Vvar__0___24Anonymous__15296] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15296)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15296)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__15292,Vvar__0___24Anonymous__15296)) )
| ? [Vvar__0___24Anonymous__15297] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15297)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15297)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__15292,Vvar__0___24Anonymous__15297)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15292) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__15298] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15298)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15298)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__15298)) )
| ? [Vvar__0___24Anonymous__15299] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15299)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15299)
& cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15299) )
| ( 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.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__35225] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35225)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__35225)
& cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__35225 )
| ( 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('$_def_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> V2__x = V3__y ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.commut',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V4__y),V3__x))
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V2__R2,V6__z),V4__y))
=> cCoq_2eInit_2eLogic_2eex2___24a3(V0__A,c_24__lam__1373___24a3(V0__A,V2__R2,V3__x),c_24__lam__2757___24a3(V0__A,V1__R1,V6__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.equiv',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V0__A,V1__R)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.inclusion',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V3__x),V4__y))
=> p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.reflexive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> p(happ(happ(V1__R,V2__x),V2__x)) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__60___24a1(V0__A) ).
fof('$_def_Coq.Relations.Relation_Definitions.same_relation',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__R1,V2__R2)
<=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2)
& cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__R2,V1__R1) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.symmetric',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> p(happ(happ(V1__R,V3__y),V2__x)) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Definitions.transitive',axiom,
! [V0__A,V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> p(happ(happ(V1__R,V2__x),V4__z)) ) ) ) ) ) ) ).
fof('$_def_Coq.Relations.Relation_Operators.transp',axiom,
! [V0__A,V1__R,V2__x,V3__y] :
( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,V1__R,V2__x,V3__y)
<=> p(happ(happ(V1__R,V3__y),V2__x)) ) ).
fof('$_def_Coq.Relations.Relation_Operators.union',axiom,
! [V0__A,V1__R1,V2__R2,V3__x,V4__y] :
( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V0__A,V1__R1,V2__R2,V3__x,V4__y)
<=> ( p(happ(happ(V1__R1,V3__x),V4__y))
| p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ).
fof('$_def_Coq.Setoids.Setoid.Setoid_Theory',axiom,
cCoq_2eSetoids_2eSetoid_2eSetoid__Theory = cCoq_2eClasses_2eRelationClasses_2eEquivalence ).
fof('$_def_Coq.ZArith.BinInt.Z.ge',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).
fof('$_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('$_def_Coq.ZArith.BinInt.Z.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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.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__1129] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1129)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1129)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__1133] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1133)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1133)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__1129,Vvar__0___24Anonymous__1133)) )
| ? [Vvar__0___24Anonymous__1134] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1134)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1134)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__1129,Vvar__0___24Anonymous__1134) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1135] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1135)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1135)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__1139] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1139)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1139)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__1139,Vvar__0___24Anonymous__1135) )
| ? [Vvar__0___24Anonymous__1140] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1140)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1140)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__1135,Vvar__0___24Anonymous__1140)) ) ) ) ) ) ) ) ).
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__1162] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1162)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1162)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1163] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1163)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1163)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__1164] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1164)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1164)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__1168] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1168)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1168)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__1164,Vvar__0___24Anonymous__1168) )
| ? [Vvar__0___24Anonymous__1169] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1169)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1169)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__1170] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1170)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1170)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1174] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1174)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1174)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__1175] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1175)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1175)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__1170,Vvar__0___24Anonymous__1175)) ) ) ) ) ) ) ) ).
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__1149] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1149)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1149)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1153] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1153)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1153)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1149,Vvar__0___24Anonymous__1153)) )
| ? [Vvar__0___24Anonymous__1154] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1154)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1154)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1149,Vvar__0___24Anonymous__1154)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__1155] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1155)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1155)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1159] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1159)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1159)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1155,Vvar__0___24Anonymous__1159)) )
| ? [Vvar__0___24Anonymous__1160] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1160)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1160)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__1155,Vvar__0___24Anonymous__1160)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__1179] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1179)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1179)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__1179)) ) ) ) ).
fof('$_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__1144] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1144)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1144)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1144) )
| ? [Vvar__0___24Anonymous__1145] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1145)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1145)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1145) ) ) ) ).
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('$_def_Coq.ZArith.Zbool.Zeq_bool',axiom,
! [V0__x,V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
| ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).
fof('$_def_Coq.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__12374] :
( t(Vvar__1___24Anonymous__12374,V1__A)
& ? [Vvar__2___24Anonymous__12375] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__12375)
& ( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__12375)
=> ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__12374,Vvar__2___24Anonymous__12375)
& ( ( Vvar__2___24Anonymous__12375 = 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__12374)) ) )
| ? [Vvar__1___24Anonymous__12386] :
( t(Vvar__1___24Anonymous__12386,V1__A)
& ? [Vvar__2___24Anonymous__12387] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__12387)
& Vvar__2___24Anonymous__12375 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__12386,Vvar__2___24Anonymous__12387)
& ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__12374))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__12375) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Refl.make_impl',axiom,
! [V1__A,V2__eval,V3__l,V4__goal] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> p(V4__goal) ) )
| ? [Vvar__1___24Anonymous__22780] :
( t(Vvar__1___24Anonymous__22780,V1__A)
& ? [Vvar__2___24Anonymous__22781] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__22781)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__22780,Vvar__2___24Anonymous__22781)
& ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
<=> ( p(happ(V2__eval,Vvar__1___24Anonymous__22780))
=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__22781,V4__goal) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op1',axiom,
! [V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V5__o)
=> ( ( V5__o = cCoq_2emicromega_2eRingMicromega_2eEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__28448___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonEqual
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__28456___24a3(V0__R,V1__rO,V2__req) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__28464___24a3(V0__R,V1__rO,V4__rlt) )
| ( V5__o = cCoq_2emicromega_2eRingMicromega_2eNonStrict
& cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V0__R,V1__rO,V2__req,V3__rle,V4__rlt,V5__o) = c_24__lam__28472___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).
fof('$_def_Coq.micromega.RingMicromega.eval_op2',axiom,
! [V0__R,V1__req,V2__rle,V3__rlt,V4__o] :
( cType___24t(V0__R)
=> ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V4__o)
=> ( ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V1__req )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpNEq
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__14667___24a2(V0__R,V1__req) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = V2__rle )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGe
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__14675___24a2(V0__R,V2__rle) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpLt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__14683___24a2(V0__R,V3__rlt) )
| ( V4__o = cCoq_2emicromega_2eRingMicromega_2eOpGt
& cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V0__R,V1__req,V2__rle,V3__rlt,V4__o) = c_24__lam__14691___24a2(V0__R,V3__rlt) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.clause',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.cnf_tt',axiom,
! [V0__Term_27,V1__Annot] : cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V0__Term_27,V1__Annot) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2emicromega_2eTauto_2eclause___24a2(V0__Term_27,V1__Annot)) ).
fof('$_def_Coq.micromega.Tauto.eval_f',axiom,
! [V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f] :
( cType___24t(V0__TA)
=> ( cType___24t(V1__TX)
=> ( cType___24t(V2__AA)
=> ( cType___24t(V3__AF)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,V7__f)
=> ( ( V7__f = cCoq_2emicromega_2eTauto_2eTT___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24True) ) )
| ( V7__f = cCoq_2emicromega_2eTauto_2eFF___24a4(V0__TA,V1__TX,V2__AA,V3__AF)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(c_24False) ) )
| ? [Vvar__4___24Anonymous__33725] :
( t(Vvar__4___24Anonymous__33725,V1__TX)
& V7__f = cCoq_2emicromega_2eTauto_2eX___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33725)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V4__ex,Vvar__4___24Anonymous__33725)) ) )
| ? [Vvar__4___24Anonymous__33730] :
( t(Vvar__4___24Anonymous__33730,V0__TA)
& ? [Vvar__5___24Anonymous__33731] :
( t(Vvar__5___24Anonymous__33731,V2__AA)
& V7__f = cCoq_2emicromega_2eTauto_2eA___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33730,Vvar__5___24Anonymous__33731)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> p(happ(V5__ea,Vvar__4___24Anonymous__33730)) ) ) )
| ? [Vvar__4___24Anonymous__33737] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33737)
& ? [Vvar__5___24Anonymous__33738] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__33738)
& V7__f = cCoq_2emicromega_2eTauto_2eCj___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33737,Vvar__5___24Anonymous__33738)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__33737)
& cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__33738) ) ) ) )
| ? [Vvar__4___24Anonymous__33744] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33744)
& ? [Vvar__5___24Anonymous__33745] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__5___24Anonymous__33745)
& V7__f = cCoq_2emicromega_2eTauto_2eD___24a6(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33744,Vvar__5___24Anonymous__33745)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__33744)
| cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__5___24Anonymous__33745) ) ) ) )
| ? [Vvar__4___24Anonymous__33751] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33751)
& V7__f = cCoq_2emicromega_2eTauto_2eN___24a5(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33751)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ~ cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__33751) ) )
| ? [Vvar__4___24Anonymous__33756] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33756)
& ? [Vvar__5___24Anonymous__33757] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V3__AF,Vvar__5___24Anonymous__33757)
& ? [Vvar__6___24Anonymous__33758] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__6___24Anonymous__33758)
& V7__f = cCoq_2emicromega_2eTauto_2eI___24a7(V0__TA,V1__TX,V2__AA,V3__AF,Vvar__4___24Anonymous__33756,Vvar__5___24Anonymous__33757,Vvar__6___24Anonymous__33758)
& ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,V7__f)
<=> ( cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__4___24Anonymous__33756)
=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V0__TA,V1__TX,V2__AA,V3__AF,V4__ex,V5__ea,Vvar__6___24Anonymous__33758) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.micromega.Tauto.eval_tt',axiom,
! [V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt] :
( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V4__env,V5__tt)
<=> p(happ(happ(V3__eval_27,V4__env),cCoq_2eInit_2eDatatypes_2efst___24a3(V1__Term_27,V2__Annot,V5__tt))) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.Fapp',axiom,
! [V0__C,V1__Fcons,V3__l,V4__m] :
( cType___24t(V0__C)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),V3__l)
=> ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C))
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = V4__m )
| ? [Vvar__1___24Anonymous__19896] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1___24Anonymous__19896)
& ? [Vvar__2___24Anonymous__19897] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__19897)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__19896,Vvar__2___24Anonymous__19897)
& cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,V3__l,V4__m) = happ(happ(V1__Fcons,Vvar__1___24Anonymous__19896),cCoq_2esetoid__ring_2eField__theory_2eFapp___24a4(V0__C,V1__Fcons,Vvar__2___24Anonymous__19897,V4__m)) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27] :
( cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V13__e,V14__e_27)
<=> ! [V15__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__R,V15__l)
=> p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V13__e)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V15__l,V14__e_27))) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.PCond',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le] :
( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),V15__le)
=> ( ( V15__le = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> p(c_24True) ) )
| ? [Vvar__1___24Anonymous__13096] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__13096)
& ? [Vvar__2___24Anonymous__13097] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__13097)
& ( cType___24t(V0__R)
=> ( cType___24t(V8__C)
=> ( cType___24t(V10__Cpow)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__13097)
=> ( V15__le = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__13096,Vvar__2___24Anonymous__13097)
& ( ( Vvar__2___24Anonymous__13097 = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C))
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__13096)),V1__rO)) ) )
| ? [Vvar__1___24Anonymous__13108] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V8__C,Vvar__1___24Anonymous__13108)
& ? [Vvar__2___24Anonymous__13109] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__2___24Anonymous__13109)
& Vvar__2___24Anonymous__13097 = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V8__C),Vvar__1___24Anonymous__13108,Vvar__2___24Anonymous__13109)
& ( cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,V15__le)
<=> ( ~ p(happ(happ(V7__req,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__1___24Anonymous__13096)),V1__rO))
& cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__phi,V10__Cpow,V11__Cp__phi,V12__rpow,V14__l,Vvar__2___24Anonymous__13097) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__19360] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__19360)
& ? [Vvar__2__rsplit__common__19361] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__19361)
& ? [Vvar__3__rsplit__right__19362] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__19362)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__19360,Vvar__2__rsplit__common__19361,Vvar__3__rsplit__right__19362)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V0__C,V1__r) = Vvar__2__rsplit__common__19361 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__19349] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__19349)
& ? [Vvar__2__rsplit__common__19350] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__19350)
& ? [Vvar__3__rsplit__right__19351] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__19351)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__19349,Vvar__2__rsplit__common__19350,Vvar__3__rsplit__right__19351)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V0__C,V1__r) = Vvar__1__rsplit__left__19349 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
! [V0__C,V1__r] :
( cType___24t(V0__C)
=> ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(V0__C,V1__r)
=> ? [Vvar__1__rsplit__left__19369] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__1__rsplit__left__19369)
& ? [Vvar__2__rsplit__common__19370] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2__rsplit__common__19370)
& ? [Vvar__3__rsplit__right__19371] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3__rsplit__right__19371)
& V1__r = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V0__C,Vvar__1__rsplit__left__19369,Vvar__2__rsplit__common__19370,Vvar__3__rsplit__right__19371)
& cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V0__C,V1__r) = Vvar__3__rsplit__right__19371 ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nopp',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNopp = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(cCoq_2eNumbers_2eBinNums_2eN) ).
fof('$_def_Coq.setoid_ring.InitialRing.Nsub',axiom,
cCoq_2esetoid__ring_2eInitialRing_2eNsub = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V5__x)
=> ( ( V5__x = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = V1__rO )
| ? [Vvar__0___24Anonymous__21959] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21959)
& V5__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__21959)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__x) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,Vvar__0___24Anonymous__21959) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__21845] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21845)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21845)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21845)
& ( ? [Vvar__0___24Anonymous__21849] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21849)
& Vvar__0___24Anonymous__21845 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21849)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21845))) )
| ? [Vvar__0___24Anonymous__21850] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21850)
& Vvar__0___24Anonymous__21845 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21850)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21845))) )
| ( Vvar__0___24Anonymous__21845 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V2__radd,V1__rI),V1__rI)) ) ) ) ) ) )
| ? [Vvar__0___24Anonymous__21851] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21851)
& ( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21851)
=> ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21851)
& ( ? [Vvar__0___24Anonymous__21855] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21855)
& Vvar__0___24Anonymous__21851 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__21855)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21851)) )
| ? [Vvar__0___24Anonymous__21856] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21856)
& Vvar__0___24Anonymous__21851 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__21856)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__21851)) )
| ( Vvar__0___24Anonymous__21851 = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),V1__rI) ) ) ) ) ) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
! [V0__R,V1__rI,V2__radd,V3__rmul,V5__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
=> ( ? [Vvar__0___24Anonymous__5938] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5938)
& V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5938)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V2__radd,V1__rI),happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__5938))) )
| ? [Vvar__0___24Anonymous__5939] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5939)
& V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5939)
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = happ(happ(V3__rmul,happ(happ(V2__radd,V1__rI),V1__rI)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,Vvar__0___24Anonymous__5939)) )
| ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).
fof('$_def_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__z)
=> ( ( V6__z = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__ropp,V6__z) = V1__rO )
| ? [Vvar__0___24Anonymous__21879] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21879)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__21879)
& 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__21879) )
| ? [Vvar__0___24Anonymous__21880] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__21880)
& V6__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__21880)
& 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__21880)) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
! [V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe] :
( cType___24t(V0__R)
=> ( cType___24t(V7__C)
=> ( cType___24t(V9__Cpow)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,V14__pe)
=> ( ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V1__rO )
| ( V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V7__C)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = V2__rI )
| ? [Vvar__1___24Anonymous__13894] :
( t(Vvar__1___24Anonymous__13894,V7__C)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V7__C,Vvar__1___24Anonymous__13894)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V8__phi,Vvar__1___24Anonymous__13894) )
| ? [Vvar__1___24Anonymous__13896] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__13896)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V7__C,Vvar__1___24Anonymous__13896)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V0__R,V1__rO,Vvar__1___24Anonymous__13896,V13__l) )
| ? [Vvar__1___24Anonymous__13898] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13898)
& ? [Vvar__2___24Anonymous__13899] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__13899)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V7__C,Vvar__1___24Anonymous__13898,Vvar__2___24Anonymous__13899)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V3__radd,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13898)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__13899)) ) )
| ? [Vvar__1___24Anonymous__13902] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13902)
& ? [Vvar__2___24Anonymous__13903] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__13903)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V7__C,Vvar__1___24Anonymous__13902,Vvar__2___24Anonymous__13903)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V5__rsub,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13902)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__13903)) ) )
| ? [Vvar__1___24Anonymous__13906] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13906)
& ? [Vvar__2___24Anonymous__13907] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__2___24Anonymous__13907)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V7__C,Vvar__1___24Anonymous__13906,Vvar__2___24Anonymous__13907)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V4__rmul,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13906)),cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__2___24Anonymous__13907)) ) )
| ? [Vvar__1___24Anonymous__13910] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13910)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V7__C,Vvar__1___24Anonymous__13910)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(V6__ropp,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13910)) )
| ? [Vvar__1___24Anonymous__13912] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V7__C,Vvar__1___24Anonymous__13912)
& ? [Vvar__2___24Anonymous__13913] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__13913)
& V14__pe = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V7__C,Vvar__1___24Anonymous__13912,Vvar__2___24Anonymous__13913)
& cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,V14__pe) = happ(happ(V11__rpow,cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__C,V8__phi,V9__Cpow,V10__Cp__phi,V11__rpow,V13__l,Vvar__1___24Anonymous__13912)),happ(V10__Cp__phi,Vvar__2___24Anonymous__13913)) ) ) ) ) ) ) ) ).
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__15024] :
( t(Vvar__1___24Anonymous__15024,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__15024)
& ( ? [Vvar__1___24Anonymous__15034] :
( t(Vvar__1___24Anonymous__15034,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__15034)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__15024),Vvar__1___24Anonymous__15034) )
| ? [Vvar__1___24Anonymous__15036] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15036)
& ? [Vvar__2___24Anonymous__15037] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__15037)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__15036,Vvar__2___24Anonymous__15037)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__15040] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__15040)
& ? [Vvar__2___24Anonymous__15041] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15041)
& ? [Vvar__3___24Anonymous__15042] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__15042)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__15040,Vvar__2___24Anonymous__15041,Vvar__3___24Anonymous__15042)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__15047] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15047)
& ? [Vvar__2___24Anonymous__15048] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__15048)
& ( 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__15047,Vvar__2___24Anonymous__15048)
& ( ? [Vvar__1___24Anonymous__15068] :
( t(Vvar__1___24Anonymous__15068,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__15068)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__15070] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15070)
& ? [Vvar__2___24Anonymous__15071] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__15071)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15047)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15070)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__15070,Vvar__2___24Anonymous__15071)
& ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__15047,Vvar__1___24Anonymous__15070) = 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__15048,Vvar__2___24Anonymous__15071) )
| ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__15047,Vvar__1___24Anonymous__15070) = 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__15047,Vvar__1___24Anonymous__15070) = 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__15076] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__15076)
& ? [Vvar__2___24Anonymous__15077] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15077)
& ? [Vvar__3___24Anonymous__15078] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__15078)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__15076,Vvar__2___24Anonymous__15077,Vvar__3___24Anonymous__15078)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
| ? [Vvar__1___24Anonymous__15083] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__15083)
& ? [Vvar__2___24Anonymous__15084] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15084)
& ? [Vvar__3___24Anonymous__15085] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__15085)
& ( 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__15083,Vvar__2___24Anonymous__15084,Vvar__3___24Anonymous__15085)
& ( ? [Vvar__1___24Anonymous__15118] :
( t(Vvar__1___24Anonymous__15118,V0__C)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__15118)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
| ? [Vvar__1___24Anonymous__15120] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__15120)
& ? [Vvar__2___24Anonymous__15121] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__15121)
& V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__15120,Vvar__2___24Anonymous__15121)
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
| ? [Vvar__1___24Anonymous__15124] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__15124)
& ? [Vvar__2___24Anonymous__15125] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15125)
& ? [Vvar__3___24Anonymous__15126] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__15126)
& ( cType___24t(V0__C)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15084)
=> ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__15125)
=> ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__15124,Vvar__2___24Anonymous__15125,Vvar__3___24Anonymous__15126)
& ( ( cType___24t(V0__C)
=> ( c_24__type__10622___24t(V0__C,V1__ceqb)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__15083)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__15124)
=> ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__15084,Vvar__2___24Anonymous__15125) = cCoq_2eInit_2eDatatypes_2eEq
& ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__15083,Vvar__1___24Anonymous__15124) = 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__15085,Vvar__3___24Anonymous__15126) )
| ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__15083,Vvar__1___24Anonymous__15124) = 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__15084,Vvar__2___24Anonymous__15125) = 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__15084,Vvar__2___24Anonymous__15125) = cCoq_2eInit_2eDatatypes_2eGt
& cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__28633___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).
fof('$_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('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
( cType___24t(V0__R)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
=> ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
| ? [Vvar__0___24Anonymous__29278] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29278)
& V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29278)
& cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V2__rmul,V3__x,Vvar__0___24Anonymous__29278) ) ) ) ) ).
fof('$_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__7701] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7701)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__7701)
& 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__7702__7705___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7701)),c_24__let__var__6__p__7702__7705___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7701))) )
| ? [Vvar__0___24Anonymous__7703] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7703)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__7703)
& 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__7704__7706___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7703)),c_24__let__var__6__p__7704__7706___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__7703)) )
| ( 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('$_def_HahnAcyclic.pref_union',axiom,
! [V0__X,V1__r,V2__r_27,V3__x,V4__y] :
( cHahnAcyclic_2epref__union___24a5(V0__X,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
| ( p(happ(happ(V2__r_27,V3__x),V4__y))
& ~ p(happ(happ(V1__r,V4__y),V3__x)) ) ) ) ).
fof('$_def_hahn.HahnBase.Equality.sort',axiom,
! [V0__t] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V0__t)
=> ? [Vvar__0__sort__1121] :
( cType___24t(Vvar__0__sort__1121)
& ? [Vvar__1___24Anonymous__1122] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__1121,Vvar__1___24Anonymous__1122)
& ? [Vvar__2___24Anonymous__1123] :
( cType___24t(Vvar__2___24Anonymous__1123)
& V0__t = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__1121,Vvar__1___24Anonymous__1122,Vvar__2___24Anonymous__1123)
& chahn_2eHahnBase_2eEquality_2esort___24a1(V0__t) = Vvar__0__sort__1121 ) ) ) ) ).
fof('$_def_hahn.HahnBase.NW',axiom,
! [V0__P] :
( chahn_2eHahnBase_2eNW___24a1(V0__P)
<=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2ett)) ) ).
fof('$_def_hahn.HahnBase.eq_op',axiom,
! [V0__T] : chahn_2eHahnBase_2eeq__op___24a1(V0__T) = chahn_2eHahnBase_2eEquality_2eop___24a2(chahn_2eHahnBase_2eEquality_2esort___24a1(V0__T),chahn_2eHahnBase_2eEquality_2eclass___24a1(V0__T)) ).
fof('$_def_hahn.HahnBase.nat_eqType',axiom,
chahn_2eHahnBase_2enat__eqType = chahn_2eHahnBase_2eEquality_2ePack___24a3(cCoq_2eInit_2eDatatypes_2enat,chahn_2eHahnBase_2enat__eqMixin,cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_def_hahn.HahnDom.doma',axiom,
! [V0__A,V1__r,V2__d] :
( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> p(happ(V2__d,V3__x)) ) ) ) ) ).
fof('$_def_hahn.HahnDom.domb',axiom,
! [V0__A,V1__r,V2__d] :
( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> p(happ(V2__d,V4__y)) ) ) ) ) ).
fof('$_def_hahn.HahnEquational.good_ctx',axiom,
! [V0__A,V1__P] :
( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
<=> ( chahn_2eHahnBase_2eNW___24a1(c_24__lam__1915___24a2(V0__A,V1__P))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__1942___24a2(V0__A,V1__P)) ) ) ).
fof('$_def_hahn.HahnFuneq.funeq',axiom,
! [V0__A,V1__B,V2__f,V3__r] :
( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V3__r,V4__a),V5__b))
=> happ(V2__f,V4__a) = happ(V2__f,V5__b) ) ) ) ) ).
fof('$_def_hahn.HahnList.undup',axiom,
! [V1__A,V2__l] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A) )
| ? [Vvar__1___24Anonymous__2282] :
( t(Vvar__1___24Anonymous__2282,V1__A)
& ? [Vvar__2___24Anonymous__2283] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__2283)
& ( cType___24t(V1__A)
=> ( t(Vvar__1___24Anonymous__2282,V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__2283)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283)) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283),c_24__prop__2299___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__2283) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283)) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283),c_24__prop__2311___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__2282,chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__2283)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.max_elt',axiom,
! [V0__A,V1__r,V2__a] :
( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.wmax_elt',axiom,
! [V0__A,V1__r,V2__a] :
( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> V2__a = V3__b ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.acyclic',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ).
fof('$_def_hahn.HahnRelationsBasic.bunion',axiom,
! [V0__A,V1__B,V2__P,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2ebunion___24a6(V0__A,V1__B,V2__P,V3__r,V4__x,V5__y)
<=> ? [V6__a] :
( t(V6__a,V0__A)
& p(happ(V2__P,V6__a))
& p(happ(happ(happ(V3__r,V6__a),V4__x),V5__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_refl',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( V2__x = V3__y
| p(happ(happ(V1__r,V2__x),V3__y))
| p(happ(happ(V1__r,V3__y),V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.clos_sym',axiom,
! [V0__A,V1__r,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eclos__sym___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ( p(happ(happ(V1__r,V2__x),V3__y))
| p(happ(happ(V1__r,V3__y),V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.codom_rel',axiom,
! [V0__A,V1__r,V2__y] :
( chahn_2eHahnRelationsBasic_2ecodom__rel___24a3(V0__A,V1__r,V2__y)
<=> ? [V3__x] :
( t(V3__x,V0__A)
& p(happ(happ(V1__r,V3__x),V2__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.collect_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2ecollect__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ? [V6__x_27] :
( t(V6__x_27,V0__A)
& ? [V7__y_27] :
( t(V7__y_27,V0__A)
& p(happ(happ(V3__r,V6__x_27),V7__y_27))
& happ(V2__f,V6__x_27) = V4__x
& happ(V2__f,V7__y_27) = V5__y ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.cross_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__a,V4__b] :
( chahn_2eHahnRelationsBasic_2ecross__rel___24a5(V0__A,V1__r,V2__r_27,V3__a,V4__b)
<=> ( p(happ(V1__r,V3__a))
& p(happ(V2__r_27,V4__b)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.dom_rel',axiom,
! [V0__A,V1__r,V2__x] :
( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V1__r,V2__x)
<=> ? [V3__y] :
( t(V3__y,V0__A)
& p(happ(happ(V1__r,V2__x),V3__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eeq__rel___24a5(V0__A,V1__B,V2__f,V3__x,V4__y)
<=> happ(V2__f,V3__x) = happ(V2__f,V4__y) ) ).
fof('$_def_hahn.HahnRelationsBasic.eqv_rel',axiom,
! [V0__A,V1__cond,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4(V0__A,V1__cond,V2__x,V3__y)
<=> ( V2__x = V3__y
& p(happ(V1__cond,V2__x)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.functional',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> ( p(happ(happ(V1__r,V2__x),V4__z))
=> V3__y = V4__z ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.immediate',axiom,
! [V0__A,V1__r,V2__a,V3__b] :
( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V4__c] :
( t(V4__c,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V4__c))
=> ( p(happ(happ(V1__r,V4__c),V3__b))
=> p(c_24False) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.inter_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2einter__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.irreflexive',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V2__x))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.is_total',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r)
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__cond,V3__a))
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(V1__cond,V5__b))
=> ( V3__a != V5__b
=> ( p(happ(happ(V2__r,V3__a),V5__b))
| p(happ(happ(V2__r,V5__b),V3__a)) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.map_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2emap__rel___24a6(V0__A,V1__B,V2__f,V3__r_27_27,V4__x,V5__y)
<=> p(happ(happ(V3__r_27_27,happ(V2__f,V4__x)),happ(V2__f,V5__y))) ) ).
fof('$_def_hahn.HahnRelationsBasic.minus_rel',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eminus__rel___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ( p(happ(happ(V1__r,V3__x),V4__y))
& ~ p(happ(happ(V2__r_27,V3__x),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.pow_rel',axiom,
! [V1__A,V2__r,V3__n] :
( cType___24t(V1__A)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( ( V3__n = cCoq_2eInit_2eDatatypes_2eO
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V1__A,c_24__lam__312___24a1(V1__A)) )
| ? [Vvar__0___24Anonymous__2558] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2558)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2558)
& chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V3__n) = chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,Vvar__0___24Anonymous__2558),V2__r) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
! [V0__A,V1__B,V2__f,V3__r,V4__x,V5__y] :
( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6(V0__A,V1__B,V2__f,V3__r,V4__x,V5__y)
<=> ( p(happ(happ(V3__r,V4__x),V5__y))
& happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_rel',axiom,
! [V0__A,V1__cond,V2__r,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2erestr__rel___24a5(V0__A,V1__cond,V2__r,V3__x,V4__y)
<=> ( p(happ(happ(V2__r,V3__x),V4__y))
& p(happ(V1__cond,V3__x))
& p(happ(V1__cond,V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.restr_subset',axiom,
! [V0__A,V1__cond,V2__r,V3__r_27] :
( chahn_2eHahnRelationsBasic_2erestr__subset___24a4(V0__A,V1__cond,V2__r,V3__r_27)
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(happ(V1__cond,V4__a))
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(V1__cond,V6__b))
=> ( p(happ(happ(V2__r,V4__a),V6__b))
=> p(happ(happ(V3__r_27,V4__a),V6__b)) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.seq',axiom,
! [V0__A,V1__r,V2__r_27,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,V2__r_27,V3__x,V4__y)
<=> ? [V5__z] :
( t(V5__z,V0__A)
& p(happ(happ(V1__r,V3__x),V5__z))
& p(happ(happ(V2__r_27,V5__z),V4__y)) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.singl_rel',axiom,
! [V0__A,V1__a,V2__b,V3__x,V4__y] :
( chahn_2eHahnRelationsBasic_2esingl__rel___24a5(V0__A,V1__a,V2__b,V3__x,V4__y)
<=> ( V3__x = V1__a
& V4__y = V2__b ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_partial_order',axiom,
! [V0__A,V1__r] :
( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_total_order',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2estrict__total__order___24a3(V0__A,V1__cond,V2__r)
<=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V2__r)
& chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.upward_closed',axiom,
! [V0__A,V1__r,V2__P] :
( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> ( p(happ(V2__P,V4__y))
=> p(happ(V2__P,V3__x)) ) ) ) ) ) ).
fof('$_def_hahn.HahnSets.set_collect',axiom,
! [V0__A,V1__B,V2__f,V3__s,V4__x] :
( chahn_2eHahnSets_2eset__collect___24a5(V0__A,V1__B,V2__f,V3__s,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V3__s,V5__y))
& happ(V2__f,V5__y) = V4__x ) ) ).
fof('$_def_hahn.HahnSets.set_compl',axiom,
! [V0__A,V1__s,V2__x] :
( chahn_2eHahnSets_2eset__compl___24a3(V0__A,V1__s,V2__x)
<=> ~ p(happ(V1__s,V2__x)) ) ).
fof('$_def_hahn.HahnSets.set_disjoint',axiom,
! [V0__A,V1__s,V2__s_27] :
( chahn_2eHahnSets_2eset__disjoint___24a3(V0__A,V1__s,V2__s_27)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> ( p(happ(V2__s_27,V3__x))
=> p(c_24False) ) ) ) ) ).
fof('$_def_hahn.HahnSets.set_empty',axiom,
! [V0__A,V1__x] :
( chahn_2eHahnSets_2eset__empty___24a2(V0__A,V1__x)
<=> p(c_24False) ) ).
fof('$_def_hahn.HahnSets.set_equiv',axiom,
! [V0__A,V1__s,V2__s_27] :
( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__s,V2__s_27)
<=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V1__s,V2__s_27)
& chahn_2eHahnSets_2eset__subset___24a3(V0__A,V2__s_27,V1__s) ) ) ).
fof('$_def_hahn.HahnSets.set_full',axiom,
! [V0__A,V1__x] :
( chahn_2eHahnSets_2eset__full___24a2(V0__A,V1__x)
<=> p(c_24True) ) ).
fof('$_def_hahn.HahnSets.set_inter',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( chahn_2eHahnSets_2eset__inter___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
& p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_def_hahn.HahnSets.set_map',axiom,
! [V0__A,V1__B,V2__f,V3__d,V4__x] :
( chahn_2eHahnSets_2eset__map___24a5(V0__A,V1__B,V2__f,V3__d,V4__x)
<=> p(happ(V3__d,happ(V2__f,V4__x))) ) ).
fof('$_def_hahn.HahnSets.set_minus',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( chahn_2eHahnSets_2eset__minus___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
& ~ p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_def_hahn.HahnSets.set_subset',axiom,
! [V0__A,V1__s,V2__s_27] :
( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V1__s,V2__s_27)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__s,V3__x))
=> p(happ(V2__s_27,V3__x)) ) ) ) ).
fof('$_def_hahn.HahnSets.set_union',axiom,
! [V0__A,V1__s,V2__s_27,V3__x] :
( chahn_2eHahnSets_2eset__union___24a4(V0__A,V1__s,V2__s_27,V3__x)
<=> ( p(happ(V1__s,V3__x))
| p(happ(V2__s_27,V3__x)) ) ) ).
fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__500,Vvar__1___24Anonymous__501,Vvar__0__P__502,Vvar__1___24Anonymous__503] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__500) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__502) ).
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__253] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__253) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1244,Vvar__1___24Anonymous__1245,Vvar__0__A__1246] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1244,Vvar__1___24Anonymous__1245) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1246) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__268,Vvar__0__A__269,Vvar__1___24Anonymous__270,Vvar__2___24Anonymous__271] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__268) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__269,Vvar__1___24Anonymous__270,Vvar__2___24Anonymous__271) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__1097,Vvar__1__B__1098,Vvar__2___24Anonymous__1099,Vvar__0__A__1100,Vvar__1__B__1101,Vvar__2___24Anonymous__1102] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__1097,Vvar__1__B__1098) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__1100,Vvar__1__B__1101) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1188] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1188) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__244] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__244) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__232,Vvar__0___24Anonymous__233] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__232) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__233) ).
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__11445,Vvar__1__TX__11446,Vvar__2__AA__11447,Vvar__3__AF__11448,Vvar__0__TA__11449,Vvar__1__TX__11450,Vvar__2__AA__11451,Vvar__3__AF__11452] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11445,Vvar__1__TX__11446,Vvar__2__AA__11447,Vvar__3__AF__11448) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11449,Vvar__1__TX__11450,Vvar__2__AA__11451,Vvar__3__AF__11452) ).
fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__19130,Vvar__0__C__19131] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19130) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19131) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__12644,Vvar__0__C__12645] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12644) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12645) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__12420,Vvar__1___24Anonymous__12421,Vvar__0__C__12422,Vvar__1___24Anonymous__12423,Vvar__2___24Anonymous__12424] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12420,Vvar__1___24Anonymous__12421) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12422,Vvar__1___24Anonymous__12423,Vvar__2___24Anonymous__12424) ).
fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__12454,Vvar__1___24Anonymous__12455] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12454,Vvar__1___24Anonymous__12455) ).
fof('$_fix_15285_1_add_carry',axiom,
! [V2__x,V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ( ? [Vvar__0___24Anonymous__15300] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15300)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15300)
& ( ? [Vvar__0___24Anonymous__15304] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15304)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15304)
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__15285__1__add__carry___24a2(Vvar__0___24Anonymous__15300,Vvar__0___24Anonymous__15304)) )
| ? [Vvar__0___24Anonymous__15305] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15305)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15305)
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__15285__1__add__carry___24a2(Vvar__0___24Anonymous__15300,Vvar__0___24Anonymous__15305)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__15300)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__15306] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15306)
& ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15306)
& ( ? [Vvar__0___24Anonymous__15310] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15310)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15310)
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__15285__1__add__carry___24a2(Vvar__0___24Anonymous__15306,Vvar__0___24Anonymous__15310)) )
| ? [Vvar__0___24Anonymous__15311] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15311)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15311)
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__15306,Vvar__0___24Anonymous__15311)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__15306)) ) ) ) ) )
| ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
& ( ? [Vvar__0___24Anonymous__15312] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15312)
& V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__15312)
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__15312)) )
| ? [Vvar__0___24Anonymous__15313] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15313)
& V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__15313)
& c_24__fix__15285__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__15313)) )
| ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
& c_24__fix__15285__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__508,Vvar__0__P__509,Vvar__1___24Anonymous__510,Vvar__1___24Anonymous__511] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__508) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__509)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__508 = Vvar__0__P__509 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__504,Vvar__0__P__505,Vvar__1___24Anonymous__506,Vvar__1___24Anonymous__507] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__504) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__505)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__504 = Vvar__0__P__505 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__1251,Vvar__0__A__1252] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1251) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1252)
=> Vvar__0__A__1251 = Vvar__0__A__1252 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__254,Vvar__0___24Anonymous__255] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__254) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__255)
=> Vvar__0___24Anonymous__254 = Vvar__0___24Anonymous__255 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__1247,Vvar__0__A__1248,Vvar__1___24Anonymous__1249,Vvar__1___24Anonymous__1250] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1247,Vvar__1___24Anonymous__1249) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1248,Vvar__1___24Anonymous__1250)
=> ( Vvar__1___24Anonymous__1249 = Vvar__1___24Anonymous__1250
& Vvar__0__A__1247 = Vvar__0__A__1248 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__274,Vvar__0__A__275,Vvar__1___24Anonymous__276,Vvar__1___24Anonymous__277,Vvar__2___24Anonymous__278,Vvar__2___24Anonymous__279] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__274,Vvar__1___24Anonymous__276,Vvar__2___24Anonymous__278) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__275,Vvar__1___24Anonymous__277,Vvar__2___24Anonymous__279)
=> ( Vvar__2___24Anonymous__278 = Vvar__2___24Anonymous__279
& Vvar__1___24Anonymous__276 = Vvar__1___24Anonymous__277
& Vvar__0__A__274 = Vvar__0__A__275 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__272,Vvar__0__A__273] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__272) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__273)
=> Vvar__0__A__272 = Vvar__0__A__273 ) ).
fof('$_inj_Coq.Init.Datatypes.pair',axiom,
! [Vvar__0__A__3499,Vvar__0__A__3500,Vvar__1__B__3501,Vvar__1__B__3502,Vvar__2___24Anonymous__3503,Vvar__2___24Anonymous__3504,Vvar__3___24Anonymous__3505,Vvar__3___24Anonymous__3506] :
( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__3499,Vvar__1__B__3501,Vvar__2___24Anonymous__3503,Vvar__3___24Anonymous__3505) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__3500,Vvar__1__B__3502,Vvar__2___24Anonymous__3504,Vvar__3___24Anonymous__3506)
=> ( Vvar__3___24Anonymous__3505 = Vvar__3___24Anonymous__3506
& Vvar__2___24Anonymous__3503 = Vvar__2___24Anonymous__3504
& Vvar__1__B__3501 = Vvar__1__B__3502
& Vvar__0__A__3499 = Vvar__0__A__3500 ) ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__10908,Vvar__0__A__10909,Vvar__1__P__10910,Vvar__1__P__10911,Vvar__2__x__10912,Vvar__2__x__10913,Vvar__3___24Anonymous__10914,Vvar__3___24Anonymous__10915] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__10908,Vvar__1__P__10910,Vvar__2__x__10912) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__10909,Vvar__1__P__10911,Vvar__2__x__10913)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__10912 = Vvar__2__x__10913
& Vvar__1__P__10910 = Vvar__1__P__10911
& Vvar__0__A__10908 = Vvar__0__A__10909 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__1103,Vvar__0__A__1104,Vvar__1__B__1105,Vvar__1__B__1106,Vvar__2___24Anonymous__1107,Vvar__2___24Anonymous__1108] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__1103,Vvar__1__B__1105) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__1104,Vvar__1__B__1106)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__1105 = Vvar__1__B__1106
& Vvar__0__A__1103 = Vvar__0__A__1104 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__1109,Vvar__0__A__1110,Vvar__1__B__1111,Vvar__1__B__1112,Vvar__2___24Anonymous__1113,Vvar__2___24Anonymous__1114] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__1109,Vvar__1__B__1111) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__1110,Vvar__1__B__1112)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__1111 = Vvar__1__B__1112
& Vvar__0__A__1109 = Vvar__0__A__1110 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__1189,Vvar__0___24Anonymous__1190] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1189) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1190)
=> Vvar__0___24Anonymous__1189 = Vvar__0___24Anonymous__1190 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__247,Vvar__0___24Anonymous__248] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__247) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__248)
=> Vvar__0___24Anonymous__247 = Vvar__0___24Anonymous__248 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__245,Vvar__0___24Anonymous__246] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__245) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__246)
=> Vvar__0___24Anonymous__245 = Vvar__0___24Anonymous__246 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__234,Vvar__0___24Anonymous__235] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__234) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__235)
=> Vvar__0___24Anonymous__234 = Vvar__0___24Anonymous__235 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__236,Vvar__0___24Anonymous__237] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__236) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__237)
=> Vvar__0___24Anonymous__236 = Vvar__0___24Anonymous__237 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__11479,Vvar__0__TA__11480,Vvar__1__TX__11481,Vvar__1__TX__11482,Vvar__2__AA__11483,Vvar__2__AA__11484,Vvar__3__AF__11485,Vvar__3__AF__11486,Vvar__4___24Anonymous__11487,Vvar__4___24Anonymous__11488,Vvar__5___24Anonymous__11489,Vvar__5___24Anonymous__11490] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__11479,Vvar__1__TX__11481,Vvar__2__AA__11483,Vvar__3__AF__11485,Vvar__4___24Anonymous__11487,Vvar__5___24Anonymous__11489) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__11480,Vvar__1__TX__11482,Vvar__2__AA__11484,Vvar__3__AF__11486,Vvar__4___24Anonymous__11488,Vvar__5___24Anonymous__11490)
=> ( Vvar__5___24Anonymous__11489 = Vvar__5___24Anonymous__11490
& Vvar__4___24Anonymous__11487 = Vvar__4___24Anonymous__11488
& Vvar__3__AF__11485 = Vvar__3__AF__11486
& Vvar__2__AA__11483 = Vvar__2__AA__11484
& Vvar__1__TX__11481 = Vvar__1__TX__11482
& Vvar__0__TA__11479 = Vvar__0__TA__11480 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__11491,Vvar__0__TA__11492,Vvar__1__TX__11493,Vvar__1__TX__11494,Vvar__2__AA__11495,Vvar__2__AA__11496,Vvar__3__AF__11497,Vvar__3__AF__11498,Vvar__4___24Anonymous__11499,Vvar__4___24Anonymous__11500,Vvar__5___24Anonymous__11501,Vvar__5___24Anonymous__11502] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__11491,Vvar__1__TX__11493,Vvar__2__AA__11495,Vvar__3__AF__11497,Vvar__4___24Anonymous__11499,Vvar__5___24Anonymous__11501) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__11492,Vvar__1__TX__11494,Vvar__2__AA__11496,Vvar__3__AF__11498,Vvar__4___24Anonymous__11500,Vvar__5___24Anonymous__11502)
=> ( Vvar__5___24Anonymous__11501 = Vvar__5___24Anonymous__11502
& Vvar__4___24Anonymous__11499 = Vvar__4___24Anonymous__11500
& Vvar__3__AF__11497 = Vvar__3__AF__11498
& Vvar__2__AA__11495 = Vvar__2__AA__11496
& Vvar__1__TX__11493 = Vvar__1__TX__11494
& Vvar__0__TA__11491 = Vvar__0__TA__11492 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__11503,Vvar__0__TA__11504,Vvar__1__TX__11505,Vvar__1__TX__11506,Vvar__2__AA__11507,Vvar__2__AA__11508,Vvar__3__AF__11509,Vvar__3__AF__11510,Vvar__4___24Anonymous__11511,Vvar__4___24Anonymous__11512,Vvar__5___24Anonymous__11513,Vvar__5___24Anonymous__11514] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__11503,Vvar__1__TX__11505,Vvar__2__AA__11507,Vvar__3__AF__11509,Vvar__4___24Anonymous__11511,Vvar__5___24Anonymous__11513) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__11504,Vvar__1__TX__11506,Vvar__2__AA__11508,Vvar__3__AF__11510,Vvar__4___24Anonymous__11512,Vvar__5___24Anonymous__11514)
=> ( Vvar__5___24Anonymous__11513 = Vvar__5___24Anonymous__11514
& Vvar__4___24Anonymous__11511 = Vvar__4___24Anonymous__11512
& Vvar__3__AF__11509 = Vvar__3__AF__11510
& Vvar__2__AA__11507 = Vvar__2__AA__11508
& Vvar__1__TX__11505 = Vvar__1__TX__11506
& Vvar__0__TA__11503 = Vvar__0__TA__11504 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__11461,Vvar__0__TA__11462,Vvar__1__TX__11463,Vvar__1__TX__11464,Vvar__2__AA__11465,Vvar__2__AA__11466,Vvar__3__AF__11467,Vvar__3__AF__11468] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11461,Vvar__1__TX__11463,Vvar__2__AA__11465,Vvar__3__AF__11467) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11462,Vvar__1__TX__11464,Vvar__2__AA__11466,Vvar__3__AF__11468)
=> ( Vvar__3__AF__11467 = Vvar__3__AF__11468
& Vvar__2__AA__11465 = Vvar__2__AA__11466
& Vvar__1__TX__11463 = Vvar__1__TX__11464
& Vvar__0__TA__11461 = Vvar__0__TA__11462 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__11525,Vvar__0__TA__11526,Vvar__1__TX__11527,Vvar__1__TX__11528,Vvar__2__AA__11529,Vvar__2__AA__11530,Vvar__3__AF__11531,Vvar__3__AF__11532,Vvar__4___24Anonymous__11533,Vvar__4___24Anonymous__11534,Vvar__5___24Anonymous__11535,Vvar__5___24Anonymous__11536,Vvar__6___24Anonymous__11537,Vvar__6___24Anonymous__11538] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__11525,Vvar__1__TX__11527,Vvar__2__AA__11529,Vvar__3__AF__11531,Vvar__4___24Anonymous__11533,Vvar__5___24Anonymous__11535,Vvar__6___24Anonymous__11537) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__11526,Vvar__1__TX__11528,Vvar__2__AA__11530,Vvar__3__AF__11532,Vvar__4___24Anonymous__11534,Vvar__5___24Anonymous__11536,Vvar__6___24Anonymous__11538)
=> ( Vvar__6___24Anonymous__11537 = Vvar__6___24Anonymous__11538
& Vvar__5___24Anonymous__11535 = Vvar__5___24Anonymous__11536
& Vvar__4___24Anonymous__11533 = Vvar__4___24Anonymous__11534
& Vvar__3__AF__11531 = Vvar__3__AF__11532
& Vvar__2__AA__11529 = Vvar__2__AA__11530
& Vvar__1__TX__11527 = Vvar__1__TX__11528
& Vvar__0__TA__11525 = Vvar__0__TA__11526 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__11515,Vvar__0__TA__11516,Vvar__1__TX__11517,Vvar__1__TX__11518,Vvar__2__AA__11519,Vvar__2__AA__11520,Vvar__3__AF__11521,Vvar__3__AF__11522,Vvar__4___24Anonymous__11523,Vvar__4___24Anonymous__11524] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__11515,Vvar__1__TX__11517,Vvar__2__AA__11519,Vvar__3__AF__11521,Vvar__4___24Anonymous__11523) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__11516,Vvar__1__TX__11518,Vvar__2__AA__11520,Vvar__3__AF__11522,Vvar__4___24Anonymous__11524)
=> ( Vvar__4___24Anonymous__11523 = Vvar__4___24Anonymous__11524
& Vvar__3__AF__11521 = Vvar__3__AF__11522
& Vvar__2__AA__11519 = Vvar__2__AA__11520
& Vvar__1__TX__11517 = Vvar__1__TX__11518
& Vvar__0__TA__11515 = Vvar__0__TA__11516 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__11453,Vvar__0__TA__11454,Vvar__1__TX__11455,Vvar__1__TX__11456,Vvar__2__AA__11457,Vvar__2__AA__11458,Vvar__3__AF__11459,Vvar__3__AF__11460] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11453,Vvar__1__TX__11455,Vvar__2__AA__11457,Vvar__3__AF__11459) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11454,Vvar__1__TX__11456,Vvar__2__AA__11458,Vvar__3__AF__11460)
=> ( Vvar__3__AF__11459 = Vvar__3__AF__11460
& Vvar__2__AA__11457 = Vvar__2__AA__11458
& Vvar__1__TX__11455 = Vvar__1__TX__11456
& Vvar__0__TA__11453 = Vvar__0__TA__11454 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__11469,Vvar__0__TA__11470,Vvar__1__TX__11471,Vvar__1__TX__11472,Vvar__2__AA__11473,Vvar__2__AA__11474,Vvar__3__AF__11475,Vvar__3__AF__11476,Vvar__4___24Anonymous__11477,Vvar__4___24Anonymous__11478] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__11469,Vvar__1__TX__11471,Vvar__2__AA__11473,Vvar__3__AF__11475,Vvar__4___24Anonymous__11477) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__11470,Vvar__1__TX__11472,Vvar__2__AA__11474,Vvar__3__AF__11476,Vvar__4___24Anonymous__11478)
=> ( Vvar__4___24Anonymous__11477 = Vvar__4___24Anonymous__11478
& Vvar__3__AF__11475 = Vvar__3__AF__11476
& Vvar__2__AA__11473 = Vvar__2__AA__11474
& Vvar__1__TX__11471 = Vvar__1__TX__11472
& Vvar__0__TA__11469 = Vvar__0__TA__11470 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
! [Vvar__0__C__19134,Vvar__0__C__19135] :
( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19134) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__19135)
=> Vvar__0__C__19134 = Vvar__0__C__19135 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
! [Vvar__0__C__19132,Vvar__0__C__19133] :
( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19132) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__19133)
=> Vvar__0__C__19132 = Vvar__0__C__19133 ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
! [Vvar__0__C__19140,Vvar__0__C__19141,Vvar__1___24Anonymous__19142,Vvar__1___24Anonymous__19143] :
( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__19140,Vvar__1___24Anonymous__19142) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__19141,Vvar__1___24Anonymous__19143)
=> ( Vvar__1___24Anonymous__19142 = Vvar__1___24Anonymous__19143
& Vvar__0__C__19140 = Vvar__0__C__19141 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
! [Vvar__0__C__19144,Vvar__0__C__19145,Vvar__1___24Anonymous__19146,Vvar__1___24Anonymous__19147,Vvar__2___24Anonymous__19148,Vvar__2___24Anonymous__19149] :
( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__19144,Vvar__1___24Anonymous__19146,Vvar__2___24Anonymous__19148) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__19145,Vvar__1___24Anonymous__19147,Vvar__2___24Anonymous__19149)
=> ( Vvar__2___24Anonymous__19148 = Vvar__2___24Anonymous__19149
& Vvar__1___24Anonymous__19146 = Vvar__1___24Anonymous__19147
& Vvar__0__C__19144 = Vvar__0__C__19145 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
! [Vvar__0__C__19136,Vvar__0__C__19137,Vvar__1___24Anonymous__19138,Vvar__1___24Anonymous__19139] :
( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__19136,Vvar__1___24Anonymous__19138) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__19137,Vvar__1___24Anonymous__19139)
=> ( Vvar__1___24Anonymous__19138 = Vvar__1___24Anonymous__19139
& Vvar__0__C__19136 = Vvar__0__C__19137 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
! [Vvar__0__C__19170,Vvar__0__C__19171,Vvar__1___24Anonymous__19172,Vvar__1___24Anonymous__19173,Vvar__2___24Anonymous__19174,Vvar__2___24Anonymous__19175] :
( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__19170,Vvar__1___24Anonymous__19172,Vvar__2___24Anonymous__19174) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__19171,Vvar__1___24Anonymous__19173,Vvar__2___24Anonymous__19175)
=> ( Vvar__2___24Anonymous__19174 = Vvar__2___24Anonymous__19175
& Vvar__1___24Anonymous__19172 = Vvar__1___24Anonymous__19173
& Vvar__0__C__19170 = Vvar__0__C__19171 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
! [Vvar__0__C__19166,Vvar__0__C__19167,Vvar__1___24Anonymous__19168,Vvar__1___24Anonymous__19169] :
( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__19166,Vvar__1___24Anonymous__19168) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__19167,Vvar__1___24Anonymous__19169)
=> ( Vvar__1___24Anonymous__19168 = Vvar__1___24Anonymous__19169
& Vvar__0__C__19166 = Vvar__0__C__19167 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
! [Vvar__0__C__19156,Vvar__0__C__19157,Vvar__1___24Anonymous__19158,Vvar__1___24Anonymous__19159,Vvar__2___24Anonymous__19160,Vvar__2___24Anonymous__19161] :
( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__19156,Vvar__1___24Anonymous__19158,Vvar__2___24Anonymous__19160) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__19157,Vvar__1___24Anonymous__19159,Vvar__2___24Anonymous__19161)
=> ( Vvar__2___24Anonymous__19160 = Vvar__2___24Anonymous__19161
& Vvar__1___24Anonymous__19158 = Vvar__1___24Anonymous__19159
& Vvar__0__C__19156 = Vvar__0__C__19157 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
! [Vvar__0__C__19162,Vvar__0__C__19163,Vvar__1___24Anonymous__19164,Vvar__1___24Anonymous__19165] :
( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__19162,Vvar__1___24Anonymous__19164) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__19163,Vvar__1___24Anonymous__19165)
=> ( Vvar__1___24Anonymous__19164 = Vvar__1___24Anonymous__19165
& Vvar__0__C__19162 = Vvar__0__C__19163 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
! [Vvar__0__C__19176,Vvar__0__C__19177,Vvar__1___24Anonymous__19178,Vvar__1___24Anonymous__19179,Vvar__2___24Anonymous__19180,Vvar__2___24Anonymous__19181] :
( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__19176,Vvar__1___24Anonymous__19178,Vvar__2___24Anonymous__19180) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__19177,Vvar__1___24Anonymous__19179,Vvar__2___24Anonymous__19181)
=> ( Vvar__2___24Anonymous__19180 = Vvar__2___24Anonymous__19181
& Vvar__1___24Anonymous__19178 = Vvar__1___24Anonymous__19179
& Vvar__0__C__19176 = Vvar__0__C__19177 ) ) ).
fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
! [Vvar__0__C__19150,Vvar__0__C__19151,Vvar__1___24Anonymous__19152,Vvar__1___24Anonymous__19153,Vvar__2___24Anonymous__19154,Vvar__2___24Anonymous__19155] :
( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__19150,Vvar__1___24Anonymous__19152,Vvar__2___24Anonymous__19154) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__19151,Vvar__1___24Anonymous__19153,Vvar__2___24Anonymous__19155)
=> ( Vvar__2___24Anonymous__19154 = Vvar__2___24Anonymous__19155
& Vvar__1___24Anonymous__19152 = Vvar__1___24Anonymous__19153
& Vvar__0__C__19150 = Vvar__0__C__19151 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
! [Vvar__0__C__12648,Vvar__0__C__12649] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12648) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12649)
=> Vvar__0__C__12648 = Vvar__0__C__12649 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
! [Vvar__0__C__12646,Vvar__0__C__12647] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12646) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12647)
=> Vvar__0__C__12646 = Vvar__0__C__12647 ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
! [Vvar__0__C__12654,Vvar__0__C__12655,Vvar__1___24Anonymous__12656,Vvar__1___24Anonymous__12657] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__12654,Vvar__1___24Anonymous__12656) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__12655,Vvar__1___24Anonymous__12657)
=> ( Vvar__1___24Anonymous__12656 = Vvar__1___24Anonymous__12657
& Vvar__0__C__12654 = Vvar__0__C__12655 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
! [Vvar__0__C__12658,Vvar__0__C__12659,Vvar__1___24Anonymous__12660,Vvar__1___24Anonymous__12661,Vvar__2___24Anonymous__12662,Vvar__2___24Anonymous__12663] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__12658,Vvar__1___24Anonymous__12660,Vvar__2___24Anonymous__12662) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__12659,Vvar__1___24Anonymous__12661,Vvar__2___24Anonymous__12663)
=> ( Vvar__2___24Anonymous__12662 = Vvar__2___24Anonymous__12663
& Vvar__1___24Anonymous__12660 = Vvar__1___24Anonymous__12661
& Vvar__0__C__12658 = Vvar__0__C__12659 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
! [Vvar__0__C__12650,Vvar__0__C__12651,Vvar__1___24Anonymous__12652,Vvar__1___24Anonymous__12653] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__12650,Vvar__1___24Anonymous__12652) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__12651,Vvar__1___24Anonymous__12653)
=> ( Vvar__1___24Anonymous__12652 = Vvar__1___24Anonymous__12653
& Vvar__0__C__12650 = Vvar__0__C__12651 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
! [Vvar__0__C__12670,Vvar__0__C__12671,Vvar__1___24Anonymous__12672,Vvar__1___24Anonymous__12673,Vvar__2___24Anonymous__12674,Vvar__2___24Anonymous__12675] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__12670,Vvar__1___24Anonymous__12672,Vvar__2___24Anonymous__12674) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__12671,Vvar__1___24Anonymous__12673,Vvar__2___24Anonymous__12675)
=> ( Vvar__2___24Anonymous__12674 = Vvar__2___24Anonymous__12675
& Vvar__1___24Anonymous__12672 = Vvar__1___24Anonymous__12673
& Vvar__0__C__12670 = Vvar__0__C__12671 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
! [Vvar__0__C__12676,Vvar__0__C__12677,Vvar__1___24Anonymous__12678,Vvar__1___24Anonymous__12679] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__12676,Vvar__1___24Anonymous__12678) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__12677,Vvar__1___24Anonymous__12679)
=> ( Vvar__1___24Anonymous__12678 = Vvar__1___24Anonymous__12679
& Vvar__0__C__12676 = Vvar__0__C__12677 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
! [Vvar__0__C__12680,Vvar__0__C__12681,Vvar__1___24Anonymous__12682,Vvar__1___24Anonymous__12683,Vvar__2___24Anonymous__12684,Vvar__2___24Anonymous__12685] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__12680,Vvar__1___24Anonymous__12682,Vvar__2___24Anonymous__12684) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__12681,Vvar__1___24Anonymous__12683,Vvar__2___24Anonymous__12685)
=> ( Vvar__2___24Anonymous__12684 = Vvar__2___24Anonymous__12685
& Vvar__1___24Anonymous__12682 = Vvar__1___24Anonymous__12683
& Vvar__0__C__12680 = Vvar__0__C__12681 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
! [Vvar__0__C__12664,Vvar__0__C__12665,Vvar__1___24Anonymous__12666,Vvar__1___24Anonymous__12667,Vvar__2___24Anonymous__12668,Vvar__2___24Anonymous__12669] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__12664,Vvar__1___24Anonymous__12666,Vvar__2___24Anonymous__12668) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__12665,Vvar__1___24Anonymous__12667,Vvar__2___24Anonymous__12669)
=> ( Vvar__2___24Anonymous__12668 = Vvar__2___24Anonymous__12669
& Vvar__1___24Anonymous__12666 = Vvar__1___24Anonymous__12667
& Vvar__0__C__12664 = Vvar__0__C__12665 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
! [Vvar__0__C__12435,Vvar__0__C__12436,Vvar__1___24Anonymous__12437,Vvar__1___24Anonymous__12438,Vvar__2___24Anonymous__12439,Vvar__2___24Anonymous__12440,Vvar__3___24Anonymous__12441,Vvar__3___24Anonymous__12442] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12435,Vvar__1___24Anonymous__12437,Vvar__2___24Anonymous__12439,Vvar__3___24Anonymous__12441) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12436,Vvar__1___24Anonymous__12438,Vvar__2___24Anonymous__12440,Vvar__3___24Anonymous__12442)
=> ( Vvar__3___24Anonymous__12441 = Vvar__3___24Anonymous__12442
& Vvar__2___24Anonymous__12439 = Vvar__2___24Anonymous__12440
& Vvar__1___24Anonymous__12437 = Vvar__1___24Anonymous__12438
& Vvar__0__C__12435 = Vvar__0__C__12436 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
! [Vvar__0__C__12425,Vvar__0__C__12426,Vvar__1___24Anonymous__12427,Vvar__1___24Anonymous__12428] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12425,Vvar__1___24Anonymous__12427) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12426,Vvar__1___24Anonymous__12428)
=> ( Vvar__1___24Anonymous__12427 = Vvar__1___24Anonymous__12428
& Vvar__0__C__12425 = Vvar__0__C__12426 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
! [Vvar__0__C__12429,Vvar__0__C__12430,Vvar__1___24Anonymous__12431,Vvar__1___24Anonymous__12432,Vvar__2___24Anonymous__12433,Vvar__2___24Anonymous__12434] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12429,Vvar__1___24Anonymous__12431,Vvar__2___24Anonymous__12433) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12430,Vvar__1___24Anonymous__12432,Vvar__2___24Anonymous__12434)
=> ( Vvar__2___24Anonymous__12433 = Vvar__2___24Anonymous__12434
& Vvar__1___24Anonymous__12431 = Vvar__1___24Anonymous__12432
& Vvar__0__C__12429 = Vvar__0__C__12430 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
! [Vvar__0___24Anonymous__12460,Vvar__0___24Anonymous__12461,Vvar__1___24Anonymous__12462,Vvar__1___24Anonymous__12463] :
( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__12460,Vvar__1___24Anonymous__12462) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__12461,Vvar__1___24Anonymous__12463)
=> ( Vvar__1___24Anonymous__12462 = Vvar__1___24Anonymous__12463
& Vvar__0___24Anonymous__12460 = Vvar__0___24Anonymous__12461 ) ) ).
fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
! [Vvar__0___24Anonymous__12456,Vvar__0___24Anonymous__12457,Vvar__1___24Anonymous__12458,Vvar__1___24Anonymous__12459] :
( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12456,Vvar__1___24Anonymous__12458) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12457,Vvar__1___24Anonymous__12459)
=> ( Vvar__1___24Anonymous__12458 = Vvar__1___24Anonymous__12459
& Vvar__0___24Anonymous__12456 = Vvar__0___24Anonymous__12457 ) ) ).
fof('$_inversion_Coq.Arith.Between.between',axiom,
! [Vvar__0__P__15616,Vvar__1__k__15618,Vvar__2___24Anonymous__15619] :
( c_24__type__15633___24t(Vvar__0__P__15616,Vvar__1__k__15618,Vvar__2___24Anonymous__15619,Vvar__0__P__15616)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__15618)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__15619)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__15616,Vvar__1__k__15618,Vvar__2___24Anonymous__15619)
=> ( Vvar__2___24Anonymous__15619 = Vvar__1__k__15618
| ? [Vvar__2__l__15627] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__15627)
& cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__15616,Vvar__1__k__15618,Vvar__2__l__15627)
& p(happ(Vvar__0__P__15616,Vvar__2__l__15627))
& Vvar__2___24Anonymous__15619 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__15627) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
! [Vvar__0__Q__15639,Vvar__1__k__15641,Vvar__2___24Anonymous__15642] :
( c_24__type__15658___24t(Vvar__0__Q__15639,Vvar__1__k__15641,Vvar__2___24Anonymous__15642,Vvar__0__Q__15639)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__15641)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__15642)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__15639,Vvar__1__k__15641,Vvar__2___24Anonymous__15642)
=> ( ? [Vvar__2__l__15647] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__15647)
& cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__15639,Vvar__1__k__15641,Vvar__2__l__15647)
& Vvar__2___24Anonymous__15642 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__15647) )
| ? [Vvar__2__l__15652] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__15652)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__15641,Vvar__2__l__15652))
& p(happ(Vvar__0__Q__15639,Vvar__2__l__15652))
& Vvar__2___24Anonymous__15642 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__15652) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__490,Vvar__1___24Anonymous__491,VX492] :
( cProp___24t(Vvar__0__P__490)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__491)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__490,Vvar__1___24Anonymous__491,VX492)
=> ( ( p(Vvar__0__P__490)
& Vvar__1___24Anonymous__491 = cCoq_2eInit_2eDatatypes_2etrue
& VX492 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__490) )
| ( ~ p(Vvar__0__P__490)
& Vvar__1___24Anonymous__491 = cCoq_2eInit_2eDatatypes_2efalse
& VX492 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__490) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__3451,Vvar__1__Q__3452,Vvar__2___24Anonymous__3453] :
( cProp___24t(Vvar__0__P__3451)
=> ( cProp___24t(Vvar__1__Q__3452)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__3453)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__3451,Vvar__1__Q__3452,Vvar__2___24Anonymous__3453)
=> ( ( p(Vvar__0__P__3451)
& Vvar__2___24Anonymous__3453 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__3452)
& Vvar__2___24Anonymous__3453 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__3507,Vvar__1__Plt__3508,Vvar__2__Pgt__3509,Vvar__3___24Anonymous__3510] :
( cProp___24t(Vvar__0__Peq__3507)
=> ( cProp___24t(Vvar__1__Plt__3508)
=> ( cProp___24t(Vvar__2__Pgt__3509)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__3510)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__3507,Vvar__1__Plt__3508,Vvar__2__Pgt__3509,Vvar__3___24Anonymous__3510)
=> ( ( p(Vvar__0__Peq__3507)
& Vvar__3___24Anonymous__3510 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__3508)
& Vvar__3___24Anonymous__3510 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__3509)
& Vvar__3___24Anonymous__3510 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX567] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX567)
=> ( VX567 = cCoq_2eInit_2eDatatypes_2etrue
| VX567 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX568] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX568)
=> ( VX568 = cCoq_2eInit_2eDatatypes_2eEq
| VX568 = cCoq_2eInit_2eDatatypes_2eLt
| VX568 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__262,VX263] :
( cType___24t(Vvar__0__A__262)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__262,VX263)
=> ( VX263 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__262)
| ? [Vvar__1___24Anonymous__266] :
( t(Vvar__1___24Anonymous__266,Vvar__0__A__262)
& ? [Vvar__2___24Anonymous__267] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__262,Vvar__2___24Anonymous__267)
& VX263 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__262,Vvar__1___24Anonymous__266,Vvar__2___24Anonymous__267) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX251] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX251)
=> ( VX251 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__252] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__252)
& VX251 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__252) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__1239,VX1240] :
( cType___24t(Vvar__0__A__1239)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__1239,VX1240)
=> ( ? [Vvar__1___24Anonymous__1242] :
( t(Vvar__1___24Anonymous__1242,Vvar__0__A__1239)
& VX1240 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__1239,Vvar__1___24Anonymous__1242) )
| VX1240 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__1239) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
! [Vvar__0__A__3491,Vvar__1__B__3492,VX3493] :
( cType___24t(Vvar__0__A__3491)
=> ( cType___24t(Vvar__1__B__3492)
=> ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__3491,Vvar__1__B__3492,VX3493)
=> ? [Vvar__2___24Anonymous__3496] :
( t(Vvar__2___24Anonymous__3496,Vvar__0__A__3491)
& ? [Vvar__3___24Anonymous__3497] :
( t(Vvar__3___24Anonymous__3497,Vvar__1__B__3492)
& VX3493 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__3491,Vvar__1__B__3492,Vvar__2___24Anonymous__3496,Vvar__3___24Anonymous__3497) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX132] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX132)
=> VX132 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__1060,Vvar__1___24Anonymous__1061] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__1060)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__1061)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__1060,Vvar__1___24Anonymous__1061))
=> ( Vvar__1___24Anonymous__1061 = Vvar__0__n__1060
| ? [Vvar__1__m__1065] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__1065)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__1060,Vvar__1__m__1065))
& Vvar__1___24Anonymous__1061 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__1065) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__10887,Vvar__1__P__10888,VX10891] :
( cType___24t(Vvar__0__A__10887)
=> ( c_24__type__10901___24t(Vvar__0__A__10887,Vvar__1__P__10888,Vvar__1__P__10888)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__10887,Vvar__1__P__10888,VX10891)
=> ? [Vvar__2__x__10896] :
( t(Vvar__2__x__10896,Vvar__0__A__10887)
& p(happ(Vvar__1__P__10888,Vvar__2__x__10896))
& VX10891 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__10887,Vvar__1__P__10888,Vvar__2__x__10896) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__1085,Vvar__1__B__1086,VX1087] :
( cProp___24t(Vvar__0__A__1085)
=> ( cProp___24t(Vvar__1__B__1086)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__1085,Vvar__1__B__1086,VX1087)
=> ( ( p(Vvar__0__A__1085)
& VX1087 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__1085,Vvar__1__B__1086) )
| ( p(Vvar__1__B__1086)
& VX1087 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__1085,Vvar__1__B__1086) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__420,Vvar__1__R__421,Vvar__2__x__426] :
( cType___24t(Vvar__0__A__420)
=> ( c_24__type__455___24t(Vvar__0__A__420,Vvar__1__R__421,Vvar__2__x__426,Vvar__1__R__421)
=> ( t(Vvar__2__x__426,Vvar__0__A__420)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__420,Vvar__1__R__421,Vvar__2__x__426)
=> ( ! [Vvar__var__var__var__var__3__y__436__438__440__442__444] :
( t(Vvar__var__var__var__var__3__y__436__438__440__442__444,Vvar__0__A__420)
=> ( p(happ(happ(Vvar__1__R__421,Vvar__var__var__var__var__3__y__436__438__440__442__444),Vvar__2__x__426))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__420,Vvar__1__R__421,Vvar__var__var__var__var__3__y__436__438__440__442__444) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Exists',axiom,
! [Vvar__0__A__12052,Vvar__1__P__12053,Vvar__2___24Anonymous__12056] :
( cType___24t(Vvar__0__A__12052)
=> ( c_24__type__12076___24t(Vvar__0__A__12052,Vvar__1__P__12053,Vvar__2___24Anonymous__12056,Vvar__1__P__12053)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12052,Vvar__2___24Anonymous__12056)
=> ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__12052,Vvar__1__P__12053,Vvar__2___24Anonymous__12056)
=> ( ? [Vvar__2__x__12062] :
( t(Vvar__2__x__12062,Vvar__0__A__12052)
& ? [Vvar__3__l__12063] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12052,Vvar__3__l__12063)
& p(happ(Vvar__1__P__12053,Vvar__2__x__12062))
& Vvar__2___24Anonymous__12056 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12052,Vvar__2__x__12062,Vvar__3__l__12063) ) )
| ? [Vvar__2__x__12069] :
( t(Vvar__2__x__12069,Vvar__0__A__12052)
& ? [Vvar__3__l__12070] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12052,Vvar__3__l__12070)
& cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__12052,Vvar__1__P__12053,Vvar__3__l__12070)
& Vvar__2___24Anonymous__12056 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12052,Vvar__2__x__12069,Vvar__3__l__12070) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.Forall',axiom,
! [Vvar__0__A__12078,Vvar__1__P__12079,Vvar__2___24Anonymous__12082] :
( cType___24t(Vvar__0__A__12078)
=> ( c_24__type__12100___24t(Vvar__0__A__12078,Vvar__1__P__12079,Vvar__2___24Anonymous__12082,Vvar__1__P__12079)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12078,Vvar__2___24Anonymous__12082)
=> ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__12078,Vvar__1__P__12079,Vvar__2___24Anonymous__12082)
=> ( Vvar__2___24Anonymous__12082 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12078)
| ? [Vvar__2__x__12092] :
( t(Vvar__2__x__12092,Vvar__0__A__12078)
& ? [Vvar__3__l__12093] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12078,Vvar__3__l__12093)
& p(happ(Vvar__1__P__12079,Vvar__2__x__12092))
& cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__12078,Vvar__1__P__12079,Vvar__3__l__12093)
& Vvar__2___24Anonymous__12082 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12078,Vvar__2__x__12092,Vvar__3__l__12093) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__2685,Vvar__1___24Anonymous__2686] :
( cType___24t(Vvar__0__A__2685)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2685,Vvar__1___24Anonymous__2686)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__2685,Vvar__1___24Anonymous__2686)
=> ( Vvar__1___24Anonymous__2686 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__2685)
| ? [Vvar__1__x__2690] :
( t(Vvar__1__x__2690,Vvar__0__A__2685)
& ? [Vvar__2__l__2691] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__2685,Vvar__2__l__2691)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__2685,Vvar__1__x__2690,Vvar__2__l__2691))
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__2685,Vvar__2__l__2691)
& Vvar__1___24Anonymous__2686 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__2685,Vvar__1__x__2690,Vvar__2__l__2691) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
! [Vvar__0__A__12699,Vvar__1__eqA__12700,Vvar__2__x__12705,Vvar__3___24Anonymous__12706] :
( cType___24t(Vvar__0__A__12699)
=> ( c_24__type__12739___24t(Vvar__0__A__12699,Vvar__1__eqA__12700,Vvar__2__x__12705,Vvar__3___24Anonymous__12706,Vvar__1__eqA__12700)
=> ( t(Vvar__2__x__12705,Vvar__0__A__12699)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12699,Vvar__3___24Anonymous__12706)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__12699,Vvar__1__eqA__12700,Vvar__2__x__12705,Vvar__3___24Anonymous__12706)
=> ( ? [Vvar__3__y__12715] :
( t(Vvar__3__y__12715,Vvar__0__A__12699)
& ? [Vvar__4__l__12716] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12699,Vvar__4__l__12716)
& p(happ(happ(Vvar__1__eqA__12700,Vvar__2__x__12705),Vvar__3__y__12715))
& Vvar__3___24Anonymous__12706 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12699,Vvar__3__y__12715,Vvar__4__l__12716) ) )
| ? [Vvar__3__y__12725] :
( t(Vvar__3__y__12725,Vvar__0__A__12699)
& ? [Vvar__4__l__12726] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12699,Vvar__4__l__12726)
& cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__12699,Vvar__1__eqA__12700,Vvar__2__x__12705,Vvar__4__l__12726)
& Vvar__3___24Anonymous__12706 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12699,Vvar__3__y__12725,Vvar__4__l__12726) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
! [Vvar__0__A__12741,Vvar__1__eqA__12742,Vvar__2___24Anonymous__12747] :
( cType___24t(Vvar__0__A__12741)
=> ( c_24__type__12774___24t(Vvar__0__A__12741,Vvar__1__eqA__12742,Vvar__2___24Anonymous__12747,Vvar__1__eqA__12742)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12741,Vvar__2___24Anonymous__12747)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__12741,Vvar__1__eqA__12742,Vvar__2___24Anonymous__12747)
=> ( Vvar__2___24Anonymous__12747 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__12741)
| ? [Vvar__2__x__12761] :
( t(Vvar__2__x__12761,Vvar__0__A__12741)
& ? [Vvar__3__l__12762] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__12741,Vvar__3__l__12762)
& ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__12741,Vvar__1__eqA__12742,Vvar__2__x__12761,Vvar__3__l__12762)
& cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__12741,Vvar__1__eqA__12742,Vvar__3__l__12762)
& Vvar__2___24Anonymous__12747 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__12741,Vvar__2__x__12761,Vvar__3__l__12762) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX1186] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1186)
=> ( VX1186 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__1187] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1187)
& VX1186 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1187) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX238] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX238)
=> ( VX238 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__239] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__239)
& VX238 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__239) )
| ? [Vvar__0___24Anonymous__240] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__240)
& VX238 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__240) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX227] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX227)
=> ( ? [Vvar__0___24Anonymous__228] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__228)
& VX227 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__228) )
| ? [Vvar__0___24Anonymous__229] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__229)
& VX227 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__229) )
| VX227 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__2744,Vvar__1__R__2745] :
( cType___24t(Vvar__0__A__2744)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2744,Vvar__1__R__2745)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__2744,Vvar__1__R__2745)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__2744,Vvar__1__R__2745)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2744,Vvar__1__R__2745)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__2736,Vvar__1__R__2737] :
( cType___24t(Vvar__0__A__2736)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2736,Vvar__1__R__2737)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__2736,Vvar__1__R__2737)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__2736,Vvar__1__R__2737)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2736,Vvar__1__R__2737)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__2736,Vvar__1__R__2737)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__2728,Vvar__1__R__2729] :
( cType___24t(Vvar__0__A__2728)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2728,Vvar__1__R__2729)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__2728,Vvar__1__R__2729)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__2728,Vvar__1__R__2729)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2728,Vvar__1__R__2729)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__2728,Vvar__1__R__2729)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__2721,Vvar__1__R__2722] :
( cType___24t(Vvar__0__A__2721)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2721,Vvar__1__R__2722)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__2721,Vvar__1__R__2722)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__2721,Vvar__1__R__2722)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__2721,Vvar__1__R__2722)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__2823,Vvar__1__R__2824,Vvar__2__x__2825,Vvar__3___24Anonymous__2826] :
( cType___24t(Vvar__0__A__2823)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2823,Vvar__1__R__2824)
=> ( t(Vvar__2__x__2825,Vvar__0__A__2823)
=> ( t(Vvar__3___24Anonymous__2826,Vvar__0__A__2823)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__2823,Vvar__1__R__2824,Vvar__2__x__2825,Vvar__3___24Anonymous__2826)
=> ( ? [Vvar__3__y__2831] :
( t(Vvar__3__y__2831,Vvar__0__A__2823)
& p(happ(happ(Vvar__1__R__2824,Vvar__2__x__2825),Vvar__3__y__2831))
& Vvar__3___24Anonymous__2826 = Vvar__3__y__2831 )
| Vvar__3___24Anonymous__2826 = Vvar__2__x__2825 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__2932,Vvar__1__R__2933,Vvar__1___24Anonymous__2934,Vvar__2___24Anonymous__2935] :
( cType___24t(Vvar__0__A__2932)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2932,Vvar__1__R__2933)
=> ( t(Vvar__1___24Anonymous__2934,Vvar__0__A__2932)
=> ( t(Vvar__2___24Anonymous__2935,Vvar__0__A__2932)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__2932,Vvar__1__R__2933,Vvar__1___24Anonymous__2934,Vvar__2___24Anonymous__2935)
=> ( ? [Vvar__2__x__2939] :
( t(Vvar__2__x__2939,Vvar__0__A__2932)
& ? [Vvar__3__y__2940] :
( t(Vvar__3__y__2940,Vvar__0__A__2932)
& p(happ(happ(Vvar__1__R__2933,Vvar__2__x__2939),Vvar__3__y__2940))
& Vvar__2___24Anonymous__2935 = Vvar__3__y__2940
& Vvar__1___24Anonymous__2934 = Vvar__2__x__2939 ) )
| ? [Vvar__2__x__2944] :
( t(Vvar__2__x__2944,Vvar__0__A__2932)
& Vvar__2___24Anonymous__2935 = Vvar__2__x__2944
& Vvar__1___24Anonymous__2934 = Vvar__2__x__2944 )
| ? [Vvar__2__x__2947] :
( t(Vvar__2__x__2947,Vvar__0__A__2932)
& ? [Vvar__3__y__2948] :
( t(Vvar__3__y__2948,Vvar__0__A__2932)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__2932,Vvar__1__R__2933,Vvar__2__x__2947,Vvar__3__y__2948)
& Vvar__2___24Anonymous__2935 = Vvar__2__x__2947
& Vvar__1___24Anonymous__2934 = Vvar__3__y__2948 ) )
| ? [Vvar__2__x__2952] :
( t(Vvar__2__x__2952,Vvar__0__A__2932)
& ? [Vvar__3__y__2953] :
( t(Vvar__3__y__2953,Vvar__0__A__2932)
& ? [Vvar__4__z__2954] :
( t(Vvar__4__z__2954,Vvar__0__A__2932)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__2932,Vvar__1__R__2933,Vvar__2__x__2952,Vvar__3__y__2953)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__2932,Vvar__1__R__2933,Vvar__3__y__2953,Vvar__4__z__2954)
& Vvar__2___24Anonymous__2935 = Vvar__4__z__2954
& Vvar__1___24Anonymous__2934 = Vvar__2__x__2952 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__2993,Vvar__1__R__2994,Vvar__2__x__2995,Vvar__3___24Anonymous__2996] :
( cType___24t(Vvar__0__A__2993)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2993,Vvar__1__R__2994)
=> ( t(Vvar__2__x__2995,Vvar__0__A__2993)
=> ( t(Vvar__3___24Anonymous__2996,Vvar__0__A__2993)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__2993,Vvar__1__R__2994,Vvar__2__x__2995,Vvar__3___24Anonymous__2996)
=> ( Vvar__3___24Anonymous__2996 = Vvar__2__x__2995
| ? [Vvar__3__y__3004] :
( t(Vvar__3__y__3004,Vvar__0__A__2993)
& ? [Vvar__4__z__3005] :
( t(Vvar__4__z__3005,Vvar__0__A__2993)
& ( p(happ(happ(Vvar__1__R__2994,Vvar__2__x__2995),Vvar__3__y__3004))
| p(happ(happ(Vvar__1__R__2994,Vvar__3__y__3004),Vvar__2__x__2995)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__2993,Vvar__1__R__2994,Vvar__3__y__3004,Vvar__4__z__3005)
& Vvar__3___24Anonymous__2996 = Vvar__4__z__3005 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__3028,Vvar__1__R__3029,Vvar__2__x__3030,Vvar__3___24Anonymous__3031] :
( cType___24t(Vvar__0__A__3028)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__3028,Vvar__1__R__3029)
=> ( t(Vvar__2__x__3030,Vvar__0__A__3028)
=> ( t(Vvar__3___24Anonymous__3031,Vvar__0__A__3028)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__3028,Vvar__1__R__3029,Vvar__2__x__3030,Vvar__3___24Anonymous__3031)
=> ( Vvar__3___24Anonymous__3031 = Vvar__2__x__3030
| ? [Vvar__3__y__3039] :
( t(Vvar__3__y__3039,Vvar__0__A__3028)
& ? [Vvar__4__z__3040] :
( t(Vvar__4__z__3040,Vvar__0__A__3028)
& ( p(happ(happ(Vvar__1__R__3029,Vvar__3__y__3039),Vvar__4__z__3040))
| p(happ(happ(Vvar__1__R__3029,Vvar__4__z__3040),Vvar__3__y__3039)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__3028,Vvar__1__R__3029,Vvar__2__x__3030,Vvar__3__y__3039)
& Vvar__3___24Anonymous__3031 = Vvar__4__z__3040 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__112,Vvar__1__R__113,Vvar__2__x__114,Vvar__3___24Anonymous__115] :
( cType___24t(Vvar__0__A__112)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__112,Vvar__1__R__113)
=> ( t(Vvar__2__x__114,Vvar__0__A__112)
=> ( t(Vvar__3___24Anonymous__115,Vvar__0__A__112)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__112,Vvar__1__R__113,Vvar__2__x__114,Vvar__3___24Anonymous__115)
=> ( ? [Vvar__3__y__120] :
( t(Vvar__3__y__120,Vvar__0__A__112)
& p(happ(happ(Vvar__1__R__113,Vvar__2__x__114),Vvar__3__y__120))
& Vvar__3___24Anonymous__115 = Vvar__3__y__120 )
| Vvar__3___24Anonymous__115 = Vvar__2__x__114
| ? [Vvar__3__y__128] :
( t(Vvar__3__y__128,Vvar__0__A__112)
& ? [Vvar__4__z__129] :
( t(Vvar__4__z__129,Vvar__0__A__112)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__112,Vvar__1__R__113,Vvar__2__x__114,Vvar__3__y__128)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__112,Vvar__1__R__113,Vvar__3__y__128,Vvar__4__z__129)
& Vvar__3___24Anonymous__115 = Vvar__4__z__129 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__2870,Vvar__1__R__2871,Vvar__2__x__2872,Vvar__3___24Anonymous__2873] :
( cType___24t(Vvar__0__A__2870)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2870,Vvar__1__R__2871)
=> ( t(Vvar__2__x__2872,Vvar__0__A__2870)
=> ( t(Vvar__3___24Anonymous__2873,Vvar__0__A__2870)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__2870,Vvar__1__R__2871,Vvar__2__x__2872,Vvar__3___24Anonymous__2873)
=> ( Vvar__3___24Anonymous__2873 = Vvar__2__x__2872
| ? [Vvar__3__y__2881] :
( t(Vvar__3__y__2881,Vvar__0__A__2870)
& ? [Vvar__4__z__2882] :
( t(Vvar__4__z__2882,Vvar__0__A__2870)
& p(happ(happ(Vvar__1__R__2871,Vvar__2__x__2872),Vvar__3__y__2881))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__2870,Vvar__1__R__2871,Vvar__3__y__2881,Vvar__4__z__2882)
& Vvar__3___24Anonymous__2873 = Vvar__4__z__2882 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__2905,Vvar__1__R__2906,Vvar__2__x__2907,Vvar__3___24Anonymous__2908] :
( cType___24t(Vvar__0__A__2905)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2905,Vvar__1__R__2906)
=> ( t(Vvar__2__x__2907,Vvar__0__A__2905)
=> ( t(Vvar__3___24Anonymous__2908,Vvar__0__A__2905)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__2905,Vvar__1__R__2906,Vvar__2__x__2907,Vvar__3___24Anonymous__2908)
=> ( Vvar__3___24Anonymous__2908 = Vvar__2__x__2907
| ? [Vvar__3__y__2916] :
( t(Vvar__3__y__2916,Vvar__0__A__2905)
& ? [Vvar__4__z__2917] :
( t(Vvar__4__z__2917,Vvar__0__A__2905)
& p(happ(happ(Vvar__1__R__2906,Vvar__3__y__2916),Vvar__4__z__2917))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__2905,Vvar__1__R__2906,Vvar__2__x__2907,Vvar__3__y__2916)
& Vvar__3___24Anonymous__2908 = Vvar__4__z__2917 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__70,Vvar__1__R__71,Vvar__2__x__72,Vvar__3___24Anonymous__73] :
( cType___24t(Vvar__0__A__70)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__70,Vvar__1__R__71)
=> ( t(Vvar__2__x__72,Vvar__0__A__70)
=> ( t(Vvar__3___24Anonymous__73,Vvar__0__A__70)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__70,Vvar__1__R__71,Vvar__2__x__72,Vvar__3___24Anonymous__73)
=> ( ? [Vvar__3__y__78] :
( t(Vvar__3__y__78,Vvar__0__A__70)
& p(happ(happ(Vvar__1__R__71,Vvar__2__x__72),Vvar__3__y__78))
& Vvar__3___24Anonymous__73 = Vvar__3__y__78 )
| ? [Vvar__3__y__83] :
( t(Vvar__3__y__83,Vvar__0__A__70)
& ? [Vvar__4__z__84] :
( t(Vvar__4__z__84,Vvar__0__A__70)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__70,Vvar__1__R__71,Vvar__2__x__72,Vvar__3__y__83)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__70,Vvar__1__R__71,Vvar__3__y__83,Vvar__4__z__84)
& Vvar__3___24Anonymous__73 = Vvar__4__z__84 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__2774,Vvar__1__R__2775,Vvar__2__x__2776,Vvar__3___24Anonymous__2777] :
( cType___24t(Vvar__0__A__2774)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2774,Vvar__1__R__2775)
=> ( t(Vvar__2__x__2776,Vvar__0__A__2774)
=> ( t(Vvar__3___24Anonymous__2777,Vvar__0__A__2774)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__2774,Vvar__1__R__2775,Vvar__2__x__2776,Vvar__3___24Anonymous__2777)
=> ( ? [Vvar__3__y__2782] :
( t(Vvar__3__y__2782,Vvar__0__A__2774)
& p(happ(happ(Vvar__1__R__2775,Vvar__2__x__2776),Vvar__3__y__2782))
& Vvar__3___24Anonymous__2777 = Vvar__3__y__2782 )
| ? [Vvar__3__y__2787] :
( t(Vvar__3__y__2787,Vvar__0__A__2774)
& ? [Vvar__4__z__2788] :
( t(Vvar__4__z__2788,Vvar__0__A__2774)
& p(happ(happ(Vvar__1__R__2775,Vvar__2__x__2776),Vvar__3__y__2787))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__2774,Vvar__1__R__2775,Vvar__3__y__2787,Vvar__4__z__2788)
& Vvar__3___24Anonymous__2777 = Vvar__4__z__2788 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__87,Vvar__1__R__88,Vvar__2__x__89,Vvar__3___24Anonymous__90] :
( cType___24t(Vvar__0__A__87)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__87,Vvar__1__R__88)
=> ( t(Vvar__2__x__89,Vvar__0__A__87)
=> ( t(Vvar__3___24Anonymous__90,Vvar__0__A__87)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__87,Vvar__1__R__88,Vvar__2__x__89,Vvar__3___24Anonymous__90)
=> ( ? [Vvar__3__y__95] :
( t(Vvar__3__y__95,Vvar__0__A__87)
& p(happ(happ(Vvar__1__R__88,Vvar__2__x__89),Vvar__3__y__95))
& Vvar__3___24Anonymous__90 = Vvar__3__y__95 )
| ? [Vvar__3__y__100] :
( t(Vvar__3__y__100,Vvar__0__A__87)
& ? [Vvar__4__z__101] :
( t(Vvar__4__z__101,Vvar__0__A__87)
& p(happ(happ(Vvar__1__R__88,Vvar__3__y__100),Vvar__4__z__101))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__87,Vvar__1__R__88,Vvar__2__x__89,Vvar__3__y__100)
& Vvar__3___24Anonymous__90 = Vvar__4__z__101 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__379,Vvar__1___24Anonymous__380,Vvar__2___24Anonymous__381] :
( cType___24t(Vvar__0__A__379)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__1___24Anonymous__380)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__2___24Anonymous__381)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__379,Vvar__1___24Anonymous__380,Vvar__2___24Anonymous__381)
=> ( ( Vvar__2___24Anonymous__381 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__379)
& Vvar__1___24Anonymous__380 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__379) )
| ? [Vvar__1__x__385] :
( t(Vvar__1__x__385,Vvar__0__A__379)
& ? [Vvar__2__l__386] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__2__l__386)
& ? [Vvar__3__l_27__387] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__3__l_27__387)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__379,Vvar__2__l__386,Vvar__3__l_27__387)
& Vvar__2___24Anonymous__381 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__379,Vvar__1__x__385,Vvar__3__l_27__387)
& Vvar__1___24Anonymous__380 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__379,Vvar__1__x__385,Vvar__2__l__386) ) ) )
| ? [Vvar__1__x__390] :
( t(Vvar__1__x__390,Vvar__0__A__379)
& ? [Vvar__2__y__391] :
( t(Vvar__2__y__391,Vvar__0__A__379)
& ? [Vvar__3__l__392] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__3__l__392)
& Vvar__2___24Anonymous__381 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__379,Vvar__1__x__390,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__379,Vvar__2__y__391,Vvar__3__l__392))
& Vvar__1___24Anonymous__380 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__379,Vvar__2__y__391,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__379,Vvar__1__x__390,Vvar__3__l__392)) ) ) )
| ? [Vvar__1__l__394] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__1__l__394)
& ? [Vvar__2__l_27__395] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__2__l_27__395)
& ? [Vvar__3__l_27_27__396] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__379,Vvar__3__l_27_27__396)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__379,Vvar__1__l__394,Vvar__2__l_27__395)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__379,Vvar__2__l_27__395,Vvar__3__l_27_27__396)
& Vvar__2___24Anonymous__381 = Vvar__3__l_27_27__396
& Vvar__1___24Anonymous__380 = Vvar__1__l__394 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015] :
( cType___24t(Vvar__0__R__5984)
=> ( t(Vvar__1__rO__5985,Vvar__0__R__5984)
=> ( t(Vvar__2__rI__5986,Vvar__0__R__5984)
=> ( c_24__type__6416___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__3__rplus__5987)
=> ( c_24__type__6517___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__4__rtimes__5992)
=> ( c_24__type__6618___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__5__rminus__5997)
=> ( c_24__type__6708___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__6__ropp__6002)
=> ( c_24__type__6809___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__7__req__6005)
=> ( c_24__type__6910___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__8__rle__6010)
=> ( c_24__type__7011___24t(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015,Vvar__9__rlt__6015)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005,Vvar__8__rle__6010,Vvar__9__rlt__6015)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__5984,Vvar__7__req__6005)
& ! [Vvar__var__var__var__var__11__x1__6059__6065__6170__6176__6182] :
( t(Vvar__var__var__var__var__11__x1__6059__6065__6170__6176__6182,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__12__x2__6060__6066__6171__6177__6183] :
( t(Vvar__var__var__var__var__12__x2__6060__6066__6171__6177__6183,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__11__x1__6059__6065__6170__6176__6182),Vvar__var__var__var__var__12__x2__6060__6066__6171__6177__6183))
=> ! [Vvar__var__var__var__var__14__y1__6061__6067__6172__6178__6184] :
( t(Vvar__var__var__var__var__14__y1__6061__6067__6172__6178__6184,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__15__y2__6062__6068__6173__6179__6185] :
( t(Vvar__var__var__var__var__15__y2__6062__6068__6173__6179__6185,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__14__y1__6061__6067__6172__6178__6184),Vvar__var__var__var__var__15__y2__6062__6068__6173__6179__6185))
=> p(happ(happ(Vvar__7__req__6005,happ(happ(Vvar__3__rplus__5987,Vvar__var__var__var__var__11__x1__6059__6065__6170__6176__6182),Vvar__var__var__var__var__14__y1__6061__6067__6172__6178__6184)),happ(happ(Vvar__3__rplus__5987,Vvar__var__var__var__var__12__x2__6060__6066__6171__6177__6183),Vvar__var__var__var__var__15__y2__6062__6068__6173__6179__6185))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__6072__6078__6188__6194__6200] :
( t(Vvar__var__var__var__var__12__x1__6072__6078__6188__6194__6200,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__13__x2__6073__6079__6189__6195__6201] :
( t(Vvar__var__var__var__var__13__x2__6073__6079__6189__6195__6201,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__12__x1__6072__6078__6188__6194__6200),Vvar__var__var__var__var__13__x2__6073__6079__6189__6195__6201))
=> ! [Vvar__var__var__var__var__15__y1__6074__6080__6190__6196__6202] :
( t(Vvar__var__var__var__var__15__y1__6074__6080__6190__6196__6202,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__16__y2__6075__6081__6191__6197__6203] :
( t(Vvar__var__var__var__var__16__y2__6075__6081__6191__6197__6203,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__15__y1__6074__6080__6190__6196__6202),Vvar__var__var__var__var__16__y2__6075__6081__6191__6197__6203))
=> p(happ(happ(Vvar__7__req__6005,happ(happ(Vvar__4__rtimes__5992,Vvar__var__var__var__var__12__x1__6072__6078__6188__6194__6200),Vvar__var__var__var__var__15__y1__6074__6080__6190__6196__6202)),happ(happ(Vvar__4__rtimes__5992,Vvar__var__var__var__var__13__x2__6073__6079__6189__6195__6201),Vvar__var__var__var__var__16__y2__6075__6081__6191__6197__6203))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__6085__6088__6206__6209__6212] :
( t(Vvar__var__var__var__var__13__x1__6085__6088__6206__6209__6212,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__14__x2__6086__6089__6207__6210__6213] :
( t(Vvar__var__var__var__var__14__x2__6086__6089__6207__6210__6213,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__13__x1__6085__6088__6206__6209__6212),Vvar__var__var__var__var__14__x2__6086__6089__6207__6210__6213))
=> p(happ(happ(Vvar__7__req__6005,happ(Vvar__6__ropp__6002,Vvar__var__var__var__var__13__x1__6085__6088__6206__6209__6212)),happ(Vvar__6__ropp__6002,Vvar__var__var__var__var__14__x2__6086__6089__6207__6210__6213))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__6092__6098__6215__6221__6227] :
( t(Vvar__var__var__var__var__14__x1__6092__6098__6215__6221__6227,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__15__x2__6093__6099__6216__6222__6228] :
( t(Vvar__var__var__var__var__15__x2__6093__6099__6216__6222__6228,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__14__x1__6092__6098__6215__6221__6227),Vvar__var__var__var__var__15__x2__6093__6099__6216__6222__6228))
=> ! [Vvar__var__var__var__var__17__y1__6094__6100__6217__6223__6229] :
( t(Vvar__var__var__var__var__17__y1__6094__6100__6217__6223__6229,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__18__y2__6095__6101__6218__6224__6230] :
( t(Vvar__var__var__var__var__18__y2__6095__6101__6218__6224__6230,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__17__y1__6094__6100__6217__6223__6229),Vvar__var__var__var__var__18__y2__6095__6101__6218__6224__6230))
=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__var__14__x1__6092__6098__6215__6221__6227),Vvar__var__var__var__var__17__y1__6094__6100__6217__6223__6229))
<=> p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__var__15__x2__6093__6099__6216__6222__6228),Vvar__var__var__var__var__18__y2__6095__6101__6218__6224__6230)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__6105__6111__6233__6239__6245] :
( t(Vvar__var__var__var__var__15__x1__6105__6111__6233__6239__6245,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__16__x2__6106__6112__6234__6240__6246] :
( t(Vvar__var__var__var__var__16__x2__6106__6112__6234__6240__6246,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__15__x1__6105__6111__6233__6239__6245),Vvar__var__var__var__var__16__x2__6106__6112__6234__6240__6246))
=> ! [Vvar__var__var__var__var__18__y1__6107__6113__6235__6241__6247] :
( t(Vvar__var__var__var__var__18__y1__6107__6113__6235__6241__6247,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__19__y2__6108__6114__6236__6242__6248] :
( t(Vvar__var__var__var__var__19__y2__6108__6114__6236__6242__6248,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__18__y1__6107__6113__6235__6241__6247),Vvar__var__var__var__var__19__y2__6108__6114__6236__6242__6248))
=> ( p(happ(happ(Vvar__9__rlt__6015,Vvar__var__var__var__var__15__x1__6105__6111__6233__6239__6245),Vvar__var__var__var__var__18__y1__6107__6113__6235__6241__6247))
<=> p(happ(happ(Vvar__9__rlt__6015,Vvar__var__var__var__var__16__x2__6106__6112__6234__6240__6246),Vvar__var__var__var__var__19__y2__6108__6114__6236__6242__6248)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__5984,Vvar__1__rO__5985,Vvar__2__rI__5986,Vvar__3__rplus__5987,Vvar__4__rtimes__5992,Vvar__5__rminus__5997,Vvar__6__ropp__6002,Vvar__7__req__6005)
& ! [Vvar__var__var__var__17__n__6119__6120__6251__6252] :
( t(Vvar__var__var__var__17__n__6119__6120__6251__6252,Vvar__0__R__5984)
=> p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__17__n__6119__6120__6251__6252),Vvar__var__var__var__17__n__6119__6120__6251__6252)) )
& ! [Vvar__var__var__var__var__18__n__6122__6126__6253__6257__6261] :
( t(Vvar__var__var__var__var__18__n__6122__6126__6253__6257__6261,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__19__m__6123__6127__6254__6258__6262] :
( t(Vvar__var__var__var__var__19__m__6123__6127__6254__6258__6262,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__var__18__n__6122__6126__6253__6257__6261),Vvar__var__var__var__var__19__m__6123__6127__6254__6258__6262))
=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__var__19__m__6123__6127__6254__6258__6262),Vvar__var__var__var__var__18__n__6122__6126__6253__6257__6261))
=> p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__18__n__6122__6126__6253__6257__6261),Vvar__var__var__var__var__19__m__6123__6127__6254__6258__6262)) ) ) ) )
& ! [Vvar__var__var__var__19__n__6131__6136__6265__6270] :
( t(Vvar__var__var__var__19__n__6131__6136__6265__6270,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__20__m__6132__6137__6266__6271] :
( t(Vvar__var__var__var__20__m__6132__6137__6266__6271,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__21__p__6133__6138__6267__6272] :
( t(Vvar__var__var__var__21__p__6133__6138__6267__6272,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__19__n__6131__6136__6265__6270),Vvar__var__var__var__20__m__6132__6137__6266__6271))
=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__20__m__6132__6137__6266__6271),Vvar__var__var__var__21__p__6133__6138__6267__6272))
=> p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__19__n__6131__6136__6265__6270),Vvar__var__var__var__21__p__6133__6138__6267__6272)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__6142__6144__6275__6277__6279__6281] :
( t(Vvar__var__var__var__var__var__20__n__6142__6144__6275__6277__6279__6281,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__var__21__m__6143__6145__6276__6278__6280__6282] :
( t(Vvar__var__var__var__var__var__21__m__6143__6145__6276__6278__6280__6282,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__9__rlt__6015,Vvar__var__var__var__var__var__20__n__6142__6144__6275__6277__6279__6281),Vvar__var__var__var__var__var__21__m__6143__6145__6276__6278__6280__6282))
<=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__var__var__20__n__6142__6144__6275__6277__6279__6281),Vvar__var__var__var__var__var__21__m__6143__6145__6276__6278__6280__6282))
& ~ p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__var__20__n__6142__6144__6275__6277__6279__6281),Vvar__var__var__var__var__var__21__m__6143__6145__6276__6278__6280__6282)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__6147__6149__6283__6285__6287] :
( t(Vvar__var__var__var__var__21__n__6147__6149__6283__6285__6287,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__22__m__6148__6150__6284__6286__6288] :
( t(Vvar__var__var__var__var__22__m__6148__6150__6284__6286__6288,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__9__rlt__6015,Vvar__var__var__var__var__21__n__6147__6149__6283__6285__6287),Vvar__var__var__var__var__22__m__6148__6150__6284__6286__6288))
| p(happ(happ(Vvar__7__req__6005,Vvar__var__var__var__var__21__n__6147__6149__6283__6285__6287),Vvar__var__var__var__var__22__m__6148__6150__6284__6286__6288))
| p(happ(happ(Vvar__9__rlt__6015,Vvar__var__var__var__var__22__m__6148__6150__6284__6286__6288),Vvar__var__var__var__var__21__n__6147__6149__6283__6285__6287)) ) ) )
& ! [Vvar__var__var__var__var__22__n__6152__6156__6289__6293__6297] :
( t(Vvar__var__var__var__var__22__n__6152__6156__6289__6293__6297,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__23__m__6153__6157__6290__6294__6298] :
( t(Vvar__var__var__var__var__23__m__6153__6157__6290__6294__6298,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__24__p__6154__6158__6291__6295__6299] :
( t(Vvar__var__var__var__var__24__p__6154__6158__6291__6295__6299,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__8__rle__6010,Vvar__var__var__var__var__22__n__6152__6156__6289__6293__6297),Vvar__var__var__var__var__23__m__6153__6157__6290__6294__6298))
=> p(happ(happ(Vvar__8__rle__6010,happ(happ(Vvar__3__rplus__5987,Vvar__var__var__var__var__24__p__6154__6158__6291__6295__6299),Vvar__var__var__var__var__22__n__6152__6156__6289__6293__6297)),happ(happ(Vvar__3__rplus__5987,Vvar__var__var__var__var__24__p__6154__6158__6291__6295__6299),Vvar__var__var__var__var__23__m__6153__6157__6290__6294__6298))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__6161__6165__6301__6305__6309__6313] :
( t(Vvar__var__var__var__var__var__23__n__6161__6165__6301__6305__6309__6313,Vvar__0__R__5984)
=> ! [Vvar__var__var__var__var__var__24__m__6162__6166__6302__6306__6310__6314] :
( t(Vvar__var__var__var__var__var__24__m__6162__6166__6302__6306__6310__6314,Vvar__0__R__5984)
=> ( p(happ(happ(Vvar__9__rlt__6015,Vvar__1__rO__5985),Vvar__var__var__var__var__var__23__n__6161__6165__6301__6305__6309__6313))
=> ( p(happ(happ(Vvar__9__rlt__6015,Vvar__1__rO__5985),Vvar__var__var__var__var__var__24__m__6162__6166__6302__6306__6310__6314))
=> p(happ(happ(Vvar__9__rlt__6015,Vvar__1__rO__5985),happ(happ(Vvar__4__rtimes__5992,Vvar__var__var__var__var__var__23__n__6161__6165__6301__6305__6309__6313),Vvar__var__var__var__var__var__24__m__6162__6166__6302__6306__6310__6314))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__6005,Vvar__1__rO__5985),Vvar__2__rI__5986))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX7685] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX7685)
=> ( VX7685 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX7685 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX7685 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX7685 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX7685 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX7685 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
! [Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867] :
( cType___24t(Vvar__0__R__22798)
=> ( t(Vvar__1__rO__22799,Vvar__0__R__22798)
=> ( t(Vvar__2__rI__22800,Vvar__0__R__22798)
=> ( c_24__type__23331___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__3__rplus__22801)
=> ( c_24__type__23677___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__4__rtimes__22806)
=> ( c_24__type__24023___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__5__rminus__22811)
=> ( c_24__type__24346___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__6__ropp__22816)
=> ( c_24__type__24692___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__7__req__22819)
=> ( c_24__type__25038___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__8__rle__22824)
=> ( cType___24t(Vvar__9__C__22829)
=> ( t(Vvar__10__cO__22830,Vvar__9__C__22829)
=> ( t(Vvar__11__cI__22831,Vvar__9__C__22829)
=> ( c_24__type__25384___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__12__cplus__22832)
=> ( c_24__type__25730___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__13__ctimes__22837)
=> ( c_24__type__26076___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__14__cminus__22842)
=> ( c_24__type__26399___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__15__copp__22847)
=> ( c_24__type__26745___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__16__ceqb__22850)
=> ( c_24__type__27091___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__17__cleb__22855)
=> ( c_24__type__27414___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__18__phi__22860)
=> ( cType___24t(Vvar__19__E__22863)
=> ( c_24__type__27737___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__20__pow__phi__22864)
=> ( c_24__type__28083___24t(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867,Vvar__21__rpow__22867)
=> ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__8__rle__22824,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__17__cleb__22855,Vvar__18__phi__22860,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__22798,Vvar__1__rO__22799,Vvar__2__rI__22800,Vvar__3__rplus__22801,Vvar__4__rtimes__22806,Vvar__5__rminus__22811,Vvar__6__ropp__22816,Vvar__7__req__22819,Vvar__9__C__22829,Vvar__10__cO__22830,Vvar__11__cI__22831,Vvar__12__cplus__22832,Vvar__13__ctimes__22837,Vvar__14__cminus__22842,Vvar__15__copp__22847,Vvar__16__ceqb__22850,Vvar__18__phi__22860)
& cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__22798,Vvar__2__rI__22800,Vvar__4__rtimes__22806,Vvar__7__req__22819,Vvar__19__E__22863,Vvar__20__pow__phi__22864,Vvar__21__rpow__22867)
& ! [Vvar__var__var__var__var__var__24__x__22950__22953__22963__22966__22969__22972] :
( t(Vvar__var__var__var__var__var__24__x__22950__22953__22963__22966__22969__22972,Vvar__9__C__22829)
=> ! [Vvar__var__var__var__var__var__25__y__22951__22954__22964__22967__22970__22973] :
( t(Vvar__var__var__var__var__var__25__y__22951__22954__22964__22967__22970__22973,Vvar__9__C__22829)
=> ( happ(happ(Vvar__16__ceqb__22850,Vvar__var__var__var__var__var__24__x__22950__22953__22963__22966__22969__22972),Vvar__var__var__var__var__var__25__y__22951__22954__22964__22967__22970__22973) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(Vvar__7__req__22819,happ(Vvar__18__phi__22860,Vvar__var__var__var__var__var__24__x__22950__22953__22963__22966__22969__22972)),happ(Vvar__18__phi__22860,Vvar__var__var__var__var__var__25__y__22951__22954__22964__22967__22970__22973))) ) ) )
& ! [Vvar__var__var__var__var__var__25__x__22957__22960__22975__22978__22981__22984] :
( t(Vvar__var__var__var__var__var__25__x__22957__22960__22975__22978__22981__22984,Vvar__9__C__22829)
=> ! [Vvar__var__var__var__var__var__26__y__22958__22961__22976__22979__22982__22985] :
( t(Vvar__var__var__var__var__var__26__y__22958__22961__22976__22979__22982__22985,Vvar__9__C__22829)
=> ( happ(happ(Vvar__17__cleb__22855,Vvar__var__var__var__var__var__25__x__22957__22960__22975__22978__22981__22984),Vvar__var__var__var__var__var__26__y__22958__22961__22976__22979__22982__22985) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__8__rle__22824,happ(Vvar__18__phi__22860,Vvar__var__var__var__var__var__25__x__22957__22960__22975__22978__22981__22984)),happ(Vvar__18__phi__22860,Vvar__var__var__var__var__var__26__y__22958__22961__22976__22979__22982__22985))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,VX11100] :
( cType___24t(Vvar__0__TA__11096)
=> ( cType___24t(Vvar__1__TX__11097)
=> ( cType___24t(Vvar__2__AA__11098)
=> ( cType___24t(Vvar__3__AF__11099)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,VX11100)
=> ( VX11100 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099)
| VX11100 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099)
| ? [Vvar__4___24Anonymous__11113] :
( t(Vvar__4___24Anonymous__11113,Vvar__1__TX__11097)
& VX11100 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11113) )
| ? [Vvar__4___24Anonymous__11118] :
( t(Vvar__4___24Anonymous__11118,Vvar__0__TA__11096)
& ? [Vvar__5___24Anonymous__11119] :
( t(Vvar__5___24Anonymous__11119,Vvar__2__AA__11098)
& VX11100 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11118,Vvar__5___24Anonymous__11119) ) )
| ? [Vvar__4___24Anonymous__11124] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11124)
& ? [Vvar__5___24Anonymous__11125] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__5___24Anonymous__11125)
& VX11100 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11124,Vvar__5___24Anonymous__11125) ) )
| ? [Vvar__4___24Anonymous__11130] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11130)
& ? [Vvar__5___24Anonymous__11131] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__5___24Anonymous__11131)
& VX11100 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11130,Vvar__5___24Anonymous__11131) ) )
| ? [Vvar__4___24Anonymous__11136] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11136)
& VX11100 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11136) )
| ? [Vvar__4___24Anonymous__11141] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11141)
& ? [Vvar__5___24Anonymous__11142] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__11099,Vvar__5___24Anonymous__11142)
& ? [Vvar__6___24Anonymous__11143] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__6___24Anonymous__11143)
& VX11100 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__11096,Vvar__1__TX__11097,Vvar__2__AA__11098,Vvar__3__AF__11099,Vvar__4___24Anonymous__11141,Vvar__5___24Anonymous__11142,Vvar__6___24Anonymous__11143) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__11752] :
( cProp___24t(Vvar__0___24Anonymous__11752)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__11752)
=> ( ? [Vvar__0__S__11754] :
( cType___24t(Vvar__0__S__11754)
& ? [Vvar__1__x__11755] :
( t(Vvar__1__x__11755,Vvar__0__S__11754)
& ? [Vvar__2__y__11756] :
( t(Vvar__2__y__11756,Vvar__0__S__11754)
& Vvar__0___24Anonymous__11752 = c_24__prop__11776___24a4(Vvar__0___24Anonymous__11752,Vvar__0__S__11754,Vvar__1__x__11755,Vvar__2__y__11756) ) ) )
| ? [Vvar__0__x__11757] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__11757)
& ? [Vvar__1__y__11758] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__11758)
& Vvar__0___24Anonymous__11752 = c_24__prop__11777___24a3(Vvar__0___24Anonymous__11752,Vvar__0__x__11757,Vvar__1__y__11758) ) )
| ? [Vvar__0__x__11759] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__11759)
& ? [Vvar__1__s__11760] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__11760)
& Vvar__0___24Anonymous__11752 = c_24__prop__11778___24a3(Vvar__0___24Anonymous__11752,Vvar__0__x__11759,Vvar__1__s__11760) ) )
| Vvar__0___24Anonymous__11752 = c_24True
| Vvar__0___24Anonymous__11752 = c_24False
| ? [Vvar__0__P__11761] :
( cProp___24t(Vvar__0__P__11761)
& ? [Vvar__1__Q__11762] :
( cProp___24t(Vvar__1__Q__11762)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__11761)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__11762)
& Vvar__0___24Anonymous__11752 = c_24__prop__11779___24a3(Vvar__0___24Anonymous__11752,Vvar__0__P__11761,Vvar__1__Q__11762) ) )
| ? [Vvar__0__P__11765] :
( cProp___24t(Vvar__0__P__11765)
& ? [Vvar__1__Q__11766] :
( cProp___24t(Vvar__1__Q__11766)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__11765)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__11766)
& Vvar__0___24Anonymous__11752 = c_24__prop__11780___24a3(Vvar__0___24Anonymous__11752,Vvar__0__P__11765,Vvar__1__Q__11766) ) )
| ? [Vvar__0__P__11769] :
( cProp___24t(Vvar__0__P__11769)
& ? [Vvar__1__Q__11770] :
( cProp___24t(Vvar__1__Q__11770)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__11769)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__11770)
& Vvar__0___24Anonymous__11752 = c_24__prop__11781___24a3(Vvar__0___24Anonymous__11752,Vvar__0__P__11769,Vvar__1__Q__11770) ) )
| ? [Vvar__0__P__11774] :
( cProp___24t(Vvar__0__P__11774)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__11774)
& Vvar__0___24Anonymous__11752 = c_24__prop__11782___24a2(Vvar__0___24Anonymous__11752,Vvar__0__P__11774) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [Vvar__0__C__18855,VX18856] :
( cType___24t(Vvar__0__C__18855)
=> ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,VX18856)
=> ( VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__18855)
| VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__18855)
| ? [Vvar__1___24Anonymous__18860] :
( t(Vvar__1___24Anonymous__18860,Vvar__0__C__18855)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__18855,Vvar__1___24Anonymous__18860) )
| ? [Vvar__1___24Anonymous__18862] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__18862)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__18855,Vvar__1___24Anonymous__18862) )
| ? [Vvar__1___24Anonymous__18864] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18864)
& ? [Vvar__2___24Anonymous__18865] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__2___24Anonymous__18865)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__18855,Vvar__1___24Anonymous__18864,Vvar__2___24Anonymous__18865) ) )
| ? [Vvar__1___24Anonymous__18867] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18867)
& ? [Vvar__2___24Anonymous__18868] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__2___24Anonymous__18868)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__18855,Vvar__1___24Anonymous__18867,Vvar__2___24Anonymous__18868) ) )
| ? [Vvar__1___24Anonymous__18870] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18870)
& ? [Vvar__2___24Anonymous__18871] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__2___24Anonymous__18871)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__18855,Vvar__1___24Anonymous__18870,Vvar__2___24Anonymous__18871) ) )
| ? [Vvar__1___24Anonymous__18873] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18873)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__18855,Vvar__1___24Anonymous__18873) )
| ? [Vvar__1___24Anonymous__18875] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18875)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__18855,Vvar__1___24Anonymous__18875) )
| ? [Vvar__1___24Anonymous__18877] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18877)
& ? [Vvar__2___24Anonymous__18878] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__2___24Anonymous__18878)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__18855,Vvar__1___24Anonymous__18877,Vvar__2___24Anonymous__18878) ) )
| ? [Vvar__1___24Anonymous__18880] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__18855,Vvar__1___24Anonymous__18880)
& ? [Vvar__2___24Anonymous__18881] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__18881)
& VX18856 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__18855,Vvar__1___24Anonymous__18880,Vvar__2___24Anonymous__18881) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027] :
( cType___24t(Vvar__0__R__3998)
=> ( t(Vvar__1__rO__3999,Vvar__0__R__3998)
=> ( t(Vvar__2__rI__4000,Vvar__0__R__3998)
=> ( c_24__type__4192___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__3__radd__4001)
=> ( c_24__type__4285___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__4__rmul__4006)
=> ( c_24__type__4378___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__5__rsub__4011)
=> ( c_24__type__4460___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__6__ropp__4016)
=> ( c_24__type__4553___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__7__rdiv__4019)
=> ( c_24__type__4635___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__8__rinv__4024)
=> ( c_24__type__4728___24t(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027,Vvar__9__req__4027)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__7__rdiv__4019,Vvar__8__rinv__4024,Vvar__9__req__4027)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__3998,Vvar__1__rO__3999,Vvar__2__rI__4000,Vvar__3__radd__4001,Vvar__4__rmul__4006,Vvar__5__rsub__4011,Vvar__6__ropp__4016,Vvar__9__req__4027)
& ~ p(happ(happ(Vvar__9__req__4027,Vvar__2__rI__4000),Vvar__1__rO__3999))
& ! [Vvar__var__var__var__var__var__var__12__p__4070__4072__4079__4081__4083__4085__4087] :
( t(Vvar__var__var__var__var__var__var__12__p__4070__4072__4079__4081__4083__4085__4087,Vvar__0__R__3998)
=> ! [Vvar__var__var__var__var__var__var__13__q__4071__4073__4080__4082__4084__4086__4088] :
( t(Vvar__var__var__var__var__var__var__13__q__4071__4073__4080__4082__4084__4086__4088,Vvar__0__R__3998)
=> p(happ(happ(Vvar__9__req__4027,happ(happ(Vvar__7__rdiv__4019,Vvar__var__var__var__var__var__var__12__p__4070__4072__4079__4081__4083__4085__4087),Vvar__var__var__var__var__var__var__13__q__4071__4073__4080__4082__4084__4086__4088)),happ(happ(Vvar__4__rmul__4006,Vvar__var__var__var__var__var__var__12__p__4070__4072__4079__4081__4083__4085__4087),happ(Vvar__8__rinv__4024,Vvar__var__var__var__var__var__var__13__q__4071__4073__4080__4082__4084__4086__4088)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__4075__4077__4089__4091__4093__4095__4097__4099] :
( t(Vvar__var__var__var__var__var__var__var__13__p__4075__4077__4089__4091__4093__4095__4097__4099,Vvar__0__R__3998)
=> ( ~ p(happ(happ(Vvar__9__req__4027,Vvar__var__var__var__var__var__var__var__13__p__4075__4077__4089__4091__4093__4095__4097__4099),Vvar__1__rO__3999))
=> p(happ(happ(Vvar__9__req__4027,happ(happ(Vvar__4__rmul__4006,happ(Vvar__8__rinv__4024,Vvar__var__var__var__var__var__var__var__13__p__4075__4077__4089__4091__4093__4095__4097__4099)),Vvar__var__var__var__var__var__var__var__13__p__4075__4077__4089__4091__4093__4095__4097__4099)),Vvar__2__rI__4000)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763] :
( cType___24t(Vvar__0__R__4734)
=> ( t(Vvar__1__rO__4735,Vvar__0__R__4734)
=> ( t(Vvar__2__rI__4736,Vvar__0__R__4734)
=> ( c_24__type__4928___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__3__radd__4737)
=> ( c_24__type__5021___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__4__rmul__4742)
=> ( c_24__type__5114___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__5__rsub__4747)
=> ( c_24__type__5196___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__6__ropp__4752)
=> ( c_24__type__5289___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__7__rdiv__4755)
=> ( c_24__type__5371___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__8__rinv__4760)
=> ( c_24__type__5464___24t(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763,Vvar__9__req__4763)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__7__rdiv__4755,Vvar__8__rinv__4760,Vvar__9__req__4763)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__4734,Vvar__1__rO__4735,Vvar__2__rI__4736,Vvar__3__radd__4737,Vvar__4__rmul__4742,Vvar__5__rsub__4747,Vvar__6__ropp__4752,Vvar__9__req__4763)
& ~ p(happ(happ(Vvar__9__req__4763,Vvar__2__rI__4736),Vvar__1__rO__4735))
& ! [Vvar__var__var__var__var__var__var__12__p__4806__4808__4815__4817__4819__4821__4823] :
( t(Vvar__var__var__var__var__var__var__12__p__4806__4808__4815__4817__4819__4821__4823,Vvar__0__R__4734)
=> ! [Vvar__var__var__var__var__var__var__13__q__4807__4809__4816__4818__4820__4822__4824] :
( t(Vvar__var__var__var__var__var__var__13__q__4807__4809__4816__4818__4820__4822__4824,Vvar__0__R__4734)
=> p(happ(happ(Vvar__9__req__4763,happ(happ(Vvar__7__rdiv__4755,Vvar__var__var__var__var__var__var__12__p__4806__4808__4815__4817__4819__4821__4823),Vvar__var__var__var__var__var__var__13__q__4807__4809__4816__4818__4820__4822__4824)),happ(happ(Vvar__4__rmul__4742,Vvar__var__var__var__var__var__var__12__p__4806__4808__4815__4817__4819__4821__4823),happ(Vvar__8__rinv__4760,Vvar__var__var__var__var__var__var__13__q__4807__4809__4816__4818__4820__4822__4824)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__4811__4813__4825__4827__4829__4831__4833__4835] :
( t(Vvar__var__var__var__var__var__var__var__13__p__4811__4813__4825__4827__4829__4831__4833__4835,Vvar__0__R__4734)
=> ( ~ p(happ(happ(Vvar__9__req__4763,Vvar__var__var__var__var__var__var__var__13__p__4811__4813__4825__4827__4829__4831__4833__4835),Vvar__1__rO__4735))
=> p(happ(happ(Vvar__9__req__4763,happ(happ(Vvar__4__rmul__4742,happ(Vvar__8__rinv__4760,Vvar__var__var__var__var__var__var__var__13__p__4811__4813__4825__4827__4829__4831__4833__4835)),Vvar__var__var__var__var__var__var__var__13__p__4811__4813__4825__4827__4829__4831__4833__4835)),Vvar__2__rI__4736)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
! [Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491] :
( cType___24t(Vvar__0__R__5470)
=> ( t(Vvar__1__rO__5471,Vvar__0__R__5470)
=> ( t(Vvar__2__rI__5472,Vvar__0__R__5470)
=> ( c_24__type__5618___24t(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491,Vvar__3__radd__5473)
=> ( c_24__type__5681___24t(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491,Vvar__4__rmul__5478)
=> ( c_24__type__5744___24t(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491,Vvar__5__rdiv__5483)
=> ( c_24__type__5798___24t(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491,Vvar__6__rinv__5488)
=> ( c_24__type__5861___24t(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491,Vvar__7__req__5491)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__5__rdiv__5483,Vvar__6__rinv__5488,Vvar__7__req__5491)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__5470,Vvar__1__rO__5471,Vvar__2__rI__5472,Vvar__3__radd__5473,Vvar__4__rmul__5478,Vvar__7__req__5491)
& ~ p(happ(happ(Vvar__7__req__5491,Vvar__2__rI__5472),Vvar__1__rO__5471))
& ! [Vvar__var__var__var__var__var__var__10__p__5526__5528__5535__5537__5539__5541__5543] :
( t(Vvar__var__var__var__var__var__var__10__p__5526__5528__5535__5537__5539__5541__5543,Vvar__0__R__5470)
=> ! [Vvar__var__var__var__var__var__var__11__q__5527__5529__5536__5538__5540__5542__5544] :
( t(Vvar__var__var__var__var__var__var__11__q__5527__5529__5536__5538__5540__5542__5544,Vvar__0__R__5470)
=> p(happ(happ(Vvar__7__req__5491,happ(happ(Vvar__5__rdiv__5483,Vvar__var__var__var__var__var__var__10__p__5526__5528__5535__5537__5539__5541__5543),Vvar__var__var__var__var__var__var__11__q__5527__5529__5536__5538__5540__5542__5544)),happ(happ(Vvar__4__rmul__5478,Vvar__var__var__var__var__var__var__10__p__5526__5528__5535__5537__5539__5541__5543),happ(Vvar__6__rinv__5488,Vvar__var__var__var__var__var__var__11__q__5527__5529__5536__5538__5540__5542__5544)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__11__p__5531__5533__5545__5547__5549__5551__5553__5555] :
( t(Vvar__var__var__var__var__var__var__var__11__p__5531__5533__5545__5547__5549__5551__5553__5555,Vvar__0__R__5470)
=> ( ~ p(happ(happ(Vvar__7__req__5491,Vvar__var__var__var__var__var__var__var__11__p__5531__5533__5545__5547__5549__5551__5553__5555),Vvar__1__rO__5471))
=> p(happ(happ(Vvar__7__req__5491,happ(happ(Vvar__4__rmul__5478,happ(Vvar__6__rinv__5488,Vvar__var__var__var__var__var__var__var__11__p__5531__5533__5545__5547__5549__5551__5553__5555)),Vvar__var__var__var__var__var__var__var__11__p__5531__5533__5545__5547__5549__5551__5553__5555)),Vvar__2__rI__5472)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [VX12443] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX12443)
=> ( VX12443 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
| ? [Vvar__0___24Anonymous__12444] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12444)
& ? [Vvar__1___24Anonymous__12445] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__12445)
& VX12443 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__12444,Vvar__1___24Anonymous__12445) ) )
| ? [Vvar__0___24Anonymous__12446] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__12446)
& ? [Vvar__1___24Anonymous__12447] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__12447)
& VX12443 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__12446,Vvar__1___24Anonymous__12447) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
! [Vvar__0__C__12464,VX12465] :
( cType___24t(Vvar__0__C__12464)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,VX12465)
=> ( VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__12464)
| VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__12464)
| ? [Vvar__1___24Anonymous__12469] :
( t(Vvar__1___24Anonymous__12469,Vvar__0__C__12464)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__12464,Vvar__1___24Anonymous__12469) )
| ? [Vvar__1___24Anonymous__12471] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12471)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__12464,Vvar__1___24Anonymous__12471) )
| ? [Vvar__1___24Anonymous__12473] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__1___24Anonymous__12473)
& ? [Vvar__2___24Anonymous__12474] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__2___24Anonymous__12474)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__12464,Vvar__1___24Anonymous__12473,Vvar__2___24Anonymous__12474) ) )
| ? [Vvar__1___24Anonymous__12476] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__1___24Anonymous__12476)
& ? [Vvar__2___24Anonymous__12477] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__2___24Anonymous__12477)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__12464,Vvar__1___24Anonymous__12476,Vvar__2___24Anonymous__12477) ) )
| ? [Vvar__1___24Anonymous__12479] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__1___24Anonymous__12479)
& ? [Vvar__2___24Anonymous__12480] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__2___24Anonymous__12480)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__12464,Vvar__1___24Anonymous__12479,Vvar__2___24Anonymous__12480) ) )
| ? [Vvar__1___24Anonymous__12482] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__1___24Anonymous__12482)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__12464,Vvar__1___24Anonymous__12482) )
| ? [Vvar__1___24Anonymous__12484] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__12464,Vvar__1___24Anonymous__12484)
& ? [Vvar__2___24Anonymous__12485] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__12485)
& VX12465 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__12464,Vvar__1___24Anonymous__12484,Vvar__2___24Anonymous__12485) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [Vvar__0__C__12396,VX12397] :
( cType___24t(Vvar__0__C__12396)
=> ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12396,VX12397)
=> ( ? [Vvar__1___24Anonymous__12399] :
( t(Vvar__1___24Anonymous__12399,Vvar__0__C__12396)
& VX12397 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__12396,Vvar__1___24Anonymous__12399) )
| ? [Vvar__1___24Anonymous__12401] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__12401)
& ? [Vvar__2___24Anonymous__12402] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12396,Vvar__2___24Anonymous__12402)
& VX12397 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__12396,Vvar__1___24Anonymous__12401,Vvar__2___24Anonymous__12402) ) )
| ? [Vvar__1___24Anonymous__12404] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12396,Vvar__1___24Anonymous__12404)
& ? [Vvar__2___24Anonymous__12405] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__12405)
& ? [Vvar__3___24Anonymous__12406] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__12396,Vvar__3___24Anonymous__12406)
& VX12397 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__12396,Vvar__1___24Anonymous__12404,Vvar__2___24Anonymous__12405,Vvar__3___24Anonymous__12406) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006] :
( cType___24t(Vvar__0__R__7985)
=> ( t(Vvar__1__rO__7986,Vvar__0__R__7985)
=> ( t(Vvar__2__rI__7987,Vvar__0__R__7985)
=> ( c_24__type__8234___24t(Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006,Vvar__3__radd__7988)
=> ( c_24__type__8297___24t(Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006,Vvar__4__rmul__7993)
=> ( c_24__type__8360___24t(Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006,Vvar__5__rsub__7998)
=> ( c_24__type__8414___24t(Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006,Vvar__6__ropp__8003)
=> ( c_24__type__8477___24t(Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006,Vvar__7__req__8006)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__7985,Vvar__1__rO__7986,Vvar__2__rI__7987,Vvar__3__radd__7988,Vvar__4__rmul__7993,Vvar__5__rsub__7998,Vvar__6__ropp__8003,Vvar__7__req__8006)
=> ( ! [Vvar__var__var__var__var__var__8__x__8039__8040__8093__8094__8095__8096] :
( t(Vvar__var__var__var__var__var__8__x__8039__8040__8093__8094__8095__8096,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__3__radd__7988,Vvar__1__rO__7986),Vvar__var__var__var__var__var__8__x__8039__8040__8093__8094__8095__8096)),Vvar__var__var__var__var__var__8__x__8039__8040__8093__8094__8095__8096)) )
& ! [Vvar__var__var__var__var__9__x__8042__8044__8097__8099__8101] :
( t(Vvar__var__var__var__var__9__x__8042__8044__8097__8099__8101,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__10__y__8043__8045__8098__8100__8102] :
( t(Vvar__var__var__var__var__10__y__8043__8045__8098__8100__8102,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__9__x__8042__8044__8097__8099__8101),Vvar__var__var__var__var__10__y__8043__8045__8098__8100__8102)),happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__10__y__8043__8045__8098__8100__8102),Vvar__var__var__var__var__9__x__8042__8044__8097__8099__8101))) ) )
& ! [Vvar__var__var__var__var__10__x__8047__8050__8103__8106__8109] :
( t(Vvar__var__var__var__var__10__x__8047__8050__8103__8106__8109,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__11__y__8048__8051__8104__8107__8110] :
( t(Vvar__var__var__var__var__11__y__8048__8051__8104__8107__8110,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__12__z__8049__8052__8105__8108__8111] :
( t(Vvar__var__var__var__var__12__z__8049__8052__8105__8108__8111,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__10__x__8047__8050__8103__8106__8109),happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__11__y__8048__8051__8104__8107__8110),Vvar__var__var__var__var__12__z__8049__8052__8105__8108__8111))),happ(happ(Vvar__3__radd__7988,happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__10__x__8047__8050__8103__8106__8109),Vvar__var__var__var__var__11__y__8048__8051__8104__8107__8110)),Vvar__var__var__var__var__12__z__8049__8052__8105__8108__8111))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__8054__8055__8112__8113__8114__8115] :
( t(Vvar__var__var__var__var__var__11__x__8054__8055__8112__8113__8114__8115,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__4__rmul__7993,Vvar__2__rI__7987),Vvar__var__var__var__var__var__11__x__8054__8055__8112__8113__8114__8115)),Vvar__var__var__var__var__var__11__x__8054__8055__8112__8113__8114__8115)) )
& ! [Vvar__var__var__var__var__var__12__x__8057__8058__8116__8117__8118__8119] :
( t(Vvar__var__var__var__var__var__12__x__8057__8058__8116__8117__8118__8119,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__4__rmul__7993,Vvar__1__rO__7986),Vvar__var__var__var__var__var__12__x__8057__8058__8116__8117__8118__8119)),Vvar__1__rO__7986)) )
& ! [Vvar__var__var__var__var__13__x__8060__8062__8120__8122__8124] :
( t(Vvar__var__var__var__var__13__x__8060__8062__8120__8122__8124,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__14__y__8061__8063__8121__8123__8125] :
( t(Vvar__var__var__var__var__14__y__8061__8063__8121__8123__8125,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__13__x__8060__8062__8120__8122__8124),Vvar__var__var__var__var__14__y__8061__8063__8121__8123__8125)),happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__14__y__8061__8063__8121__8123__8125),Vvar__var__var__var__var__13__x__8060__8062__8120__8122__8124))) ) )
& ! [Vvar__var__var__var__var__14__x__8065__8068__8126__8129__8132] :
( t(Vvar__var__var__var__var__14__x__8065__8068__8126__8129__8132,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__15__y__8066__8069__8127__8130__8133] :
( t(Vvar__var__var__var__var__15__y__8066__8069__8127__8130__8133,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__16__z__8067__8070__8128__8131__8134] :
( t(Vvar__var__var__var__var__16__z__8067__8070__8128__8131__8134,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__14__x__8065__8068__8126__8129__8132),happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__15__y__8066__8069__8127__8130__8133),Vvar__var__var__var__var__16__z__8067__8070__8128__8131__8134))),happ(happ(Vvar__4__rmul__7993,happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__14__x__8065__8068__8126__8129__8132),Vvar__var__var__var__var__15__y__8066__8069__8127__8130__8133)),Vvar__var__var__var__var__16__z__8067__8070__8128__8131__8134))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__8072__8075__8135__8138__8141__8144] :
( t(Vvar__var__var__var__var__var__15__x__8072__8075__8135__8138__8141__8144,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__var__16__y__8073__8076__8136__8139__8142__8145] :
( t(Vvar__var__var__var__var__var__16__y__8073__8076__8136__8139__8142__8145,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__var__17__z__8074__8077__8137__8140__8143__8146] :
( t(Vvar__var__var__var__var__var__17__z__8074__8077__8137__8140__8143__8146,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__4__rmul__7993,happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__var__15__x__8072__8075__8135__8138__8141__8144),Vvar__var__var__var__var__var__16__y__8073__8076__8136__8139__8142__8145)),Vvar__var__var__var__var__var__17__z__8074__8077__8137__8140__8143__8146)),happ(happ(Vvar__3__radd__7988,happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__var__15__x__8072__8075__8135__8138__8141__8144),Vvar__var__var__var__var__var__17__z__8074__8077__8137__8140__8143__8146)),happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__var__16__y__8073__8076__8136__8139__8142__8145),Vvar__var__var__var__var__var__17__z__8074__8077__8137__8140__8143__8146)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__8079__8081__8147__8149__8151__8153] :
( t(Vvar__var__var__var__var__var__16__x__8079__8081__8147__8149__8151__8153,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__var__17__y__8080__8082__8148__8150__8152__8154] :
( t(Vvar__var__var__var__var__var__17__y__8080__8082__8148__8150__8152__8154,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(Vvar__6__ropp__8003,happ(happ(Vvar__4__rmul__7993,Vvar__var__var__var__var__var__16__x__8079__8081__8147__8149__8151__8153),Vvar__var__var__var__var__var__17__y__8080__8082__8148__8150__8152__8154))),happ(happ(Vvar__4__rmul__7993,happ(Vvar__6__ropp__8003,Vvar__var__var__var__var__var__16__x__8079__8081__8147__8149__8151__8153)),Vvar__var__var__var__var__var__17__y__8080__8082__8148__8150__8152__8154))) ) )
& ! [Vvar__var__var__var__var__var__17__x__8084__8086__8155__8157__8159__8161] :
( t(Vvar__var__var__var__var__var__17__x__8084__8086__8155__8157__8159__8161,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__var__18__y__8085__8087__8156__8158__8160__8162] :
( t(Vvar__var__var__var__var__var__18__y__8085__8087__8156__8158__8160__8162,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(Vvar__6__ropp__8003,happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__var__17__x__8084__8086__8155__8157__8159__8161),Vvar__var__var__var__var__var__18__y__8085__8087__8156__8158__8160__8162))),happ(happ(Vvar__3__radd__7988,happ(Vvar__6__ropp__8003,Vvar__var__var__var__var__var__17__x__8084__8086__8155__8157__8159__8161)),happ(Vvar__6__ropp__8003,Vvar__var__var__var__var__var__18__y__8085__8087__8156__8158__8160__8162)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__8089__8091__8163__8165__8167__8169__8171] :
( t(Vvar__var__var__var__var__var__var__18__x__8089__8091__8163__8165__8167__8169__8171,Vvar__0__R__7985)
=> ! [Vvar__var__var__var__var__var__var__19__y__8090__8092__8164__8166__8168__8170__8172] :
( t(Vvar__var__var__var__var__var__var__19__y__8090__8092__8164__8166__8168__8170__8172,Vvar__0__R__7985)
=> p(happ(happ(Vvar__7__req__8006,happ(happ(Vvar__5__rsub__7998,Vvar__var__var__var__var__var__var__18__x__8089__8091__8163__8165__8167__8169__8171),Vvar__var__var__var__var__var__var__19__y__8090__8092__8164__8166__8168__8170__8172)),happ(happ(Vvar__3__radd__7988,Vvar__var__var__var__var__var__var__18__x__8089__8091__8163__8165__8167__8169__8171),happ(Vvar__6__ropp__8003,Vvar__var__var__var__var__var__var__19__y__8090__8092__8164__8166__8168__8170__8172)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
! [Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019] :
( cType___24t(Vvar__0__R__31999)
=> ( c_24__type__32139___24t(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019,Vvar__1__req__32000)
=> ( cType___24t(Vvar__2__C__32005)
=> ( c_24__type__32189___24t(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019,Vvar__3__cadd__32006)
=> ( c_24__type__32239___24t(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019,Vvar__4__cmul__32011)
=> ( c_24__type__32281___24t(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019,Vvar__5__phi__32016)
=> ( c_24__type__32331___24t(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019,Vvar__6__cdiv__32019)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__a__32051__32056__32061__32066__32071__32076__32081__32086] :
( t(Vvar__var__var__var__var__var__var__var__7__a__32051__32056__32061__32066__32071__32076__32081__32086,Vvar__2__C__32005)
=> ! [Vvar__var__var__var__var__var__var__var__8__b__32052__32057__32062__32067__32072__32077__32082__32087] :
( t(Vvar__var__var__var__var__var__var__var__8__b__32052__32057__32062__32067__32072__32077__32082__32087,Vvar__2__C__32005)
=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2432394___24a9(Vvar__0__R__31999,Vvar__1__req__32000,Vvar__2__C__32005,Vvar__3__cadd__32006,Vvar__4__cmul__32011,Vvar__5__phi__32016,Vvar__6__cdiv__32019,Vvar__var__var__var__var__var__var__var__7__a__32051__32056__32061__32066__32071__32076__32081__32086,Vvar__var__var__var__var__var__var__var__8__b__32052__32057__32062__32067__32072__32077__32082__32087) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
! [Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__3__req__32421,Vvar__4__Cpow__32426,Vvar__5__Cp__phi__32427,Vvar__6__rpow__32430] :
( cType___24t(Vvar__0__R__32414)
=> ( t(Vvar__1__rI__32415,Vvar__0__R__32414)
=> ( c_24__type__32516___24t(Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__3__req__32421,Vvar__4__Cpow__32426,Vvar__5__Cp__phi__32427,Vvar__6__rpow__32430,Vvar__2__rmul__32416)
=> ( c_24__type__32560___24t(Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__3__req__32421,Vvar__4__Cpow__32426,Vvar__5__Cp__phi__32427,Vvar__6__rpow__32430,Vvar__3__req__32421)
=> ( cType___24t(Vvar__4__Cpow__32426)
=> ( c_24__type__32596___24t(Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__3__req__32421,Vvar__4__Cpow__32426,Vvar__5__Cp__phi__32427,Vvar__6__rpow__32430,Vvar__5__Cp__phi__32427)
=> ( c_24__type__32640___24t(Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__3__req__32421,Vvar__4__Cpow__32426,Vvar__5__Cp__phi__32427,Vvar__6__rpow__32430,Vvar__6__rpow__32430)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__3__req__32421,Vvar__4__Cpow__32426,Vvar__5__Cp__phi__32427,Vvar__6__rpow__32430)
=> ( ! [Vvar__var__var__var__var__var__var__var__7__r__32458__32460__32462__32464__32466__32468__32470__32472] :
( t(Vvar__var__var__var__var__var__var__var__7__r__32458__32460__32462__32464__32466__32468__32470__32472,Vvar__0__R__32414)
=> ! [Vvar__var__var__var__var__var__var__var__8__n__32459__32461__32463__32465__32467__32469__32471__32473] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__32459__32461__32463__32465__32467__32469__32471__32473)
=> p(happ(happ(Vvar__3__req__32421,happ(happ(Vvar__6__rpow__32430,Vvar__var__var__var__var__var__var__var__7__r__32458__32460__32462__32464__32466__32468__32470__32472),happ(Vvar__5__Cp__phi__32427,Vvar__var__var__var__var__var__var__var__8__n__32459__32461__32463__32465__32467__32469__32471__32473))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__32414,Vvar__1__rI__32415,Vvar__2__rmul__32416,Vvar__var__var__var__var__var__var__var__7__r__32458__32460__32462__32464__32466__32468__32470__32472,Vvar__var__var__var__var__var__var__var__8__n__32459__32461__32463__32465__32467__32469__32471__32473))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224] :
( cType___24t(Vvar__0__R__9210)
=> ( c_24__type__9315___24t(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224,Vvar__1__radd__9211)
=> ( c_24__type__9345___24t(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224,Vvar__2__rmul__9216)
=> ( c_24__type__9369___24t(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224,Vvar__3__ropp__9221)
=> ( c_24__type__9399___24t(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224,Vvar__4__req__9224)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9429___24a5(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9210,c_24__type__9453___24a5(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224),Vvar__4__req__9224,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9210,Vvar__0__R__9210,Vvar__4__req__9224,Vvar__4__req__9224)),Vvar__1__radd__9211)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9486___24a5(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9210,c_24__type__9510___24a5(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224),Vvar__4__req__9224,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9210,Vvar__0__R__9210,Vvar__4__req__9224,Vvar__4__req__9224)),Vvar__2__rmul__9216)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__9537___24a5(Vvar__0__R__9210,Vvar__1__radd__9211,Vvar__2__rmul__9216,Vvar__3__ropp__9221,Vvar__4__req__9224),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__9210,Vvar__0__R__9210,Vvar__4__req__9224,Vvar__4__req__9224),Vvar__3__ropp__9221)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
! [Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456] :
( cType___24t(Vvar__0__R__29404)
=> ( t(Vvar__1__rO__29405,Vvar__0__R__29404)
=> ( t(Vvar__2__rI__29406,Vvar__0__R__29404)
=> ( c_24__type__29800___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__3__radd__29407)
=> ( c_24__type__30013___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__4__rmul__29412)
=> ( c_24__type__30226___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__5__rsub__29417)
=> ( c_24__type__30421___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__6__ropp__29422)
=> ( c_24__type__30634___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__7__req__29425)
=> ( cType___24t(Vvar__8__C__29430)
=> ( t(Vvar__9__cO__29431,Vvar__8__C__29430)
=> ( t(Vvar__10__cI__29432,Vvar__8__C__29430)
=> ( c_24__type__30847___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__11__cadd__29433)
=> ( c_24__type__31060___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__12__cmul__29438)
=> ( c_24__type__31273___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__13__csub__29443)
=> ( c_24__type__31468___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__14__copp__29448)
=> ( c_24__type__31681___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__15__ceqb__29451)
=> ( c_24__type__31876___24t(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456,Vvar__16__phi__29456)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__29404,Vvar__1__rO__29405,Vvar__2__rI__29406,Vvar__3__radd__29407,Vvar__4__rmul__29412,Vvar__5__rsub__29417,Vvar__6__ropp__29422,Vvar__7__req__29425,Vvar__8__C__29430,Vvar__9__cO__29431,Vvar__10__cI__29432,Vvar__11__cadd__29433,Vvar__12__cmul__29438,Vvar__13__csub__29443,Vvar__14__copp__29448,Vvar__15__ceqb__29451,Vvar__16__phi__29456)
=> ( p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,Vvar__9__cO__29431)),Vvar__1__rO__29405))
& p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,Vvar__10__cI__29432)),Vvar__2__rI__29406))
& ! [Vvar__var__var__var__var__var__var__19__x__29518__29520__29542__29544__29546__29548__29550] :
( t(Vvar__var__var__var__var__var__var__19__x__29518__29520__29542__29544__29546__29548__29550,Vvar__8__C__29430)
=> ! [Vvar__var__var__var__var__var__var__20__y__29519__29521__29543__29545__29547__29549__29551] :
( t(Vvar__var__var__var__var__var__var__20__y__29519__29521__29543__29545__29547__29549__29551,Vvar__8__C__29430)
=> p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,happ(happ(Vvar__11__cadd__29433,Vvar__var__var__var__var__var__var__19__x__29518__29520__29542__29544__29546__29548__29550),Vvar__var__var__var__var__var__var__20__y__29519__29521__29543__29545__29547__29549__29551))),happ(happ(Vvar__3__radd__29407,happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__19__x__29518__29520__29542__29544__29546__29548__29550)),happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__20__y__29519__29521__29543__29545__29547__29549__29551)))) ) )
& ! [Vvar__var__var__var__var__var__var__20__x__29523__29525__29552__29554__29556__29558__29560] :
( t(Vvar__var__var__var__var__var__var__20__x__29523__29525__29552__29554__29556__29558__29560,Vvar__8__C__29430)
=> ! [Vvar__var__var__var__var__var__var__21__y__29524__29526__29553__29555__29557__29559__29561] :
( t(Vvar__var__var__var__var__var__var__21__y__29524__29526__29553__29555__29557__29559__29561,Vvar__8__C__29430)
=> p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,happ(happ(Vvar__13__csub__29443,Vvar__var__var__var__var__var__var__20__x__29523__29525__29552__29554__29556__29558__29560),Vvar__var__var__var__var__var__var__21__y__29524__29526__29553__29555__29557__29559__29561))),happ(happ(Vvar__5__rsub__29417,happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__20__x__29523__29525__29552__29554__29556__29558__29560)),happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__21__y__29524__29526__29553__29555__29557__29559__29561)))) ) )
& ! [Vvar__var__var__var__var__var__var__21__x__29528__29530__29562__29564__29566__29568__29570] :
( t(Vvar__var__var__var__var__var__var__21__x__29528__29530__29562__29564__29566__29568__29570,Vvar__8__C__29430)
=> ! [Vvar__var__var__var__var__var__var__22__y__29529__29531__29563__29565__29567__29569__29571] :
( t(Vvar__var__var__var__var__var__var__22__y__29529__29531__29563__29565__29567__29569__29571,Vvar__8__C__29430)
=> p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,happ(happ(Vvar__12__cmul__29438,Vvar__var__var__var__var__var__var__21__x__29528__29530__29562__29564__29566__29568__29570),Vvar__var__var__var__var__var__var__22__y__29529__29531__29563__29565__29567__29569__29571))),happ(happ(Vvar__4__rmul__29412,happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__21__x__29528__29530__29562__29564__29566__29568__29570)),happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__22__y__29529__29531__29563__29565__29567__29569__29571)))) ) )
& ! [Vvar__var__var__var__var__var__var__22__x__29533__29534__29572__29573__29574__29575__29576] :
( t(Vvar__var__var__var__var__var__var__22__x__29533__29534__29572__29573__29574__29575__29576,Vvar__8__C__29430)
=> p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,happ(Vvar__14__copp__29448,Vvar__var__var__var__var__var__var__22__x__29533__29534__29572__29573__29574__29575__29576))),happ(Vvar__6__ropp__29422,happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__var__22__x__29533__29534__29572__29573__29574__29575__29576)))) )
& ! [Vvar__var__var__var__var__var__23__x__29536__29539__29577__29580__29583__29586] :
( t(Vvar__var__var__var__var__var__23__x__29536__29539__29577__29580__29583__29586,Vvar__8__C__29430)
=> ! [Vvar__var__var__var__var__var__24__y__29537__29540__29578__29581__29584__29587] :
( t(Vvar__var__var__var__var__var__24__y__29537__29540__29578__29581__29584__29587,Vvar__8__C__29430)
=> ( happ(happ(Vvar__15__ceqb__29451,Vvar__var__var__var__var__var__23__x__29536__29539__29577__29580__29583__29586),Vvar__var__var__var__var__var__24__y__29537__29540__29578__29581__29584__29587) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(Vvar__7__req__29425,happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__23__x__29536__29539__29577__29580__29583__29586)),happ(Vvar__16__phi__29456,Vvar__var__var__var__var__var__24__y__29537__29540__29578__29581__29584__29587))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522] :
( cType___24t(Vvar__0__R__8501)
=> ( t(Vvar__1__rO__8502,Vvar__0__R__8501)
=> ( t(Vvar__2__rI__8503,Vvar__0__R__8501)
=> ( c_24__type__8725___24t(Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522,Vvar__3__radd__8504)
=> ( c_24__type__8788___24t(Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522,Vvar__4__rmul__8509)
=> ( c_24__type__8851___24t(Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522,Vvar__5__rsub__8514)
=> ( c_24__type__8905___24t(Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522,Vvar__6__ropp__8519)
=> ( c_24__type__8968___24t(Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522,Vvar__7__req__8522)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__8501,Vvar__1__rO__8502,Vvar__2__rI__8503,Vvar__3__radd__8504,Vvar__4__rmul__8509,Vvar__5__rsub__8514,Vvar__6__ropp__8519,Vvar__7__req__8522)
=> ( ! [Vvar__var__var__var__var__var__8__x__8555__8556__8599__8600__8601__8602] :
( t(Vvar__var__var__var__var__var__8__x__8555__8556__8599__8600__8601__8602,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__3__radd__8504,Vvar__1__rO__8502),Vvar__var__var__var__var__var__8__x__8555__8556__8599__8600__8601__8602)),Vvar__var__var__var__var__var__8__x__8555__8556__8599__8600__8601__8602)) )
& ! [Vvar__var__var__var__var__9__x__8558__8560__8603__8605__8607] :
( t(Vvar__var__var__var__var__9__x__8558__8560__8603__8605__8607,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__10__y__8559__8561__8604__8606__8608] :
( t(Vvar__var__var__var__var__10__y__8559__8561__8604__8606__8608,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__9__x__8558__8560__8603__8605__8607),Vvar__var__var__var__var__10__y__8559__8561__8604__8606__8608)),happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__10__y__8559__8561__8604__8606__8608),Vvar__var__var__var__var__9__x__8558__8560__8603__8605__8607))) ) )
& ! [Vvar__var__var__var__var__10__x__8563__8566__8609__8612__8615] :
( t(Vvar__var__var__var__var__10__x__8563__8566__8609__8612__8615,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__11__y__8564__8567__8610__8613__8616] :
( t(Vvar__var__var__var__var__11__y__8564__8567__8610__8613__8616,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__12__z__8565__8568__8611__8614__8617] :
( t(Vvar__var__var__var__var__12__z__8565__8568__8611__8614__8617,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__10__x__8563__8566__8609__8612__8615),happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__11__y__8564__8567__8610__8613__8616),Vvar__var__var__var__var__12__z__8565__8568__8611__8614__8617))),happ(happ(Vvar__3__radd__8504,happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__10__x__8563__8566__8609__8612__8615),Vvar__var__var__var__var__11__y__8564__8567__8610__8613__8616)),Vvar__var__var__var__var__12__z__8565__8568__8611__8614__8617))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__8570__8571__8618__8619__8620__8621] :
( t(Vvar__var__var__var__var__var__11__x__8570__8571__8618__8619__8620__8621,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__4__rmul__8509,Vvar__2__rI__8503),Vvar__var__var__var__var__var__11__x__8570__8571__8618__8619__8620__8621)),Vvar__var__var__var__var__var__11__x__8570__8571__8618__8619__8620__8621)) )
& ! [Vvar__var__var__var__var__12__x__8573__8575__8622__8624__8626] :
( t(Vvar__var__var__var__var__12__x__8573__8575__8622__8624__8626,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__13__y__8574__8576__8623__8625__8627] :
( t(Vvar__var__var__var__var__13__y__8574__8576__8623__8625__8627,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__12__x__8573__8575__8622__8624__8626),Vvar__var__var__var__var__13__y__8574__8576__8623__8625__8627)),happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__13__y__8574__8576__8623__8625__8627),Vvar__var__var__var__var__12__x__8573__8575__8622__8624__8626))) ) )
& ! [Vvar__var__var__var__var__13__x__8578__8581__8628__8631__8634] :
( t(Vvar__var__var__var__var__13__x__8578__8581__8628__8631__8634,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__14__y__8579__8582__8629__8632__8635] :
( t(Vvar__var__var__var__var__14__y__8579__8582__8629__8632__8635,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__15__z__8580__8583__8630__8633__8636] :
( t(Vvar__var__var__var__var__15__z__8580__8583__8630__8633__8636,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__13__x__8578__8581__8628__8631__8634),happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__14__y__8579__8582__8629__8632__8635),Vvar__var__var__var__var__15__z__8580__8583__8630__8633__8636))),happ(happ(Vvar__4__rmul__8509,happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__13__x__8578__8581__8628__8631__8634),Vvar__var__var__var__var__14__y__8579__8582__8629__8632__8635)),Vvar__var__var__var__var__15__z__8580__8583__8630__8633__8636))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__8585__8588__8637__8640__8643__8646] :
( t(Vvar__var__var__var__var__var__14__x__8585__8588__8637__8640__8643__8646,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__var__15__y__8586__8589__8638__8641__8644__8647] :
( t(Vvar__var__var__var__var__var__15__y__8586__8589__8638__8641__8644__8647,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__var__16__z__8587__8590__8639__8642__8645__8648] :
( t(Vvar__var__var__var__var__var__16__z__8587__8590__8639__8642__8645__8648,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__4__rmul__8509,happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__var__14__x__8585__8588__8637__8640__8643__8646),Vvar__var__var__var__var__var__15__y__8586__8589__8638__8641__8644__8647)),Vvar__var__var__var__var__var__16__z__8587__8590__8639__8642__8645__8648)),happ(happ(Vvar__3__radd__8504,happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__var__14__x__8585__8588__8637__8640__8643__8646),Vvar__var__var__var__var__var__16__z__8587__8590__8639__8642__8645__8648)),happ(happ(Vvar__4__rmul__8509,Vvar__var__var__var__var__var__15__y__8586__8589__8638__8641__8644__8647),Vvar__var__var__var__var__var__16__z__8587__8590__8639__8642__8645__8648)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__8592__8594__8649__8651__8653__8655__8657] :
( t(Vvar__var__var__var__var__var__var__15__x__8592__8594__8649__8651__8653__8655__8657,Vvar__0__R__8501)
=> ! [Vvar__var__var__var__var__var__var__16__y__8593__8595__8650__8652__8654__8656__8658] :
( t(Vvar__var__var__var__var__var__var__16__y__8593__8595__8650__8652__8654__8656__8658,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__5__rsub__8514,Vvar__var__var__var__var__var__var__15__x__8592__8594__8649__8651__8653__8655__8657),Vvar__var__var__var__var__var__var__16__y__8593__8595__8650__8652__8654__8656__8658)),happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__var__var__15__x__8592__8594__8649__8651__8653__8655__8657),happ(Vvar__6__ropp__8519,Vvar__var__var__var__var__var__var__16__y__8593__8595__8650__8652__8654__8656__8658)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__8597__8598__8659__8660__8661__8662__8663] :
( t(Vvar__var__var__var__var__var__var__16__x__8597__8598__8659__8660__8661__8662__8663,Vvar__0__R__8501)
=> p(happ(happ(Vvar__7__req__8522,happ(happ(Vvar__3__radd__8504,Vvar__var__var__var__var__var__var__16__x__8597__8598__8659__8660__8661__8662__8663),happ(Vvar__6__ropp__8519,Vvar__var__var__var__var__var__var__16__x__8597__8598__8659__8660__8661__8662__8663))),Vvar__1__rO__8502)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__7721,Vvar__1__rO__7722,Vvar__2__rI__7723,Vvar__3__radd__7724,Vvar__4__rmul__7729,Vvar__5__req__7734] :
( cType___24t(Vvar__0__R__7721)
=> ( t(Vvar__1__rO__7722,Vvar__0__R__7721)
=> ( t(Vvar__2__rI__7723,Vvar__0__R__7721)
=> ( c_24__type__7889___24t(Vvar__0__R__7721,Vvar__1__rO__7722,Vvar__2__rI__7723,Vvar__3__radd__7724,Vvar__4__rmul__7729,Vvar__5__req__7734,Vvar__3__radd__7724)
=> ( c_24__type__7928___24t(Vvar__0__R__7721,Vvar__1__rO__7722,Vvar__2__rI__7723,Vvar__3__radd__7724,Vvar__4__rmul__7729,Vvar__5__req__7734,Vvar__4__rmul__7729)
=> ( c_24__type__7967___24t(Vvar__0__R__7721,Vvar__1__rO__7722,Vvar__2__rI__7723,Vvar__3__radd__7724,Vvar__4__rmul__7729,Vvar__5__req__7734,Vvar__5__req__7734)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__7721,Vvar__1__rO__7722,Vvar__2__rI__7723,Vvar__3__radd__7724,Vvar__4__rmul__7729,Vvar__5__req__7734)
=> ( ! [Vvar__var__var__var__var__var__6__n__7759__7760__7798__7799__7800__7801] :
( t(Vvar__var__var__var__var__var__6__n__7759__7760__7798__7799__7800__7801,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__3__radd__7724,Vvar__1__rO__7722),Vvar__var__var__var__var__var__6__n__7759__7760__7798__7799__7800__7801)),Vvar__var__var__var__var__var__6__n__7759__7760__7798__7799__7800__7801)) )
& ! [Vvar__var__var__var__var__7__n__7762__7764__7802__7804__7806] :
( t(Vvar__var__var__var__var__7__n__7762__7764__7802__7804__7806,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__8__m__7763__7765__7803__7805__7807] :
( t(Vvar__var__var__var__var__8__m__7763__7765__7803__7805__7807,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__3__radd__7724,Vvar__var__var__var__var__7__n__7762__7764__7802__7804__7806),Vvar__var__var__var__var__8__m__7763__7765__7803__7805__7807)),happ(happ(Vvar__3__radd__7724,Vvar__var__var__var__var__8__m__7763__7765__7803__7805__7807),Vvar__var__var__var__var__7__n__7762__7764__7802__7804__7806))) ) )
& ! [Vvar__var__var__var__var__8__n__7767__7770__7808__7811__7814] :
( t(Vvar__var__var__var__var__8__n__7767__7770__7808__7811__7814,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__9__m__7768__7771__7809__7812__7815] :
( t(Vvar__var__var__var__var__9__m__7768__7771__7809__7812__7815,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__10__p__7769__7772__7810__7813__7816] :
( t(Vvar__var__var__var__var__10__p__7769__7772__7810__7813__7816,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__3__radd__7724,Vvar__var__var__var__var__8__n__7767__7770__7808__7811__7814),happ(happ(Vvar__3__radd__7724,Vvar__var__var__var__var__9__m__7768__7771__7809__7812__7815),Vvar__var__var__var__var__10__p__7769__7772__7810__7813__7816))),happ(happ(Vvar__3__radd__7724,happ(happ(Vvar__3__radd__7724,Vvar__var__var__var__var__8__n__7767__7770__7808__7811__7814),Vvar__var__var__var__var__9__m__7768__7771__7809__7812__7815)),Vvar__var__var__var__var__10__p__7769__7772__7810__7813__7816))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__7774__7775__7817__7818__7819__7820] :
( t(Vvar__var__var__var__var__var__9__n__7774__7775__7817__7818__7819__7820,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__4__rmul__7729,Vvar__2__rI__7723),Vvar__var__var__var__var__var__9__n__7774__7775__7817__7818__7819__7820)),Vvar__var__var__var__var__var__9__n__7774__7775__7817__7818__7819__7820)) )
& ! [Vvar__var__var__var__var__var__10__n__7777__7778__7821__7822__7823__7824] :
( t(Vvar__var__var__var__var__var__10__n__7777__7778__7821__7822__7823__7824,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__4__rmul__7729,Vvar__1__rO__7722),Vvar__var__var__var__var__var__10__n__7777__7778__7821__7822__7823__7824)),Vvar__1__rO__7722)) )
& ! [Vvar__var__var__var__var__11__n__7780__7782__7825__7827__7829] :
( t(Vvar__var__var__var__var__11__n__7780__7782__7825__7827__7829,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__12__m__7781__7783__7826__7828__7830] :
( t(Vvar__var__var__var__var__12__m__7781__7783__7826__7828__7830,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__11__n__7780__7782__7825__7827__7829),Vvar__var__var__var__var__12__m__7781__7783__7826__7828__7830)),happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__12__m__7781__7783__7826__7828__7830),Vvar__var__var__var__var__11__n__7780__7782__7825__7827__7829))) ) )
& ! [Vvar__var__var__var__var__12__n__7785__7788__7831__7834__7837] :
( t(Vvar__var__var__var__var__12__n__7785__7788__7831__7834__7837,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__13__m__7786__7789__7832__7835__7838] :
( t(Vvar__var__var__var__var__13__m__7786__7789__7832__7835__7838,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__14__p__7787__7790__7833__7836__7839] :
( t(Vvar__var__var__var__var__14__p__7787__7790__7833__7836__7839,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__12__n__7785__7788__7831__7834__7837),happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__13__m__7786__7789__7832__7835__7838),Vvar__var__var__var__var__14__p__7787__7790__7833__7836__7839))),happ(happ(Vvar__4__rmul__7729,happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__12__n__7785__7788__7831__7834__7837),Vvar__var__var__var__var__13__m__7786__7789__7832__7835__7838)),Vvar__var__var__var__var__14__p__7787__7790__7833__7836__7839))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__7792__7795__7840__7843__7846__7849] :
( t(Vvar__var__var__var__var__var__13__n__7792__7795__7840__7843__7846__7849,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__var__14__m__7793__7796__7841__7844__7847__7850] :
( t(Vvar__var__var__var__var__var__14__m__7793__7796__7841__7844__7847__7850,Vvar__0__R__7721)
=> ! [Vvar__var__var__var__var__var__15__p__7794__7797__7842__7845__7848__7851] :
( t(Vvar__var__var__var__var__var__15__p__7794__7797__7842__7845__7848__7851,Vvar__0__R__7721)
=> p(happ(happ(Vvar__5__req__7734,happ(happ(Vvar__4__rmul__7729,happ(happ(Vvar__3__radd__7724,Vvar__var__var__var__var__var__13__n__7792__7795__7840__7843__7846__7849),Vvar__var__var__var__var__var__14__m__7793__7796__7841__7844__7847__7850)),Vvar__var__var__var__var__var__15__p__7794__7797__7842__7845__7848__7851)),happ(happ(Vvar__3__radd__7724,happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__var__13__n__7792__7795__7840__7843__7846__7849),Vvar__var__var__var__var__var__15__p__7794__7797__7842__7845__7848__7851)),happ(happ(Vvar__4__rmul__7729,Vvar__var__var__var__var__var__14__m__7793__7796__7841__7844__7847__7850),Vvar__var__var__var__var__var__15__p__7794__7797__7842__7845__7848__7851)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_hahn.HahnMinPath.min_cycle_mod',axiom,
! [Vvar__0__X__742,Vvar__1__r__743,Vvar__2__f__744,Vvar__3__n__747] :
( cType___24t(Vvar__0__X__742)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__X__742,Vvar__1__r__743)
=> ( c_24__type__788___24t(Vvar__0__X__742,Vvar__1__r__743,Vvar__2__f__744,Vvar__3__n__747,Vvar__2__f__744)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__747)
=> ( chahn_2eHahnMinPath_2emin__cycle__mod___24a4(Vvar__0__X__742,Vvar__1__r__743,Vvar__2__f__744,Vvar__3__n__747)
=> ( Vvar__3__n__747 != cCoq_2eInit_2eDatatypes_2eO
& ! [Vvar__var__var__var__5__x__757__758__769__770] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__5__x__757__758__769__770)
=> happ(Vvar__2__f__744,Vvar__var__var__var__5__x__757__758__769__770) = happ(Vvar__2__f__744,cCoq_2eInit_2eNat_2emodulo___24a2(Vvar__var__var__var__5__x__757__758__769__770,Vvar__3__n__747)) )
& ! [Vvar__var__var__var__6__i__760__761__771__772] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__6__i__760__761__771__772)
=> p(happ(happ(Vvar__1__r__743,happ(Vvar__2__f__744,Vvar__var__var__var__6__i__760__761__771__772)),happ(Vvar__2__f__744,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__var__var__var__6__i__760__761__771__772)))) )
& ! [Vvar__var__var__var__var__7__i__763__766__773__776__779] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__var__7__i__763__766__773__776__779)
=> ! [Vvar__var__var__var__var__8__j__764__767__774__777__780] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__var__8__j__764__767__774__777__780)
=> ( p(happ(happ(Vvar__1__r__743,happ(Vvar__2__f__744,Vvar__var__var__var__var__7__i__763__766__773__776__779)),happ(Vvar__2__f__744,Vvar__var__var__var__var__8__j__764__767__774__777__780)))
=> cCoq_2eInit_2eNat_2emodulo___24a2(Vvar__var__var__var__var__8__j__764__767__774__777__780,Vvar__3__n__747) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__var__var__var__var__7__i__763__766__773__776__779),Vvar__3__n__747) ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_lam_10',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__10___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24False) ) ).
fof('$_lam_12917',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__12917___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ).
fof('$_lam_1373',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1373___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_14667',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__14667___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_14675',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__14675___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_14683',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__14683___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_14691',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__14691___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_15958',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__15958___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_15963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__15963___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_1779',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1779___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_1791',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__1791___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_18',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__18___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_1800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__1800___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ).
fof('$_lam_1892',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__1892___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_1895',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1895___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_1901',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1901___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_1915',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1915___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(Vv__CANONICAL__0),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__1) ) ).
fof('$_lam_1942',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__1942___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__1565___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,c_24__lam__1892___24a1(Vv__CANONICAL__0),c_24__lam__1948___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3))),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,c_24__lam__1892___24a1(Vv__CANONICAL__0),c_24__lam__1956___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ).
fof('$_lam_1948',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1948___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_1956',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1956___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_1963',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__1963___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_1966',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__1966___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).
fof('$_lam_1972',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1972___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2) ).
fof('$_lam_1978',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1978___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ).
fof('$_lam_1987',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1987___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(Vv__CANONICAL__0,happ(Vv__CANONICAL__1,Vv__CANONICAL__3),happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_1996',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__1996___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_202',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__202___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__4),Vv__CANONICAL__5))
& p(happ(Vv__CANONICAL__3,Vv__CANONICAL__5)) ) ) ).
fof('$_lam_2029',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2029___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ).
fof('$_lam_2040',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2040___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
& p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_22',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__22___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_22265',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__22265___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_22276',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__22276___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_2429',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2429___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> chahn_2eHahnMinPath_2emin__cycle__mod___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__2) ) ).
fof('$_lam_2436',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__2436___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO))) ) ).
fof('$_lam_2460',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2460___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4))
| p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_2633',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2633___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
| p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_2757',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__2757___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_lam_28448',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__28448___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_28456',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__28456___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ~ p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__1)) ) ).
fof('$_lam_28464',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__28464___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_28472',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__28472___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__1),Vv__CANONICAL__3)) ) ).
fof('$_lam_28633',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__28633___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__28561___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__11)) ).
fof('$_lam_3076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__3076___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(happ(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ).
fof('$_lam_312',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__312___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_3160',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__3160___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_3244',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__3244___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__329___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(cCoq_2eLists_2eList_2eIn___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__1)) ) ).
fof('$_lam_35041',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__35041___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3))
& ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ( p(happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ).
fof('$_lam_674',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__674___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO) = Vv__CANONICAL__1 ) ).
fof('$_lam_681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__681___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3)) = Vv__CANONICAL__1 ) ).
fof('$_lam_699',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__699___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__5,Vv__CANONICAL__3))
=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__5)),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5)))) ) ) ) ).
fof('$_lam_741',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__741___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__5,Vv__CANONICAL__3))
=> ! [Vv__CANONICAL__7] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__7)
=> ( ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__5,Vv__CANONICAL__7))
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__7,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__3))) )
=> ( p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__5)),happ(Vv__CANONICAL__2,Vv__CANONICAL__7)))
=> Vv__CANONICAL__7 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5) ) ) ) ) ) ) ).
fof('$_lam_974',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__974___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_prop_11776',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__S__11754,Vvar__1__x__11755,Vvar__2__y__11756] :
( p(c_24__prop__11776___24a4(Vvar__0___24Anonymous__11752,Vvar__0__S__11754,Vvar__1__x__11755,Vvar__2__y__11756))
<=> Vvar__1__x__11755 = Vvar__2__y__11756 ) ).
fof('$_prop_11777',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__x__11757,Vvar__1__y__11758] :
( p(c_24__prop__11777___24a3(Vvar__0___24Anonymous__11752,Vvar__0__x__11757,Vvar__1__y__11758))
<=> Vvar__0__x__11757 = Vvar__1__y__11758 ) ).
fof('$_prop_11778',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__x__11759,Vvar__1__s__11760] :
( p(c_24__prop__11778___24a3(Vvar__0___24Anonymous__11752,Vvar__0__x__11759,Vvar__1__s__11760))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__11759,Vvar__1__s__11760) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_11779',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__P__11761,Vvar__1__Q__11762] :
( p(c_24__prop__11779___24a3(Vvar__0___24Anonymous__11752,Vvar__0__P__11761,Vvar__1__Q__11762))
<=> ( p(Vvar__0__P__11761)
& p(Vvar__1__Q__11762) ) ) ).
fof('$_prop_11780',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__P__11765,Vvar__1__Q__11766] :
( p(c_24__prop__11780___24a3(Vvar__0___24Anonymous__11752,Vvar__0__P__11765,Vvar__1__Q__11766))
<=> ( p(Vvar__0__P__11765)
| p(Vvar__1__Q__11766) ) ) ).
fof('$_prop_11781',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__P__11769,Vvar__1__Q__11770] :
( p(c_24__prop__11781___24a3(Vvar__0___24Anonymous__11752,Vvar__0__P__11769,Vvar__1__Q__11770))
<=> ( p(Vvar__0__P__11769)
=> p(Vvar__1__Q__11770) ) ) ).
fof('$_prop_11782',axiom,
! [Vvar__0___24Anonymous__11752,Vvar__0__P__11774] :
( p(c_24__prop__11782___24a2(Vvar__0___24Anonymous__11752,Vvar__0__P__11774))
<=> ~ p(Vvar__0__P__11774) ) ).
fof('$_prop_1233',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1233___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_1234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1234___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_1238',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( p(c_24__prop__1238___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
<=> ~ p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ).
fof('$_prop_13059',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__13059___24a1(Vv__CANONICAL__0))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_prop_14164',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__14164___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_14165',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__14120] :
( p(c_24__prop__14165___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__14120))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__14120)) ) ).
fof('$_prop_14166',axiom,
! [V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__14120] :
( p(c_24__prop__14166___24a4(V0__A,V1__eqA,V4__x,Vvar__1___24Anonymous__14120))
<=> ~ p(happ(happ(V1__eqA,V4__x),Vvar__1___24Anonymous__14120)) ) ).
fof('$_prop_14199',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( p(c_24__prop__14199___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3))
<=> ~ p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ).
fof('$_prop_14917',axiom,
! [V7__A] :
( p(c_24__prop__14917___24a1(V7__A))
<=> ~ ~ p(V7__A) ) ).
fof('$_prop_14918',axiom,
! [V7__A] :
( p(c_24__prop__14918___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_15977',axiom,
! [Vv__CANONICAL__2] :
( p(c_24__prop__15977___24a1(Vv__CANONICAL__2))
<=> ~ p(Vv__CANONICAL__2) ) ).
fof('$_prop_16049',axiom,
! [V6__A] :
( p(c_24__prop__16049___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_16117',axiom,
! [V6__A] :
( p(c_24__prop__16117___24a1(V6__A))
<=> ~ p(V6__A) ) ).
fof('$_prop_16215',axiom,
! [V7__A] :
( p(c_24__prop__16215___24a1(V7__A))
<=> ~ p(V7__A) ) ).
fof('$_prop_22272',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( p(c_24__prop__22272___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2))
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_prop_2299',axiom,
! [V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283] :
( p(c_24__prop__2299___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283)) ) ).
fof('$_prop_2311',axiom,
! [V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283] :
( p(c_24__prop__2311___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__2282,Vvar__2___24Anonymous__2283)) ) ).
fof('$_prop_33563',axiom,
! [V0__C] :
( p(c_24__prop__33563___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_33567',axiom,
! [Vv__CANONICAL__0] :
( p(c_24__prop__33567___24a1(Vv__CANONICAL__0))
<=> ~ p(Vv__CANONICAL__0) ) ).
fof('$_prop_33568',axiom,
! [V0__C] :
( p(c_24__prop__33568___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_33570',axiom,
! [V0__C] :
( p(c_24__prop__33570___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_33572',axiom,
! [V0__C] :
( p(c_24__prop__33572___24a1(V0__C))
<=> ~ p(V0__C) ) ).
fof('$_prop_35139',axiom,
! [V1__S,V2__x,V3__y] :
( p(c_24__prop__35139___24a3(V1__S,V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_35143',axiom,
! [V2__x,V3__y] :
( p(c_24__prop__35143___24a2(V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_35148',axiom,
! [V6__P,V7__Q] :
( p(c_24__prop__35148___24a2(V6__P,V7__Q))
<=> ( p(V6__P)
& p(V7__Q) ) ) ).
fof('$_prop_35155',axiom,
! [V7__P,V8__Q] :
( p(c_24__prop__35155___24a2(V7__P,V8__Q))
<=> ( p(V7__P)
| p(V8__Q) ) ) ).
fof('$_prop_35162',axiom,
! [V8__P,V9__Q] :
( p(c_24__prop__35162___24a2(V8__P,V9__Q))
<=> ( p(V8__P)
=> p(V9__Q) ) ) ).
fof('$_prop_35170',axiom,
! [V9__P] :
( p(c_24__prop__35170___24a1(V9__P))
<=> ~ p(V9__P) ) ).
fof('$_prop_35174',axiom,
! [V1__S,V2__x,V3__y] :
( p(c_24__prop__35174___24a3(V1__S,V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_35178',axiom,
! [V2__x,V3__y] :
( p(c_24__prop__35178___24a2(V2__x,V3__y))
<=> V2__x = V3__y ) ).
fof('$_prop_35183',axiom,
! [V6__P,V7__Q] :
( p(c_24__prop__35183___24a2(V6__P,V7__Q))
<=> ( p(V6__P)
& p(V7__Q) ) ) ).
fof('$_prop_35190',axiom,
! [V7__P,V8__Q] :
( p(c_24__prop__35190___24a2(V7__P,V8__Q))
<=> ( p(V7__P)
| p(V8__Q) ) ) ).
fof('$_prop_35197',axiom,
! [V8__P,V9__Q] :
( p(c_24__prop__35197___24a2(V8__P,V9__Q))
<=> ( p(V8__P)
=> p(V9__Q) ) ) ).
fof('$_prop_35205',axiom,
! [V9__P] :
( p(c_24__prop__35205___24a1(V9__P))
<=> ~ p(V9__P) ) ).
fof('$_prop_35227',axiom,
! [V0__x,V1__y] :
( p(c_24__prop__35227___24a2(V0__x,V1__y))
<=> V0__x = V1__y ) ).
fof('$_prop_378',axiom,
! [V0__n,V1__m] :
( p(c_24__prop__378___24a2(V0__n,V1__m))
<=> V0__n = V1__m ) ).
fof('$_prop_569',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__569___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_570',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__570___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_571',axiom,
! [V0__A] :
( p(c_24__prop__571___24a1(V0__A))
<=> ~ p(V0__A) ) ).
fof('$_type_1006',axiom,
! [Vvar__1007] :
( c_24__type__1006___24t(Vvar__1007)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__1007,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_1027',axiom,
! [Vvar__1028] :
( c_24__type__1027___24t(Vvar__1028)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__1028,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1046',axiom,
! [Vvar__1047] :
( c_24__type__1046___24t(Vvar__1047)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__1047,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_10622',axiom,
! [Vv__CANONICAL__0,Vvar__10623] :
( c_24__type__10622___24t(Vv__CANONICAL__0,Vvar__10623)
<=> ! [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__10623,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_10645',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10646] :
( c_24__type__10645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10646)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__10646,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_10659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10660] :
( c_24__type__10659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10660)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__10660,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_10666',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10667] :
( c_24__type__10666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10667)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__10667,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_10670',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10671] :
( c_24__type__10670___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10671)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> t(happ(Vvar__10671,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).
fof('$_type_1068',axiom,
! [Vvar__1069] :
( c_24__type__1068___24t(Vvar__1069)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1069,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_10901',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10902] :
( c_24__type__10901___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__10902)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__10902,Vv__CANONICAL__2)) ) ) ).
fof('$_type_10905',axiom,
! [Vvar__10906] :
( c_24__type__10905___24t(Vvar__10906)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__10906,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1095',axiom,
! [Vvar__1096] :
( c_24__type__1095___24t(Vvar__1096)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__1096,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_11150',axiom,
! [Vvar__11151] :
( c_24__type__11150___24t(Vvar__11151)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__11151,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1117',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1118] :
( c_24__type__1117___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1118)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__1118,Vv__CANONICAL__2)) ) ) ).
fof('$_type_1127',axiom,
! [Vvar__1128] :
( c_24__type__1127___24t(Vvar__1128)
<=> ! [Vv__CANONICAL__0] :
( chahn_2eHahnBase_2eEquality_2etype___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__1128,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1142',axiom,
! [Vvar__1143] :
( c_24__type__1142___24t(Vvar__1143)
<=> ! [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__1143,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1146',axiom,
! [Vvar__1147] :
( c_24__type__1146___24t(Vvar__1147)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1147,Vv__CANONICAL__0)) ) ) ).
fof('$_type_1177',axiom,
! [Vvar__1178] :
( c_24__type__1177___24t(Vvar__1178)
<=> ! [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__1178,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1180',axiom,
! [Vvar__1181] :
( c_24__type__1180___24t(Vvar__1181)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1181,Vv__CANONICAL__0)) ) ) ).
fof('$_type_11937',axiom,
! [Vvar__11938] :
( c_24__type__11937___24t(Vvar__11938)
<=> ! [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__11938,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1197] :
( c_24__type__1196___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__1197)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1197,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_12076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12077] :
( c_24__type__12076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12077)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12077,Vv__CANONICAL__3)) ) ) ).
fof('$_type_12100',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12101] :
( c_24__type__12100___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12101)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12101,Vv__CANONICAL__3)) ) ) ).
fof('$_type_1236',axiom,
! [Vvar__1237] :
( c_24__type__1236___24t(Vvar__1237)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__1238___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__1237,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12393',axiom,
! [Vvar__12394] :
( c_24__type__12393___24t(Vvar__12394)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__12394,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_1254',axiom,
! [Vvar__1255] :
( c_24__type__1254___24t(Vvar__1255)
<=> ! [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__1255,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1256',axiom,
! [Vvar__1257] :
( c_24__type__1256___24t(Vvar__1257)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__1257,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12686',axiom,
! [Vvar__12687] :
( c_24__type__12686___24t(Vvar__12687)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__12687,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12689',axiom,
! [Vvar__12690] :
( c_24__type__12689___24t(Vvar__12690)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__12690,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12694',axiom,
! [Vvar__12695] :
( c_24__type__12694___24t(Vvar__12695)
<=> ! [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__12695,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_12697',axiom,
! [Vvar__12698] :
( c_24__type__12697___24t(Vvar__12698)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__12698,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_12739',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12740] :
( c_24__type__12739___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__12740)
<=> ! [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__12740,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_12774',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12775] :
( c_24__type__12774___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__12775)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__12775,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_12783',axiom,
! [Vvar__12784] :
( c_24__type__12783___24t(Vvar__12784)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___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__12784,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).
fof('$_type_12813',axiom,
! [Vvar__12814] :
( c_24__type__12813___24t(Vvar__12814)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__12814,Vv__CANONICAL__0)) ) ) ).
fof('$_type_12820',axiom,
! [Vvar__12821] :
( c_24__type__12820___24t(Vvar__12821)
<=> ! [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__12821,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_13057',axiom,
! [Vvar__13058] :
( c_24__type__13057___24t(Vvar__13058)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__13059___24a1(Vv__CANONICAL__0),happ(Vvar__13058,Vv__CANONICAL__0)) ) ) ).
fof('$_type_13071',axiom,
! [Vvar__13072] :
( c_24__type__13071___24t(Vvar__13072)
<=> ! [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__13072,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_13083',axiom,
! [Vvar__13084] :
( c_24__type__13083___24t(Vvar__13084)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> t(happ(happ(happ(Vvar__13084,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).
fof('$_type_13309',axiom,
! [Vvar__13310] :
( c_24__type__13309___24t(Vvar__13310)
<=> ! [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__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3213___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__10670___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__13329___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__13338___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__8),Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__13310,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_13329',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13330] :
( c_24__type__13329___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13330)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(Vvar__13330,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_13338',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13339] :
( c_24__type__13338___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__13339)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__13339,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_13399',axiom,
! [Vv__CANONICAL__0,Vvar__13400] :
( c_24__type__13399___24t(Vv__CANONICAL__0,Vvar__13400)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__13400,Vv__CANONICAL__1)) ) ) ).
fof('$_type_13479',axiom,
! [Vvar__13480] :
( c_24__type__13479___24t(Vvar__13480)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__13399___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__13480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_138',axiom,
! [Vvar__139] :
( c_24__type__138___24t(Vvar__139)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__139,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_14080',axiom,
! [Vvar__14081] :
( c_24__type__14080___24t(Vvar__14081)
<=> ! [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__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3213___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( cType___24t(Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__10670___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cType___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( c_24__type__13329___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__13338___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__9,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__7,Vv__CANONICAL__13)
=> t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__14081,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_14144',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14145] :
( c_24__type__14144___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14145)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__14145,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14153',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14154] :
( c_24__type__14153___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14154)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__14154,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14162',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14163] :
( c_24__type__14162___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14163)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__14164___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__14163,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14185',axiom,
! [Vvar__14186] :
( c_24__type__14185___24t(Vvar__14186)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__14197___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__0,Vv__CANONICAL__4)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(Vvar__14186,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_14197',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14198] :
( c_24__type__14197___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__14198)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),Vv__CANONICAL__3),c_24__prop__14199___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3),happ(happ(Vvar__14198,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_14226',axiom,
! [Vvar__14227] :
( c_24__type__14226___24t(Vvar__14227)
<=> ! [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__14227,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14263',axiom,
! [Vvar__14264] :
( c_24__type__14263___24t(Vvar__14264)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(happ(Vvar__14264,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14267',axiom,
! [Vvar__14268] :
( c_24__type__14267___24t(Vvar__14268)
<=> ! [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__14268,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14420',axiom,
! [Vvar__14421] :
( c_24__type__14420___24t(Vvar__14421)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__14421,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14441',axiom,
! [Vvar__14442] :
( c_24__type__14441___24t(Vvar__14442)
<=> ! [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__14442,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14728',axiom,
! [Vvar__14729] :
( c_24__type__14728___24t(Vvar__14729)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__14729,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_14742',axiom,
! [Vvar__14743] :
( c_24__type__14742___24t(Vvar__14743)
<=> ! [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__14743,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_14747',axiom,
! [Vvar__14748] :
( c_24__type__14747___24t(Vvar__14748)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__14748,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).
fof('$_type_14829',axiom,
! [Vvar__14830] :
( c_24__type__14829___24t(Vvar__14830)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__14830,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_14892',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14893] :
( c_24__type__14892___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__14893)
<=> ( p(happ(happ(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2))
=> cProp___24t(Vvar__14893) ) ) ).
fof('$_type_15148',axiom,
! [Vvar__15149] :
( c_24__type__15148___24t(Vvar__15149)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__10622___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__15149,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_1544',axiom,
! [Vv__CANONICAL__0,Vvar__1545] :
( c_24__type__1544___24t(Vv__CANONICAL__0,Vvar__1545)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__1545,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_15633',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15634] :
( c_24__type__15633___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15634)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__15634,Vv__CANONICAL__3)) ) ) ).
fof('$_type_1565',axiom,
! [Vv__CANONICAL__0,Vvar__1566] :
( c_24__type__1565___24t(Vv__CANONICAL__0,Vvar__1566)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__1566,Vv__CANONICAL__1)) ) ) ).
fof('$_type_15658',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15659] :
( c_24__type__15658___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__15659)
<=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(Vvar__15659,Vv__CANONICAL__3)) ) ) ).
fof('$_type_15663',axiom,
! [Vvar__15664] :
( c_24__type__15663___24t(Vvar__15664)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__15664,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_15674',axiom,
! [Vvar__15675] :
( c_24__type__15674___24t(Vvar__15675)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2etrue,happ(Vvar__15675,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_15677',axiom,
! [Vvar__15678] :
( c_24__type__15677___24t(Vvar__15678)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ( ~ p(Vv__CANONICAL__0)
=> cCoq_2eBool_2eBool_2ereflect___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2efalse,happ(Vvar__15678,Vv__CANONICAL__0)) ) ) ) ).
fof('$_type_15952',axiom,
! [Vv__CANONICAL__0,Vvar__15953] :
( c_24__type__15952___24t(Vv__CANONICAL__0,Vvar__15953)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ( cCoq_2eInit_2eLogic_2eex___24a2(Vv__CANONICAL__0,cCoq_2eInit_2eLogic_2eunique___24a2(Vv__CANONICAL__0,c_24__lam__15958___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)))
=> cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,c_24__lam__15963___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(Vvar__15953,Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_15964',axiom,
! [Vvar__15965] :
( c_24__type__15964___24t(Vvar__15965)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on___24t(Vv__CANONICAL__0,happ(Vvar__15965,Vv__CANONICAL__0)) ) ) ).
fof('$_type_15974',axiom,
! [Vvar__15975] :
( c_24__type__15974___24t(Vvar__15975)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__15964___24t(Vv__CANONICAL__0)
=> ( ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__1)
| ~ p(Vv__CANONICAL__1) ) )
=> ! [Vv__CANONICAL__2] :
( cProp___24t(Vv__CANONICAL__2)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__2,c_24__prop__15977___24a1(Vv__CANONICAL__2),happ(happ(Vvar__15975,Vv__CANONICAL__0),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_165',axiom,
! [Vv__CANONICAL__0,Vvar__166] :
( c_24__type__165___24t(Vv__CANONICAL__0,Vvar__166)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__166,Vv__CANONICAL__1)) ) ) ).
fof('$_type_16873',axiom,
! [Vvar__16874] :
( c_24__type__16873___24t(Vvar__16874)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__258___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__16874,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_16875',axiom,
! [Vvar__16876] :
( c_24__type__16875___24t(Vvar__16876)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__258___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__16876,Vv__CANONICAL__0)) ) ) ).
fof('$_type_16919',axiom,
! [Vvar__16920] :
( c_24__type__16919___24t(Vvar__16920)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__16922___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))
=> ! [Vv__CANONICAL__3] :
( c_24__type__16934___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__16920,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_16922',axiom,
! [Vv__CANONICAL__0,Vvar__16923] :
( c_24__type__16922___24t(Vv__CANONICAL__0,Vvar__16923)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__16923,Vv__CANONICAL__1)) ) ) ).
fof('$_type_16934',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16935] :
( c_24__type__16934___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__16935)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
=> t(happ(happ(happ(Vvar__16935,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3))) ) ) ) ) ).
fof('$_type_170',axiom,
! [Vv__CANONICAL__0,Vvar__171] :
( c_24__type__170___24t(Vv__CANONICAL__0,Vvar__171)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__171,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_17295',axiom,
! [Vvar__17296] :
( c_24__type__17295___24t(Vvar__17296)
<=> ! [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__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3213___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( cType___24t(Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( c_24__type__10670___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cType___24t(Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( c_24__type__13329___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__11)
=> ! [Vv__CANONICAL__12] :
( c_24__type__13338___24t(Vv__CANONICAL__0,Vv__CANONICAL__8,Vv__CANONICAL__10,Vv__CANONICAL__12)
=> ! [Vv__CANONICAL__13] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__13)
=> ! [Vv__CANONICAL__14] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__8,Vv__CANONICAL__14)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__17296,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__12),Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_1735',axiom,
! [Vv__CANONICAL__0,Vvar__1736] :
( c_24__type__1735___24t(Vv__CANONICAL__0,Vvar__1736)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__1736,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_176',axiom,
! [Vv__CANONICAL__0,Vvar__177] :
( c_24__type__176___24t(Vv__CANONICAL__0,Vvar__177)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__177,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_179',axiom,
! [Vv__CANONICAL__0,Vvar__180] :
( c_24__type__179___24t(Vv__CANONICAL__0,Vvar__180)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__180,Vv__CANONICAL__1)) ) ) ).
fof('$_type_19185',axiom,
! [Vvar__19186] :
( c_24__type__19185___24t(Vvar__19186)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__19186,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19188',axiom,
! [Vvar__19189] :
( c_24__type__19188___24t(Vvar__19189)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__19189,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19193',axiom,
! [Vvar__19194] :
( c_24__type__19193___24t(Vvar__19194)
<=> ! [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__19194,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_19202',axiom,
! [Vvar__19203] :
( c_24__type__19202___24t(Vvar__19203)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__19203,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19356',axiom,
! [Vvar__19357] :
( c_24__type__19356___24t(Vvar__19357)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__19357,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_1959',axiom,
! [Vvar__1960] :
( c_24__type__1959___24t(Vvar__1960)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__179___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__1960,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_19908',axiom,
! [Vvar__19909] :
( c_24__type__19908___24t(Vvar__19909)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__19913___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__19909,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_19913',axiom,
! [Vv__CANONICAL__0,Vvar__19914] :
( c_24__type__19913___24t(Vv__CANONICAL__0,Vvar__19914)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),happ(happ(Vvar__19914,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_20063',axiom,
! [Vv__CANONICAL__0,Vvar__20064] :
( c_24__type__20063___24t(Vv__CANONICAL__0,Vvar__20064)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__20064,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_205',axiom,
! [Vvar__206] :
( c_24__type__205___24t(Vvar__206)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__206,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_217',axiom,
! [Vvar__218] :
( c_24__type__217___24t(Vvar__218)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__218,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_21923',axiom,
! [Vvar__21924] :
( c_24__type__21923___24t(Vvar__21924)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__3213___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__6)
=> t(happ(happ(happ(happ(happ(happ(happ(Vvar__21924,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ) ) ) ) ) ).
fof('$_type_21991',axiom,
! [Vvar__21992] :
( c_24__type__21991___24t(Vvar__21992)
<=> ! [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__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5967___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__21992,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ) ) ) ) ).
fof('$_type_22021',axiom,
! [Vvar__22022] :
( c_24__type__22021___24t(Vvar__22022)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__22028___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__22022,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_22028',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22029] :
( c_24__type__22028___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22029)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__22029,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_22270',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22271] :
( c_24__type__22270___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__22271)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(happ(Vv__CANONICAL__1,Vv__CANONICAL__2),c_24__prop__22272___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2),happ(Vvar__22271,Vv__CANONICAL__2)) ) ) ).
fof('$_type_225',axiom,
! [Vvar__226] :
( c_24__type__225___24t(Vvar__226)
<=> ! [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__226,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2254',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2255] :
( c_24__type__2254___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2255)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__2255,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_22792',axiom,
! [Vvar__22793] :
( c_24__type__22792___24t(Vvar__22793)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cProp___24t(Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__22793,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2313',axiom,
! [Vvar__2314] :
( c_24__type__2313___24t(Vvar__2314)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__2314,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2318',axiom,
! [Vvar__2319] :
( c_24__type__2318___24t(Vvar__2319)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__2319,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_23331',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23332] :
( c_24__type__23331___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__23332)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23332,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23677',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23678] :
( c_24__type__23677___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__23678)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23678,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24023',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24024] :
( c_24__type__24023___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24024)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24024,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24346',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__24347] :
( c_24__type__24346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__24347)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> t(happ(Vvar__24347,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_24692',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24693] :
( c_24__type__24692___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__24693)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__24693,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_249',axiom,
! [Vvar__250] :
( c_24__type__249___24t(Vvar__250)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__250,Vv__CANONICAL__0)) ) ) ).
fof('$_type_25038',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25039] :
( c_24__type__25038___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__25039)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__25039,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_2513',axiom,
! [Vvar__2514] :
( c_24__type__2513___24t(Vvar__2514)
<=> ! [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)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2514,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2523',axiom,
! [Vvar__2524] :
( c_24__type__2523___24t(Vvar__2524)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__2524,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_25384',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25385] :
( c_24__type__25384___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25385)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__25385,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_2543',axiom,
! [Vvar__2544] :
( c_24__type__2543___24t(Vvar__2544)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__2544,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_256',axiom,
! [Vvar__257] :
( c_24__type__256___24t(Vvar__257)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__257,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2563',axiom,
! [Vvar__2564] :
( c_24__type__2563___24t(Vvar__2564)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__2564,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_25730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25731] :
( c_24__type__25730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__25731)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__25731,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_2578',axiom,
! [Vvar__2579] :
( c_24__type__2578___24t(Vvar__2579)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__2579,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_258',axiom,
! [Vvar__259] :
( c_24__type__258___24t(Vvar__259)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__259,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2601] :
( c_24__type__2600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2601)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__2601,Vv__CANONICAL__2)) ) ) ).
fof('$_type_26076',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26077] :
( c_24__type__26076___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__26077)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> t(happ(happ(Vvar__26077,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).
fof('$_type_26399',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26400] :
( c_24__type__26399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26400)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__26400,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).
fof('$_type_2642',axiom,
! [Vvar__2643] :
( c_24__type__2642___24t(Vvar__2643)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__2643,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2649',axiom,
! [Vvar__2650] :
( c_24__type__2649___24t(Vvar__2650)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__2650,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2673',axiom,
! [Vvar__2674] :
( c_24__type__2673___24t(Vvar__2674)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__616___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__2674,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_26745',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26746] :
( c_24__type__26745___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__26746)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__26746,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_27091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27092] :
( c_24__type__27091___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27092)
<=> ! [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__27092,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).
fof('$_type_27414',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27415] :
( c_24__type__27414___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__27415)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
=> t(happ(Vvar__27415,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).
fof('$_type_27737',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27738] :
( c_24__type__27737___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__27738)
<=> ! [Vv__CANONICAL__22] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
=> t(happ(Vvar__27738,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).
fof('$_type_28',axiom,
! [Vvar__29] :
( c_24__type__28___24t(Vvar__29)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__29,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_280',axiom,
! [Vvar__281] :
( c_24__type__280___24t(Vvar__281)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__281,Vv__CANONICAL__0)) ) ) ).
fof('$_type_28083',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28084] :
( c_24__type__28083___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vv__CANONICAL__17,Vv__CANONICAL__18,Vv__CANONICAL__19,Vv__CANONICAL__20,Vv__CANONICAL__21,Vvar__28084)
<=> ! [Vv__CANONICAL__22] :
( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__23] :
( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
=> t(happ(happ(Vvar__28084,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_285',axiom,
! [Vvar__286] :
( c_24__type__285___24t(Vvar__286)
<=> ! [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__286,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28515',axiom,
! [Vvar__28516] :
( c_24__type__28515___24t(Vvar__28516)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__28516,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_28527',axiom,
! [Vvar__28528] :
( c_24__type__28527___24t(Vvar__28528)
<=> ! [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__28528,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_28535',axiom,
! [Vvar__28536] :
( c_24__type__28535___24t(Vvar__28536)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__28536,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_28765',axiom,
! [Vvar__28766] :
( c_24__type__28765___24t(Vvar__28766)
<=> ! [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__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( c_24__type__3213___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
=> ! [Vv__CANONICAL__7] :
( c_24__type__10622___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
=> ! [Vv__CANONICAL__8] :
( c_24__type__20063___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__9] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
=> ! [Vv__CANONICAL__10] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
=> ! [Vv__CANONICAL__11] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
=> cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__28766,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_type_29294',axiom,
! [Vvar__29295] :
( c_24__type__29294___24t(Vvar__29295)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__29295,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_295',axiom,
! [Vvar__296] :
( c_24__type__295___24t(Vvar__296)
<=> ! [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__296,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__29801] :
( c_24__type__29800___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__29801)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__29801,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30013',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30014] :
( c_24__type__30013___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30014)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30014,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30226',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30227] :
( c_24__type__30226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__30227)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__30227,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_30421',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30422] :
( c_24__type__30421___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30422)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
=> t(happ(Vvar__30422,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_3061',axiom,
! [Vvar__3062] :
( c_24__type__3061___24t(Vvar__3062)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__3062,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_30634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30635] :
( c_24__type__30634___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30635)
<=> ! [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__30635,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_307',axiom,
! [Vvar__308] :
( c_24__type__307___24t(Vvar__308)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__308,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_30847',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30848] :
( c_24__type__30847___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__30848)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__30848,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_3089',axiom,
! [Vvar__3090] :
( c_24__type__3089___24t(Vvar__3090)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3090,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31060',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31061] :
( c_24__type__31060___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31061)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__31061,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_31273',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31274] :
( c_24__type__31273___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31274)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> t(happ(happ(Vvar__31274,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).
fof('$_type_31468',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31469] :
( c_24__type__31468___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31469)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__31469,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).
fof('$_type_315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__316] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__316)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__316,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_3155',axiom,
! [Vvar__3156] :
( c_24__type__3155___24t(Vvar__3156)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3156,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31682] :
( c_24__type__31681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11,Vv__CANONICAL__12,Vv__CANONICAL__13,Vv__CANONICAL__14,Vv__CANONICAL__15,Vv__CANONICAL__16,Vvar__31682)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> ! [Vv__CANONICAL__18] :
( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__31682,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).
fof('$_type_3172',axiom,
! [Vvar__3173] :
( c_24__type__3172___24t(Vvar__3173)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3177___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__3173,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_3177',axiom,
! [Vv__CANONICAL__0,Vvar__3178] :
( c_24__type__3177___24t(Vv__CANONICAL__0,Vvar__3178)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3178,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_31876',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31877] :
( c_24__type__31876___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__31877)
<=> ! [Vv__CANONICAL__17] :
( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
=> t(happ(Vvar__31877,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).
fof('$_type_3213',axiom,
! [Vv__CANONICAL__0,Vvar__3214] :
( c_24__type__3213___24t(Vv__CANONICAL__0,Vvar__3214)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__3214,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_32139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32140] :
( c_24__type__32139___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32140)
<=> ! [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__32140,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_32189',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32190] :
( c_24__type__32189___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32190)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__32190,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_32239',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32240] :
( c_24__type__32239___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32240)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> t(happ(happ(Vvar__32240,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).
fof('$_type_32281',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32282] :
( c_24__type__32281___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32282)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> t(happ(Vvar__32282,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).
fof('$_type_3233',axiom,
! [Vvar__3234] :
( c_24__type__3233___24t(Vvar__3234)
<=> ! [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__3234,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_32331',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32332] :
( c_24__type__32331___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32332)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__32332,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_32407',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32408] :
( c_24__type__32407___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32408)
<=> ! [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__32408,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_32516',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32517] :
( c_24__type__32516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32517)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32517,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3256',axiom,
! [Vvar__3257] :
( c_24__type__3256___24t(Vvar__3257)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__3261___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__3257,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_32560',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32561] :
( c_24__type__32560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32561)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__32561,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).
fof('$_type_32596',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32597] :
( c_24__type__32596___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32597)
<=> ! [Vv__CANONICAL__7] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
=> t(happ(Vvar__32597,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).
fof('$_type_3261',axiom,
! [Vv__CANONICAL__0,Vvar__3262] :
( c_24__type__3261___24t(Vv__CANONICAL__0,Vvar__3262)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3262,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32640',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32641] :
( c_24__type__32640___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__32641)
<=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
=> t(happ(happ(Vvar__32641,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32652',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32653] :
( c_24__type__32652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32653)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(Vvar__32653,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_32659',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32660] :
( c_24__type__32659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32660)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__32660,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32764',axiom,
! [Vvar__32765] :
( c_24__type__32764___24t(Vvar__32765)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__32765,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3330',axiom,
! [Vvar__3331] :
( c_24__type__3330___24t(Vvar__3331)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3331,Vv__CANONICAL__0)) ) ) ).
fof('$_type_33561',axiom,
! [Vvar__33562] :
( c_24__type__33561___24t(Vvar__33562)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ( p(Vv__CANONICAL__0)
=> ( ~ p(Vv__CANONICAL__0)
=> t(happ(happ(Vvar__33562,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__1) ) ) ) ) ) ).
fof('$_type_33565',axiom,
! [Vv__CANONICAL__0,Vvar__33566] :
( c_24__type__33565___24t(Vv__CANONICAL__0,Vvar__33566)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,c_24__prop__33567___24a1(Vv__CANONICAL__0),Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__33566,Vv__CANONICAL__1)) ) ) ).
fof('$_type_33580',axiom,
! [Vvar__33581] :
( c_24__type__33580___24t(Vvar__33581)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__33581,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33598',axiom,
! [Vvar__33599] :
( c_24__type__33598___24t(Vvar__33599)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__33599,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_33615',axiom,
! [Vvar__33616] :
( c_24__type__33615___24t(Vvar__33616)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__33616,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3362',axiom,
! [Vvar__3363] :
( c_24__type__3362___24t(Vvar__3363)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__3363,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33632',axiom,
! [Vvar__33633] :
( c_24__type__33632___24t(Vvar__33633)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__33633,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_33659',axiom,
! [Vvar__33660] :
( c_24__type__33659___24t(Vvar__33660)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__33660,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_33682',axiom,
! [Vvar__33683] :
( c_24__type__33682___24t(Vvar__33683)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__3,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(happ(Vvar__33683,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_33795',axiom,
! [Vvar__33796] :
( c_24__type__33795___24t(Vvar__33796)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( c_24__type__4___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
=> ! [Vv__CANONICAL__5] :
( c_24__type__616___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5)
=> ! [Vv__CANONICAL__6] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__6)
=> cProp___24t(happ(happ(happ(happ(happ(happ(happ(Vvar__33796,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).
fof('$_type_33803',axiom,
! [Vvar__33804] :
( c_24__type__33803___24t(Vvar__33804)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__33804,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34',axiom,
! [Vvar__35] :
( c_24__type__34___24t(Vvar__35)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_341',axiom,
! [Vvar__342] :
( c_24__type__341___24t(Vvar__342)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__342,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34411',axiom,
! [Vvar__34412] :
( c_24__type__34411___24t(Vvar__34412)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__1196___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__5)
=> cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__34412,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_3449',axiom,
! [Vvar__3450] :
( c_24__type__3449___24t(Vvar__3450)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__3450,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3471',axiom,
! [Vvar__3472] :
( c_24__type__3471___24t(Vvar__3472)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__3472,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_35050',axiom,
! [Vvar__35051] :
( c_24__type__35050___24t(Vvar__35051)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__35051,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35223',axiom,
! [Vvar__35224] :
( c_24__type__35223___24t(Vvar__35224)
<=> ! [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_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__35224,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_353',axiom,
! [Vvar__354] :
( c_24__type__353___24t(Vvar__354)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__354,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_3530',axiom,
! [Vvar__3531] :
( c_24__type__3530___24t(Vvar__3531)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__3531,Vv__CANONICAL__0)) ) ) ).
fof('$_type_369',axiom,
! [Vvar__370] :
( c_24__type__369___24t(Vvar__370)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__370,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_37',axiom,
! [Vvar__38] :
( c_24__type__37___24t(Vvar__38)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__38,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_374',axiom,
! [Vvar__375] :
( c_24__type__374___24t(Vvar__375)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(Vvar__375,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_376',axiom,
! [Vvar__377] :
( c_24__type__376___24t(Vvar__377)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__377,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4',axiom,
! [Vv__CANONICAL__0,Vvar__5] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vvar__5)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__5,Vv__CANONICAL__1)) ) ) ).
fof('$_type_40',axiom,
! [Vvar__41] :
( c_24__type__40___24t(Vvar__41)
<=> ! [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__41,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_405',axiom,
! [Vv__CANONICAL__0,Vvar__406] :
( c_24__type__405___24t(Vv__CANONICAL__0,Vvar__406)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__406,Vv__CANONICAL__1)) ) ) ).
fof('$_type_418',axiom,
! [Vvar__419] :
( c_24__type__418___24t(Vvar__419)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__419,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_4192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4193] :
( c_24__type__4192___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4193)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4193,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4285',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__4286] :
( c_24__type__4285___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__4286)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4286,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4378',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4379] :
( c_24__type__4378___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4379)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4379,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4460',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__4461] :
( c_24__type__4460___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__4461)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__4461,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__456] :
( c_24__type__455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__456)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__456,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_4553',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__4554] :
( c_24__type__4553___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__4554)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4554,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_46',axiom,
! [Vvar__47] :
( c_24__type__46___24t(Vvar__47)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__4___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__47,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_4635',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__4636] :
( c_24__type__4635___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__4636)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__4636,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_4728',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4729] :
( c_24__type__4728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4729)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__4729,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_483',axiom,
! [Vvar__484] :
( c_24__type__483___24t(Vvar__484)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__484,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_488',axiom,
! [Vvar__489] :
( c_24__type__488___24t(Vvar__489)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__489,Vv__CANONICAL__0)) ) ) ).
fof('$_type_4928',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__4929] :
( c_24__type__4928___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__4929)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4929,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_498',axiom,
! [Vvar__499] :
( c_24__type__498___24t(Vvar__499)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__499,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_5021',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5022] :
( c_24__type__5021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5022)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5022,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5114',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5115] :
( c_24__type__5114___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5115)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5115,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5196',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5197] :
( c_24__type__5196___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5197)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5197,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_5289',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5290] :
( c_24__type__5289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5290)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5290,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5371',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5372] :
( c_24__type__5371___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5372)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__5372,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_5464',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5465] :
( c_24__type__5464___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__5465)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5465,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_5618',axiom,
! [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__5619] :
( c_24__type__5618___24t(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__5619)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5619,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5681',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5682] :
( c_24__type__5681___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5682)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5682,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_5744',axiom,
! [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__5745] :
( c_24__type__5744___24t(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__5745)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5745,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_576',axiom,
! [Vvar__577] :
( c_24__type__576___24t(Vvar__577)
<=> ! [Vv__CANONICAL__0] :
( chahn_2eHahnBase_2eEquality_2etype___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( chahn_2eHahnBase_2eEquality_2esort___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( chahn_2eHahnBase_2eEquality_2esort___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(Vvar__577,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_578',axiom,
! [Vvar__579] :
( c_24__type__578___24t(Vvar__579)
<=> ! [Vv__CANONICAL__0] :
( chahn_2eHahnBase_2eEquality_2etype___24t(Vv__CANONICAL__0)
=> chahn_2eHahnBase_2eEquality_2eaxiom___24t(chahn_2eHahnBase_2eEquality_2esort___24a1(Vv__CANONICAL__0),chahn_2eHahnBase_2eeq__op___24a1(Vv__CANONICAL__0),happ(Vvar__579,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5798',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5799] :
( c_24__type__5798___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5799)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__5799,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_586',axiom,
! [Vvar__587] :
( c_24__type__586___24t(Vvar__587)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__588___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__587,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5861',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5862] :
( c_24__type__5861___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__5862)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__5862,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_588',axiom,
! [Vvar__589] :
( c_24__type__588___24t(Vvar__589)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__589,Vv__CANONICAL__0)) ) ) ).
fof('$_type_5897',axiom,
! [Vvar__5898] :
( c_24__type__5897___24t(Vvar__5898)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__5898,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_5962',axiom,
! [Vvar__5963] :
( c_24__type__5962___24t(Vvar__5963)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
=> t(happ(happ(happ(happ(happ(Vvar__5963,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).
fof('$_type_5967',axiom,
! [Vv__CANONICAL__0,Vvar__5968] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vvar__5968)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__5968,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_60',axiom,
! [Vv__CANONICAL__0,Vvar__61] :
( c_24__type__60___24t(Vv__CANONICAL__0,Vvar__61)
<=> ! [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__61,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_616',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__617] :
( c_24__type__616___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__617)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__617,Vv__CANONICAL__2)) ) ) ).
fof('$_type_62',axiom,
! [Vvar__63] :
( c_24__type__62___24t(Vvar__63)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__63,Vv__CANONICAL__0)) ) ) ).
fof('$_type_620',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__621] :
( c_24__type__620___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__621)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__621,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6416',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6417] :
( c_24__type__6416___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6417)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6417,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_643',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__644] :
( c_24__type__643___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__644)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__644,Vv__CANONICAL__2)) ) ) ).
fof('$_type_6517',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6518] :
( c_24__type__6517___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6518)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6518,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_653',axiom,
! [Vvar__654] :
( c_24__type__653___24t(Vvar__654)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__654,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_6618',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6619] :
( c_24__type__6618___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6619)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__6619,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_667',axiom,
! [Vv__CANONICAL__0,Vvar__668] :
( c_24__type__667___24t(Vv__CANONICAL__0,Vvar__668)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__668,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_6708',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6709] :
( c_24__type__6708___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6709)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__6709,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_68',axiom,
! [Vvar__69] :
( c_24__type__68___24t(Vvar__69)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__69,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_6809',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6810] :
( c_24__type__6809___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6810)
<=> ! [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__6810,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_6910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6911] :
( c_24__type__6910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__6911)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__6911,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_7011',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7012] :
( c_24__type__7011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7012)
<=> ! [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__7012,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_7716',axiom,
! [Vvar__7717] :
( c_24__type__7716___24t(Vvar__7717)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__5967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__7717,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_788',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__789] :
( c_24__type__788___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__789)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> t(happ(Vvar__789,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_7889',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__7890] :
( c_24__type__7889___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__7890)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7890,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7928',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__7929] :
( c_24__type__7928___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__7929)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__7929,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_7967',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__7968] :
( c_24__type__7967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__7968)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__7968,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_8234',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8235] :
( c_24__type__8234___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8235)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8235,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8297',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8298] :
( c_24__type__8297___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8298)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8298,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8360',axiom,
! [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__8361] :
( c_24__type__8360___24t(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__8361)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8361,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8414',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8415] :
( c_24__type__8414___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8415)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__8415,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_8477',axiom,
! [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__8478] :
( c_24__type__8477___24t(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__8478)
<=> ! [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__8478,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_8725',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8726] :
( c_24__type__8725___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8726)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8726,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8788',axiom,
! [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__8789] :
( c_24__type__8788___24t(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__8789)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8789,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8851',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8852] :
( c_24__type__8851___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8852)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__8852,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_8905',axiom,
! [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__8906] :
( c_24__type__8905___24t(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__8906)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__8906,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_8968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8969] :
( c_24__type__8968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__8969)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__8969,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_9315',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9316] :
( c_24__type__9315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9316)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9316,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9345',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9346] :
( c_24__type__9345___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9346)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9346,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9369',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9370] :
( c_24__type__9369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9370)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9370,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9399',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9400] :
( c_24__type__9399___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9400)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9400,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_9429',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9430] :
( c_24__type__9429___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9430)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9430,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9453',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9454] :
( c_24__type__9453___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9454)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9454,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9486',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9487] :
( c_24__type__9486___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9487)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9487,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9510',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9511] :
( c_24__type__9510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9511)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9511,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_9537',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9538] :
( c_24__type__9537___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__9538)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__9538,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_typeof_Coq.Arith.Between.in_int',axiom,
c_24__type__15663___24t(cCoq_2eArith_2eBetween_2ein__int) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_dec',axiom,
c_24__type__1236___24t(cCoq_2eArith_2eCompare__dec_2ele__dec) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__3256___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Arith.Wf_nat.has_unique_least_element',axiom,
c_24__type__35050___24t(cCoq_2eArith_2eWf__nat_2ehas__unique__least__element) ).
fof('$_typeof_Coq.Bool.Bool.ReflectF',axiom,
c_24__type__15677___24t(cCoq_2eBool_2eBool_2eReflectF) ).
fof('$_typeof_Coq.Bool.Bool.ReflectT',axiom,
c_24__type__15674___24t(cCoq_2eBool_2eBool_2eReflectT) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__498___24t(cCoq_2eBool_2eBool_2ereflect) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
c_24__type__14420___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).
fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).
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('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__1256___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__256___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__1254___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__307___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__285___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.fst',axiom,
c_24__type__13071___24t(cCoq_2eInit_2eDatatypes_2efst) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__295___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__62___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.list_rec',axiom,
c_24__type__16919___24t(cCoq_2eInit_2eDatatypes_2elist__rec) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
c_24__type__3449___24t(cCoq_2eInit_2eDatatypes_2enegb) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__280___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__62___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
c_24__type__11937___24t(cCoq_2eInit_2eDatatypes_2epair) ).
fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
c_24__type__3471___24t(cCoq_2eInit_2eDatatypes_2eprod) ).
fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
c_24__type__13083___24t(cCoq_2eInit_2eDatatypes_2esnd) ).
fof('$_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('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__374___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.modulo',axiom,
c_24__type__374___24t(cCoq_2eInit_2eNat_2emodulo) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__374___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__1068___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__1068___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__1068___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.absurd_set',axiom,
c_24__type__33561___24t(cCoq_2eInit_2eSpecif_2eabsurd__set) ).
fof('$_typeof_Coq.Init.Specif.exist',axiom,
c_24__type__12783___24t(cCoq_2eInit_2eSpecif_2eexist) ).
fof('$_typeof_Coq.Init.Specif.left',axiom,
c_24__type__14742___24t(cCoq_2eInit_2eSpecif_2eleft) ).
fof('$_typeof_Coq.Init.Specif.right',axiom,
c_24__type__14747___24t(cCoq_2eInit_2eSpecif_2eright) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__10905___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__1095___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__483___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__369___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.List.filter',axiom,
c_24__type__13479___24t(cCoq_2eLists_2eList_2efilter) ).
fof('$_typeof_Coq.Lists.List.fold_right',axiom,
c_24__type__22021___24t(cCoq_2eLists_2eList_2efold__right) ).
fof('$_typeof_Coq.Lists.SetoidList.equivlistA',axiom,
c_24__type__32764___24t(cCoq_2eLists_2eSetoidList_2eequivlistA) ).
fof('$_typeof_Coq.Lists.SetoidList.removeA',axiom,
c_24__type__14185___24t(cCoq_2eLists_2eSetoidList_2eremoveA) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ConstructiveDefiniteDescription_on',axiom,
c_24__type__62___24t(cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.ExcludedMiddle',axiom,
cProp___24t(cCoq_2eLogic_2eChoiceFacts_2eExcludedMiddle) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalRelReification_on',axiom,
c_24__type__3362___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalRelReification__on) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.constructive_definite_descr_excluded_middle',axiom,
c_24__type__15974___24t(cCoq_2eLogic_2eChoiceFacts_2econstructive__definite__descr__excluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalDescription.excluded_middle_informative',axiom,
c_24__type__13057___24t(cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.Minimal',axiom,
c_24__type__16873___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimal) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.Minimization_Property',axiom,
c_24__type__16875___24t(cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle) ).
fof('$_typeof_Coq.Logic.ClassicalFacts.weak_excluded_middle',axiom,
cProp___24t(cCoq_2eLogic_2eClassicalFacts_2eweak__excluded__middle) ).
fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
c_24__type__3530___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__3233___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__3233___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__3172___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
c_24__type__12820___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
c_24__type__35223___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.eqb',axiom,
c_24__type__14226___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeqb) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
c_24__type__12820___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__3089___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
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('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
c_24__type__3330___24t(cCoq_2eNumbers_2eBinNums_2eNpos) ).
fof('$_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__249___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__249___24t(cCoq_2eNumbers_2eBinNums_2eZpos) ).
fof('$_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__488___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__488___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
c_24__type__14267___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
c_24__type__14263___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
c_24__type__14263___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__40___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.commut',axiom,
c_24__type__68___24t(cCoq_2eRelations_2eRelation__Definitions_2ecommut) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__40___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__68___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__40___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__62___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__68___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__40___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__40___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__3061___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__418___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__40___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__225___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__225___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__225___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__225___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__225___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__1142___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__1177___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__1142___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__1180___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__1146___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__1142___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__1146___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.ZArith.Zbool.Zeq_bool',axiom,
c_24__type__14441___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).
fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
c_24__type__12393___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).
fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
c_24__type__22792___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
c_24__type__28515___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).
fof('$_typeof_Coq.micromega.RingMicromega.eval_op2',axiom,
c_24__type__14728___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op2) ).
fof('$_typeof_Coq.micromega.Tauto.A',axiom,
c_24__type__33615___24t(cCoq_2emicromega_2eTauto_2eA) ).
fof('$_typeof_Coq.micromega.Tauto.Cj',axiom,
c_24__type__33632___24t(cCoq_2emicromega_2eTauto_2eCj) ).
fof('$_typeof_Coq.micromega.Tauto.D',axiom,
c_24__type__33632___24t(cCoq_2emicromega_2eTauto_2eD) ).
fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
c_24__type__33580___24t(cCoq_2emicromega_2eTauto_2eFF) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__11150___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.Tauto.I',axiom,
c_24__type__33682___24t(cCoq_2emicromega_2eTauto_2eI) ).
fof('$_typeof_Coq.micromega.Tauto.N',axiom,
c_24__type__33659___24t(cCoq_2emicromega_2eTauto_2eN) ).
fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
c_24__type__33580___24t(cCoq_2emicromega_2eTauto_2eTT) ).
fof('$_typeof_Coq.micromega.Tauto.X',axiom,
c_24__type__33598___24t(cCoq_2emicromega_2eTauto_2eX) ).
fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
c_24__type__3471___24t(cCoq_2emicromega_2eTauto_2eclause) ).
fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
c_24__type__3471___24t(cCoq_2emicromega_2eTauto_2ecnf) ).
fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
c_24__type__33803___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).
fof('$_typeof_Coq.micromega.Tauto.eval_f',axiom,
c_24__type__33795___24t(cCoq_2emicromega_2eTauto_2eeval__f) ).
fof('$_typeof_Coq.micromega.Tauto.eval_tt',axiom,
c_24__type__34411___24t(cCoq_2emicromega_2eTauto_2eeval__tt) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
c_24__type__19188___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
c_24__type__19185___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
c_24__type__19202___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
c_24__type__19193___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
c_24__type__62___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.Fapp',axiom,
c_24__type__19908___24t(cCoq_2esetoid__ring_2eField__theory_2eFapp) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.NPEequiv',axiom,
c_24__type__17295___24t(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.PCond',axiom,
c_24__type__13309___24t(cCoq_2esetoid__ring_2eField__theory_2ePCond) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_common',axiom,
c_24__type__19356___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__common) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_left',axiom,
c_24__type__19356___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__left) ).
fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit_right',axiom,
c_24__type__19356___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit__right) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
c_24__type__3089___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.Nsub',axiom,
c_24__type__12820___24t(cCoq_2esetoid__ring_2eInitialRing_2eNsub) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiN',axiom,
c_24__type__21991___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
c_24__type__5962___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
c_24__type__5962___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).
fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiZ',axiom,
c_24__type__21923___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ) ).
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__12686___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
c_24__type__12689___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
c_24__type__12694___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
c_24__type__28527___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEeval',axiom,
c_24__type__14080___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
c_24__type__12694___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
c_24__type__12697___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
c_24__type__28535___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
c_24__type__12694___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
c_24__type__62___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
c_24__type__15148___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
c_24__type__62___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).
fof('$_typeof_Coq.setoid_ring.Ring_polynom.norm_subst',axiom,
c_24__type__28765___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).
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.pow_N',axiom,
c_24__type__29294___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__7716___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_HahnAcyclic.pref_union',axiom,
c_24__type__418___24t(cHahnAcyclic_2epref__union) ).
fof('$_typeof_hahn.HahnBase.Equality.sort',axiom,
c_24__type__1127___24t(chahn_2eHahnBase_2eEquality_2esort) ).
fof('$_typeof_hahn.HahnBase.NW',axiom,
c_24__type__586___24t(chahn_2eHahnBase_2eNW) ).
fof('$_typeof_hahn.HahnBase.eqP',axiom,
c_24__type__578___24t(chahn_2eHahnBase_2eeqP) ).
fof('$_typeof_hahn.HahnBase.eq_op',axiom,
c_24__type__576___24t(chahn_2eHahnBase_2eeq__op) ).
fof('$_typeof_hahn.HahnBase.nat_eqType',axiom,
chahn_2eHahnBase_2eEquality_2etype___24t(chahn_2eHahnBase_2enat__eqType) ).
fof('$_typeof_hahn.HahnDom.doma',axiom,
c_24__type__138___24t(chahn_2eHahnDom_2edoma) ).
fof('$_typeof_hahn.HahnDom.domb',axiom,
c_24__type__138___24t(chahn_2eHahnDom_2edomb) ).
fof('$_typeof_hahn.HahnEquational.good_ctx',axiom,
c_24__type__1959___24t(chahn_2eHahnEquational_2egood__ctx) ).
fof('$_typeof_hahn.HahnFuneq.funeq',axiom,
c_24__type__653___24t(chahn_2eHahnFuneq_2efuneq) ).
fof('$_typeof_hahn.HahnList.undup',axiom,
c_24__type__2313___24t(chahn_2eHahnList_2eundup) ).
fof('$_typeof_hahn.HahnMaxElt.max_elt',axiom,
c_24__type__2318___24t(chahn_2eHahnMaxElt_2emax__elt) ).
fof('$_typeof_hahn.HahnMaxElt.wmax_elt',axiom,
c_24__type__2318___24t(chahn_2eHahnMaxElt_2ewmax__elt) ).
fof('$_typeof_hahn.HahnRelationsBasic.acyclic',axiom,
c_24__type__40___24t(chahn_2eHahnRelationsBasic_2eacyclic) ).
fof('$_typeof_hahn.HahnRelationsBasic.bunion',axiom,
c_24__type__1006___24t(chahn_2eHahnRelationsBasic_2ebunion) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl',axiom,
c_24__type__37___24t(chahn_2eHahnRelationsBasic_2eclos__refl) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
c_24__type__37___24t(chahn_2eHahnRelationsBasic_2eclos__refl__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_sym',axiom,
c_24__type__37___24t(chahn_2eHahnRelationsBasic_2eclos__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.codom_rel',axiom,
c_24__type__2318___24t(chahn_2eHahnRelationsBasic_2ecodom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.collect_rel',axiom,
c_24__type__353___24t(chahn_2eHahnRelationsBasic_2ecollect__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.cross_rel',axiom,
c_24__type__2578___24t(chahn_2eHahnRelationsBasic_2ecross__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.dom_rel',axiom,
c_24__type__2318___24t(chahn_2eHahnRelationsBasic_2edom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eq_rel',axiom,
c_24__type__5897___24t(chahn_2eHahnRelationsBasic_2eeq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_rel',axiom,
c_24__type__205___24t(chahn_2eHahnRelationsBasic_2eeqv__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.functional',axiom,
c_24__type__40___24t(chahn_2eHahnRelationsBasic_2efunctional) ).
fof('$_typeof_hahn.HahnRelationsBasic.immediate',axiom,
c_24__type__37___24t(chahn_2eHahnRelationsBasic_2eimmediate) ).
fof('$_typeof_hahn.HahnRelationsBasic.inter_rel',axiom,
c_24__type__34___24t(chahn_2eHahnRelationsBasic_2einter__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.irreflexive',axiom,
c_24__type__40___24t(chahn_2eHahnRelationsBasic_2eirreflexive) ).
fof('$_typeof_hahn.HahnRelationsBasic.is_total',axiom,
c_24__type__46___24t(chahn_2eHahnRelationsBasic_2eis__total) ).
fof('$_typeof_hahn.HahnRelationsBasic.map_rel',axiom,
c_24__type__341___24t(chahn_2eHahnRelationsBasic_2emap__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.minus_rel',axiom,
c_24__type__34___24t(chahn_2eHahnRelationsBasic_2eminus__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.pow_rel',axiom,
c_24__type__2563___24t(chahn_2eHahnRelationsBasic_2epow__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
c_24__type__2523___24t(chahn_2eHahnRelationsBasic_2erestr__eq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_rel',axiom,
c_24__type__28___24t(chahn_2eHahnRelationsBasic_2erestr__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_subset',axiom,
c_24__type__2543___24t(chahn_2eHahnRelationsBasic_2erestr__subset) ).
fof('$_typeof_hahn.HahnRelationsBasic.seq',axiom,
c_24__type__34___24t(chahn_2eHahnRelationsBasic_2eseq) ).
fof('$_typeof_hahn.HahnRelationsBasic.singl_rel',axiom,
c_24__type__2513___24t(chahn_2eHahnRelationsBasic_2esingl__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_partial_order',axiom,
c_24__type__40___24t(chahn_2eHahnRelationsBasic_2estrict__partial__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_total_order',axiom,
c_24__type__46___24t(chahn_2eHahnRelationsBasic_2estrict__total__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.upward_closed',axiom,
c_24__type__138___24t(chahn_2eHahnRelationsBasic_2eupward__closed) ).
fof('$_typeof_hahn.HahnSets.set_collect',axiom,
c_24__type__2673___24t(chahn_2eHahnSets_2eset__collect) ).
fof('$_typeof_hahn.HahnSets.set_compl',axiom,
c_24__type__2649___24t(chahn_2eHahnSets_2eset__compl) ).
fof('$_typeof_hahn.HahnSets.set_disjoint',axiom,
c_24__type__1027___24t(chahn_2eHahnSets_2eset__disjoint) ).
fof('$_typeof_hahn.HahnSets.set_empty',axiom,
c_24__type__2642___24t(chahn_2eHahnSets_2eset__empty) ).
fof('$_typeof_hahn.HahnSets.set_equiv',axiom,
c_24__type__1027___24t(chahn_2eHahnSets_2eset__equiv) ).
fof('$_typeof_hahn.HahnSets.set_full',axiom,
c_24__type__2642___24t(chahn_2eHahnSets_2eset__full) ).
fof('$_typeof_hahn.HahnSets.set_inter',axiom,
c_24__type__217___24t(chahn_2eHahnSets_2eset__inter) ).
fof('$_typeof_hahn.HahnSets.set_map',axiom,
c_24__type__1046___24t(chahn_2eHahnSets_2eset__map) ).
fof('$_typeof_hahn.HahnSets.set_minus',axiom,
c_24__type__217___24t(chahn_2eHahnSets_2eset__minus) ).
fof('$_typeof_hahn.HahnSets.set_subset',axiom,
c_24__type__1027___24t(chahn_2eHahnSets_2eset__subset) ).
fof('$_typeof_hahn.HahnSets.set_union',axiom,
c_24__type__217___24t(chahn_2eHahnSets_2eset__union) ).
fof('Coq.Arith.Between.between_ind',axiom,
! [V0__P] :
( c_24__type__258___24t(V0__P)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__P] :
( c_24__type__258___24t(V2__P)
=> ( p(happ(V2__P,V1__k))
=> ( ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V4__l)
=> ( p(happ(V2__P,V4__l))
=> ( p(happ(V0__P,V4__l))
=> p(happ(V2__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__l))) ) ) ) )
=> ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V1__k,V5__n)
=> p(happ(V2__P,V5__n)) ) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.between_not_exists',axiom,
! [V0__P] :
( c_24__type__258___24t(V0__P)
=> ! [V1__Q] :
( c_24__type__258___24t(V1__Q)
=> ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__l)
=> ( cCoq_2eArith_2eBetween_2ebetween___24a3(V0__P,V2__k,V3__l)
=> ( ! [V5__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__n)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V2__k,V3__l,V5__n)
=> ( p(happ(V0__P,V5__n))
=> ~ p(happ(V1__Q,V5__n)) ) ) )
=> ~ cCoq_2eArith_2eBetween_2eexists__between___24a3(V1__Q,V2__k,V3__l) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.exists_le_S',axiom,
! [V0__Q] :
( c_24__type__258___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ( cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__k),V2__l)) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_S',axiom,
! [V0__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__r)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r)
=> cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__q),V2__r) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_exists',axiom,
! [V0__Q] :
( c_24__type__258___24t(V0__Q)
=> ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
=> ! [V3__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__r)
=> ( cCoq_2eArith_2eBetween_2ein__int___24a3(V1__k,V2__l,V3__r)
=> ( p(happ(V0__Q,V3__r))
=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V0__Q,V1__k,V2__l) ) ) ) ) ) ) ).
fof('Coq.Arith.Between.in_int_intro',axiom,
! [V0__p] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__q)
=> ! [V2__r] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__r)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__p,V2__r))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__r,V1__q))
=> cCoq_2eArith_2eBetween_2ein__int___24a3(V0__p,V1__q,V2__r) ) ) ) ) ) ).
fof('Coq.Arith.Compare_dec.dec_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.dec_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Compare_dec.not_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.Compare_dec.not_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m) ) ) ) ).
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)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
| V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.Lt.lt_n_Sm_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.add_mod_idemp_l',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( V2__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,V2__n),V1__b),V2__n) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V0__a,V1__b),V2__n) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n)) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_0_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO))
<=> V0__n = cCoq_2eInit_2eDatatypes_2eO ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_antisymm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n))
=> V0__n = V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
<=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
& V0__n != V1__m ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1068,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__258,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_irrefl',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x)) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n))) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1068,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__258,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.mod_mod',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( V1__n != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,V1__n),V1__n) = cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,V1__n) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.mod_same',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ( V0__a != cCoq_2eInit_2eDatatypes_2eO
=> cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,V0__a) = cCoq_2eInit_2eDatatypes_2eO ) ) ).
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)
=> ( p(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.mod_upper_bound',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> ! [V1__b] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__b)
=> ( V1__b != cCoq_2eInit_2eDatatypes_2eO
=> p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,V1__b),V1__b)) ) ) ) ).
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)
=> ( p(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.Peano_dec.dec_eq_nat',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__378___24a2(V0__n,V1__m)) ) ) ).
fof('Coq.Arith.Wf_nat.dec_inh_nat_subset_has_unique_least_element',axiom,
! [V0__P] :
( c_24__type__258___24t(V0__P)
=> ( ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(happ(V0__P,V1__n))
| ~ p(happ(V0__P,V1__n)) ) )
=> ( ? [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
& p(happ(V0__P,V2__n)) )
=> cCoq_2eArith_2eWf__nat_2ehas__unique__least__element___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2ePeano_2ele,V0__P) ) ) ) ).
fof('Coq.Bool.Bool.diff_false_true',axiom,
cCoq_2eInit_2eDatatypes_2efalse != cCoq_2eInit_2eDatatypes_2etrue ).
fof('Coq.Init.Datatypes.list_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__405___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__258___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
=> ( ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.Init.Peano.le_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> p(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)
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n)) ) ).
fof('Coq.Init.Peano.plus_n_Sm',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).
fof('Coq.Init.Specif.sumbool_ind',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ! [V2__P] :
( c_24__type__1117___24t(V0__A,V1__B,V2__P)
=> ( ( p(V0__A)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__A,V1__B))) )
=> ( ( p(V1__B)
=> p(happ(V2__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__A,V1__B))) )
=> ! [V5__s] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__A,V1__B,V5__s)
=> p(happ(V2__P,V5__s)) ) ) ) ) ) ) ).
fof('Coq.Init.Tactics.decide_left',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ! [V1__decide] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__C,c_24__prop__33563___24a1(V0__C),V1__decide)
=> ( p(V0__C)
=> ! [V3__P] :
( c_24__type__33565___24t(V0__C,V3__P)
=> ( ( p(V0__C)
=> p(happ(V3__P,cCoq_2eInit_2eSpecif_2eleft___24a2(V0__C,c_24__prop__33568___24a1(V0__C)))) )
=> p(happ(V3__P,V1__decide)) ) ) ) ) ) ).
fof('Coq.Init.Tactics.decide_right',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ! [V1__decide] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(V0__C,c_24__prop__33570___24a1(V0__C),V1__decide)
=> ( ~ p(V0__C)
=> ! [V3__P] :
( c_24__type__33565___24t(V0__C,V3__P)
=> ( ( ~ p(V0__C)
=> p(happ(V3__P,cCoq_2eInit_2eSpecif_2eright___24a2(V0__C,c_24__prop__33572___24a1(V0__C)))) )
=> p(happ(V3__P,V1__decide)) ) ) ) ) ) ).
fof('Coq.Init.Wf.Acc_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__60___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__4___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V4__y),V3__x))
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__y) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V3__x))
=> p(happ(V2__P,V5__y)) ) )
=> p(happ(V2__P,V3__x)) ) ) )
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__x)
=> p(happ(V2__P,V4__x)) ) ) ) ) ) ) ).
fof('Coq.Init.Wf.Acc_intro',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__60___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ( ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V2__x))
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V3__y) ) )
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x) ) ) ) ) ).
fof('Coq.Lists.List.Exists_Forall_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__P,V3__x))
| ~ p(happ(V1__P,V3__x)) ) )
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,c_24__lam__22265___24a2(V0__A,V1__P),V2__l)
<=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ).
fof('Coq.Lists.List.Exists_dec_subproof0',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eExists___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( p(happ(V1__P,V2__x))
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V3__l)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_dec_subproof',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l_27)
=> ( ~ p(happ(V1__P,V2__a))
=> ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l_27)) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_forall',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V2__l))
=> p(happ(V1__P,V3__x)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.Forall_nil',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) ) ) ).
fof('Coq.Lists.List.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__405___24t(V0__A,V1__P)
=> ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__x,V4__l))
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> ( p(happ(V1__P,V4__l))
=> p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__x,V4__l))) ) ) ) ) )
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__l)
=> p(happ(V1__P,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.app_length',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ).
fof('Coq.Lists.List.in_app_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> ! [V2__l_27] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)))
<=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l))
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__l_27)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.in_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l))
=> ? [V4__l1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
& ? [V5__l2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
& V2__l = cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__x,V5__l2)) ) ) ) ) ) ) ).
fof('Coq.Lists.List.neg_Forall_Exists_neg',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__4___24t(V0__A,V1__P)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ! [V3___24Anonymous] :
( c_24__type__22270___24t(V0__A,V1__P,V3___24Anonymous)
=> ( ~ cCoq_2eLists_2eList_2eForall___24a3(V0__A,V1__P,V2__l)
=> cCoq_2eLists_2eList_2eExists___24a3(V0__A,c_24__lam__22276___24a2(V0__A,V1__P),V2__l) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_hd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__60___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( p(happ(happ(V1__eqA,V2__x),V3__y))
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_cons_tl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__60___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.InA_eqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__60___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__eqA,V4__x),V5__y))
=> ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V4__x,V3__l)
=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V5__y,V3__l) ) ) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.NoDupA_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__60___24t(V0__A,V1__eqA)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V3__l)
=> ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,V3__l)
=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V0__A,V1__eqA,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,V3__l)) ) ) ) ) ) ) ).
fof('Coq.Lists.SetoidList.eqasym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eqA] :
( c_24__type__60___24t(V0__A,V1__eqA)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__eqA)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__eqA) ) ) ) ).
fof('Coq.Logic.ChoiceFacts.fun_reification_descr_computational_excluded_middle_in_prop_context',axiom,
( ! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalRelReification__on___24a2(V0__A,V1__B) ) )
=> ( ! [V1__P] :
( cProp___24t(V1__P)
=> ( p(V1__P)
| ~ p(V1__P) ) )
=> ! [V2__C] :
( cProp___24t(V2__C)
=> ( ! [V3___24Anonymous] :
( c_24__type__13057___24t(V3___24Anonymous)
=> p(V2__C) )
=> p(V2__C) ) ) ) ) ).
fof('Coq.Logic.ChoiceFacts.relative_non_contradiction_of_definite_descr',axiom,
! [V0__C] :
( cProp___24t(V0__C)
=> ( ! [V1___24Anonymous] :
( c_24__type__15964___24t(V1___24Anonymous)
=> p(V0__C) )
=> ( ! [V2__A] :
( cType___24t(V2__A)
=> ! [V3__B] :
( cType___24t(V3__B)
=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalRelReification__on___24a2(V2__A,V3__B) ) )
=> p(V0__C) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.excluded_middle_entails_unrestricted_minimization',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__P] :
( c_24__type__258___24t(V1__P)
=> cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V1__P) ) ) ).
fof('Coq.Logic.ClassicalFacts.p2p1',axiom,
! [V0__or] :
( c_24__type__14829___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__14892___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__16049___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__14829___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__14892___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__16117___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__14829___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__14892___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__16215___24a1(V7__A))) )
=> ! [V8__B] :
( cProp___24t(V8__B)
=> ( p(V8__B)
=> ( p(V8__B)
=> c_24Proof = c_24Proof ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.proof_irrelevance_cci',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V1__B)
=> ( p(V1__B)
=> c_24Proof = c_24Proof ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wem_proof_irrelevance_cci',axiom,
( ! [V0__A] :
( cProp___24t(V0__A)
=> ( ~ ~ p(V0__A)
| ~ p(V0__A) ) )
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( p(V1__B)
=> ( p(V1__B)
=> ~ ( c_24Proof != c_24Proof ) ) ) ) ) ).
fof('Coq.Logic.ClassicalFacts.wproof_irrelevance_cc',axiom,
! [V0__or] :
( c_24__type__14829___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__14892___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__14917___24a1(V7__A)),c_24__prop__14918___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.all_not_not_ex',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4___24t(V0__U,V1__P)
=> ( ! [V2__n] :
( t(V2__n,V0__U)
=> ~ p(happ(V1__P,V2__n)) )
=> ~ ? [V3__n] :
( t(V3__n,V0__U)
& p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.ex_not_not_all',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4___24t(V0__U,V1__P)
=> ( ? [V2__n] :
( t(V2__n,V0__U)
& ~ p(happ(V1__P,V2__n)) )
=> ~ ! [V3__n] :
( t(V3__n,V0__U)
=> p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_ex_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_all_not_ex',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4___24t(V0__U,V1__P)
=> ( ~ ! [V2__n] :
( t(V2__n,V0__U)
=> ~ p(happ(V1__P,V2__n)) )
=> ? [V3__n] :
( t(V3__n,V0__U)
& p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_ex_all_not',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4___24t(V0__U,V1__P)
=> ( ~ ? [V2__n] :
( t(V2__n,V0__U)
& p(happ(V1__P,V2__n)) )
=> ! [V3__n] :
( t(V3__n,V0__U)
=> ~ p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Pred_Type.not_ex_not_all',axiom,
! [V0__U] :
( cType___24t(V0__U)
=> ! [V1__P] :
( c_24__type__4___24t(V0__U,V1__P)
=> ( ~ ? [V2__n] :
( t(V2__n,V0__U)
& ~ p(happ(V1__P,V2__n)) )
=> ! [V3__n] :
( t(V3__n,V0__U)
=> p(happ(V1__P,V3__n)) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.and_not_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
& ~ p(V1__Q) )
=> ~ ( p(V0__P)
| p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ( p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.imply_to_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( p(V0__P)
=> p(V1__Q) )
=> ( ~ p(V0__P)
| p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_and_or',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
& p(V1__Q) )
=> ( ~ p(V0__P)
| ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_imply_elim2',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
=> p(V1__Q) )
=> ~ p(V1__Q) ) ) ) ).
fof('Coq.Logic.Classical_Prop.not_or_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ~ ( p(V0__P)
| p(V1__Q) )
=> ( ~ p(V0__P)
& ~ p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.or_not_and',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
| ~ p(V1__Q) )
=> ~ ( p(V0__P)
& p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Classical_Prop.or_to_imply',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( ( ~ p(V0__P)
| p(V1__Q) )
=> ( p(V0__P)
=> p(V1__Q) ) ) ) ) ).
fof('Coq.Logic.Decidable.contrapositive',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> ( p(V1__B)
=> p(c_24False) ) )
<=> ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__570___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.dec_not',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__571___24a1(V0__A)) ) ) ).
fof('Coq.Logic.Decidable.dec_not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ( ~ p(V0__P)
=> p(c_24False) )
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.dec_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__569___24a2(V0__A,V1__B)) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_not_l',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> p(V1__B) )
<=> ( p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.imp_simp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
=> p(V1__B) )
=> ( ~ p(V0__A)
| p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
& p(V1__B) )
=> ( ~ p(V0__A)
| ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_and_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
& p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
=> ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> ( ~ ( p(V0__A)
<=> p(V1__B) )
=> ( ( p(V0__A)
& ~ p(V1__B) )
| ( ~ p(V0__A)
& p(V1__B) ) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_imp',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ~ ( p(V0__A)
=> p(V1__B) )
=> ( p(V0__A)
& ~ p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_imp_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(V1__B) )
=> p(c_24False) )
<=> ( p(V0__A)
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_not',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( ~ ~ p(V0__P)
=> p(V0__P) ) ) ) ).
fof('Coq.Logic.Decidable.not_not_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
=> p(c_24False) )
<=> p(V0__A) ) ) ) ).
fof('Coq.Logic.Decidable.not_or',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ~ ( p(V0__A)
| p(V1__B) )
=> ( ~ p(V0__A)
& ~ p(V1__B) ) ) ) ) ).
fof('Coq.Logic.Decidable.not_or_iff',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( ( ( p(V0__A)
| p(V1__B) )
=> p(c_24False) )
<=> ( ( p(V0__A)
=> p(c_24False) )
& ( p(V1__B)
=> p(c_24False) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_l_iff_1',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( ( p(V0__A)
=> p(c_24False) )
| p(V1__B) )
<=> ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_l_iff_2',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> ( ( ( p(V0__A)
=> p(c_24False) )
| p(V1__B) )
<=> ( p(V0__A)
=> p(V1__B) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_r_iff_1',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
=> ( ( p(V0__A)
| ( p(V1__B)
=> p(c_24False) ) )
<=> ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
fof('Coq.Logic.Decidable.or_not_r_iff_2',axiom,
! [V0__A] :
( cProp___24t(V0__A)
=> ! [V1__B] :
( cProp___24t(V1__B)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
=> ( ( p(V0__A)
| ( p(V1__B)
=> p(c_24False) ) )
<=> ( p(V1__B)
=> p(V0__A) ) ) ) ) ) ).
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.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
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_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3233,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__3155,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_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.Numbers.BinNums.positive_ind',axiom,
! [V0__P] :
( c_24__type__12813___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.add_comm',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V0__p,V1__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__q,V0__p) ) ) ).
fof('Coq.PArith.BinPos.Pos.compare_spec',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(c_24__prop__35227___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V1__y),cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__y,V0__x),cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y)) ) ) ).
fof('Coq.PArith.BinPos.Pos.sub_add',axiom,
! [V0__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
=> ! [V1__q] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__q)
=> ( p(cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V1__q,V0__p))
=> cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__p,V1__q),V1__q) = V0__p ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V6__z)
=> p(happ(V3__P,V6__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_refl_trans_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__4___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( p(happ(V2__P,V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V3__z)
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_is_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rst1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rst_rstn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_idempotent',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_is_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rt1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_rtn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_rtn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_t1n_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_tn1_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_trans_transp_permute',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__R),V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__R),V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Operators_Properties.rt1n_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__4___24t(V0__A,V2__P)
=> ! [V3__z] :
( t(V3__z,V0__A)
=> ( p(happ(V2__P,V3__z))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__R,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__y,V3__z)
=> ( p(happ(V2__P,V6__y))
=> p(happ(V2__P,V5__x)) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V6__x,V3__z)
=> p(happ(V2__P,V6__x)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_PER',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_order',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.Build_preorder',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R) ) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_antisym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.ord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.per_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Definitions.preord_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V0__A,V1__R)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__R) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( p(happ(V3__P,V2__x))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V4__x),V5__y))
| p(happ(happ(V1__R,V5__y),V4__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( ( p(happ(happ(V1__R,V5__y),V6__z))
| p(happ(happ(V1__R,V6__z),V5__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_sym_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> p(happ(happ(V2__P,V6__y),V5__x)) ) ) ) )
=> ( ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__y] :
( t(V7__y,V0__A)
=> ! [V8__z] :
( t(V8__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V6__x,V7__y)
=> ( p(happ(happ(V2__P,V6__x),V7__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__y,V8__z)
=> ( p(happ(happ(V2__P,V7__y),V8__z))
=> p(happ(happ(V2__P,V6__x),V8__z)) ) ) ) ) ) ) )
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ! [V8__a] :
( t(V8__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V7__a,V8__a)
=> p(happ(happ(V2__P,V7__a),V8__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V2__P,V3__x),V3__x)) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( p(happ(V3__P,V2__x))
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_refl_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> p(happ(happ(V2__P,V4__x),V4__x)) )
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ! [V7__z] :
( t(V7__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V5__x,V6__y)
=> ( p(happ(happ(V2__P,V5__x),V6__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__y,V7__z)
=> ( p(happ(happ(V2__P,V6__y),V7__z))
=> p(happ(happ(V2__P,V5__x),V7__z)) ) ) ) ) ) ) )
=> ! [V6__x] :
( t(V6__x,V0__A)
=> ! [V7__a] :
( t(V7__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V6__x,V7__a)
=> p(happ(happ(V2__P,V6__x),V7__a)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_1n_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_n1_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V4__y))
=> p(happ(V3__P,V4__y)) ) )
=> ( ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V1__R,V5__y),V6__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V5__y)
=> ( p(happ(V3__P,V5__y))
=> p(happ(V3__P,V6__z)) ) ) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V6__a)
=> p(happ(V3__P,V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.clos_trans_sind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__60___24t(V0__A,V2__P)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R,V3__x),V4__y))
=> p(happ(happ(V2__P,V3__x),V4__y)) ) ) )
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V4__x,V5__y)
=> ( p(happ(happ(V2__P,V4__x),V5__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__y,V6__z)
=> ( p(happ(happ(V2__P,V5__y),V6__z))
=> p(happ(happ(V2__P,V4__x),V6__z)) ) ) ) ) ) ) )
=> ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V5__x,V6__a)
=> p(happ(happ(V2__P,V5__x),V6__a)) ) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V2__x),V3__y))
| p(happ(happ(V1__R,V3__y),V2__x)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V2__x) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rst_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rstn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( ( p(happ(happ(V1__R,V3__y),V4__z))
| p(happ(happ(V1__R,V4__z),V3__y)) )
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V2__x) ) ) ) ).
fof('Coq.Relations.Relation_Operators.rtn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t1n_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V3__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V3__y,V4__z)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__R,V2__x),V3__y))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y) ) ) ) ) ) ).
fof('Coq.Relations.Relation_Operators.tn1_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__R,V3__y),V4__z))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V3__y)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V0__A,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).
fof('Coq.Relations.Relations.inverse_image_of_equivalence',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V0__A,c_24__lam__3076___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Build_Setoid_Theory',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__A,V1__R)
=> ( cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__A,V1__R)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__A,V1__R) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> p(happ(happ(V1__Aeq,V3__x),V3__x)) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> p(happ(happ(V1__Aeq,V4__y),V3__x)) ) ) ) ) ) ) ).
fof('Coq.Setoids.Setoid.Seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__A,V1__Aeq)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ! [V5__z] :
( t(V5__z,V0__A)
=> ( p(happ(happ(V1__Aeq,V3__x),V4__y))
=> ( p(happ(happ(V1__Aeq,V4__y),V5__z))
=> p(happ(happ(V1__Aeq,V3__x),V5__z)) ) ) ) ) ) ) ) ) ).
fof('Coq.ZArith.BinInt.Z.compare_refl',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V0__x) = cCoq_2eInit_2eDatatypes_2eEq ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).
fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).
fof('Coq.ZArith.Znat.inj_eq',axiom,
! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( V0__x = V1__y
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).
fof('Coq.ZArith.Znat.inj_ge',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_gt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_le',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_lt',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
fof('Coq.ZArith.Znat.inj_neq',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( cCoq_2eZArith_2eZnat_2eneq___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ) ).
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.ZArith.auxiliary.Zge_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zle_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zlt_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n))) ) ) ) ).
fof('Coq.ZArith.auxiliary.Zne_left',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
=> ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).
fof('Coq.micromega.OrderedRing.Req_em',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V7__req,V11__n),V12__m))
| ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_neq',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
=> ~ p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rlt_trichotomy',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V12__m))
| p(happ(happ(V7__req,V11__n),V12__m))
| p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rneq_0_1',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ~ p(happ(happ(V7__req,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rneq_symm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ~ p(happ(happ(V7__req,V11__n),V12__m))
=> ~ p(happ(happ(V7__req,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V11__n),V1__rO))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_neq_0',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( ( ~ p(happ(happ(V7__req,V11__n),V1__rO))
& ~ p(happ(happ(V7__req,V12__m),V1__rO)) )
=> ~ p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V12__m),V1__rO))
=> p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> ! [V11__n] :
( t(V11__n,V0__R)
=> ! [V12__m] :
( t(V12__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V11__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V12__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.mk_SOR_theory',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V7__req)
=> ( ! [V11__x1] :
( t(V11__x1,V0__R)
=> ! [V12__x2] :
( t(V12__x2,V0__R)
=> ( p(happ(happ(V7__req,V11__x1),V12__x2))
=> ! [V14__y1] :
( t(V14__y1,V0__R)
=> ! [V15__y2] :
( t(V15__y2,V0__R)
=> ( p(happ(happ(V7__req,V14__y1),V15__y2))
=> p(happ(happ(V7__req,happ(happ(V3__rplus,V11__x1),V14__y1)),happ(happ(V3__rplus,V12__x2),V15__y2))) ) ) ) ) ) )
=> ( ! [V12__x1] :
( t(V12__x1,V0__R)
=> ! [V13__x2] :
( t(V13__x2,V0__R)
=> ( p(happ(happ(V7__req,V12__x1),V13__x2))
=> ! [V15__y1] :
( t(V15__y1,V0__R)
=> ! [V16__y2] :
( t(V16__y2,V0__R)
=> ( p(happ(happ(V7__req,V15__y1),V16__y2))
=> p(happ(happ(V7__req,happ(happ(V4__rtimes,V12__x1),V15__y1)),happ(happ(V4__rtimes,V13__x2),V16__y2))) ) ) ) ) ) )
=> ( ! [V13__x1] :
( t(V13__x1,V0__R)
=> ! [V14__x2] :
( t(V14__x2,V0__R)
=> ( p(happ(happ(V7__req,V13__x1),V14__x2))
=> p(happ(happ(V7__req,happ(V6__ropp,V13__x1)),happ(V6__ropp,V14__x2))) ) ) )
=> ( ! [V14__x1] :
( t(V14__x1,V0__R)
=> ! [V15__x2] :
( t(V15__x2,V0__R)
=> ( p(happ(happ(V7__req,V14__x1),V15__x2))
=> ! [V17__y1] :
( t(V17__y1,V0__R)
=> ! [V18__y2] :
( t(V18__y2,V0__R)
=> ( p(happ(happ(V7__req,V17__y1),V18__y2))
=> ( p(happ(happ(V8__rle,V14__x1),V17__y1))
<=> p(happ(happ(V8__rle,V15__x2),V18__y2)) ) ) ) ) ) ) )
=> ( ! [V15__x1] :
( t(V15__x1,V0__R)
=> ! [V16__x2] :
( t(V16__x2,V0__R)
=> ( p(happ(happ(V7__req,V15__x1),V16__x2))
=> ! [V18__y1] :
( t(V18__y1,V0__R)
=> ! [V19__y2] :
( t(V19__y2,V0__R)
=> ( p(happ(happ(V7__req,V18__y1),V19__y2))
=> ( p(happ(happ(V9__rlt,V15__x1),V18__y1))
<=> p(happ(happ(V9__rlt,V16__x2),V19__y2)) ) ) ) ) ) ) )
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req)
=> ( ! [V17__n] :
( t(V17__n,V0__R)
=> p(happ(happ(V8__rle,V17__n),V17__n)) )
=> ( ! [V18__n] :
( t(V18__n,V0__R)
=> ! [V19__m] :
( t(V19__m,V0__R)
=> ( p(happ(happ(V8__rle,V18__n),V19__m))
=> ( p(happ(happ(V8__rle,V19__m),V18__n))
=> p(happ(happ(V7__req,V18__n),V19__m)) ) ) ) )
=> ( ! [V19__n] :
( t(V19__n,V0__R)
=> ! [V20__m] :
( t(V20__m,V0__R)
=> ! [V21__p] :
( t(V21__p,V0__R)
=> ( p(happ(happ(V8__rle,V19__n),V20__m))
=> ( p(happ(happ(V8__rle,V20__m),V21__p))
=> p(happ(happ(V8__rle,V19__n),V21__p)) ) ) ) ) )
=> ( ! [V20__n] :
( t(V20__n,V0__R)
=> ! [V21__m] :
( t(V21__m,V0__R)
=> ( p(happ(happ(V9__rlt,V20__n),V21__m))
<=> ( p(happ(happ(V8__rle,V20__n),V21__m))
& ~ p(happ(happ(V7__req,V20__n),V21__m)) ) ) ) )
=> ( ! [V21__n] :
( t(V21__n,V0__R)
=> ! [V22__m] :
( t(V22__m,V0__R)
=> ( p(happ(happ(V9__rlt,V21__n),V22__m))
| p(happ(happ(V7__req,V21__n),V22__m))
| p(happ(happ(V9__rlt,V22__m),V21__n)) ) ) )
=> ( ! [V22__n] :
( t(V22__n,V0__R)
=> ! [V23__m] :
( t(V23__m,V0__R)
=> ! [V24__p] :
( t(V24__p,V0__R)
=> ( p(happ(happ(V8__rle,V22__n),V23__m))
=> p(happ(happ(V8__rle,happ(happ(V3__rplus,V24__p),V22__n)),happ(happ(V3__rplus,V24__p),V23__m))) ) ) ) )
=> ( ! [V23__n] :
( t(V23__n,V0__R)
=> ! [V24__m] :
( t(V24__m,V0__R)
=> ( p(happ(happ(V9__rlt,V1__rO),V23__n))
=> ( p(happ(happ(V9__rlt,V1__rO),V24__m))
=> p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V23__n),V24__m))) ) ) ) )
=> ( ~ p(happ(happ(V7__req,V1__rO),V2__rI))
=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.rlt_morph_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__60___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__4___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.OrderedRing.sor_setoid_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__rlt] :
( c_24__type__60___24t(V0__R,V9__rlt)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__eval] :
( c_24__type__4___24t(V0__A,V1__eval)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
=> ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l))
<=> ( p(happ(V1__eval,V2__a))
& cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V1__eval,V3__l) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_app',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__t)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__4___24t(V0__A,V3__eval)
=> ( ! [V4__d] :
( t(V4__d,V0__A)
=> ( p(happ(V3__eval,V4__d))
| ~ p(happ(V3__eval,V4__d)) ) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__t,V2__a))
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V1__t)
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Refl.not_make_conj_cons',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__t] :
( t(V1__t,V0__A)
=> ! [V2__a] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__a)
=> ! [V3__eval] :
( c_24__type__4___24t(V0__A,V3__eval)
=> ( ( p(happ(V3__eval,V1__t))
| ~ p(happ(V3__eval,V1__t)) )
=> ( ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V1__t,V2__a))
=> ( ~ p(happ(V3__eval,V1__t))
| ~ cCoq_2emicromega_2eRefl_2emake__conj___24a3(V0__A,V3__eval,V2__a) ) ) ) ) ) ) ) ).
fof('Coq.micromega.RingMicromega.mk_SOR_addon',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__rplus] :
( c_24__type__5967___24t(V0__R,V3__rplus)
=> ! [V4__rtimes] :
( c_24__type__5967___24t(V0__R,V4__rtimes)
=> ! [V5__rminus] :
( c_24__type__5967___24t(V0__R,V5__rminus)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ! [V8__rle] :
( c_24__type__60___24t(V0__R,V8__rle)
=> ! [V9__C] :
( cType___24t(V9__C)
=> ! [V10__cO] :
( t(V10__cO,V9__C)
=> ! [V11__cI] :
( t(V11__cI,V9__C)
=> ! [V12__cplus] :
( c_24__type__10645___24t(V0__R,V9__C,V12__cplus)
=> ! [V13__ctimes] :
( c_24__type__10645___24t(V0__R,V9__C,V13__ctimes)
=> ! [V14__cminus] :
( c_24__type__10645___24t(V0__R,V9__C,V14__cminus)
=> ! [V15__copp] :
( c_24__type__10659___24t(V0__R,V9__C,V15__copp)
=> ! [V16__ceqb] :
( c_24__type__10666___24t(V0__R,V9__C,V16__ceqb)
=> ! [V17__cleb] :
( c_24__type__10666___24t(V0__R,V9__C,V17__cleb)
=> ! [V18__phi] :
( c_24__type__10670___24t(V0__R,V9__C,V18__phi)
=> ! [V19__E] :
( cType___24t(V19__E)
=> ! [V20__pow__phi] :
( c_24__type__13329___24t(V0__R,V9__C,V19__E,V20__pow__phi)
=> ! [V21__rpow] :
( c_24__type__13338___24t(V0__R,V9__C,V19__E,V21__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V2__rI,V4__rtimes,V7__req,V19__E,V20__pow__phi,V21__rpow)
=> ( ! [V24__x] :
( t(V24__x,V9__C)
=> ! [V25__y] :
( t(V25__y,V9__C)
=> ( happ(happ(V16__ceqb,V24__x),V25__y) = cCoq_2eInit_2eDatatypes_2efalse
=> ~ p(happ(happ(V7__req,happ(V18__phi,V24__x)),happ(V18__phi,V25__y))) ) ) )
=> ( ! [V25__x] :
( t(V25__x,V9__C)
=> ! [V26__y] :
( t(V26__y,V9__C)
=> ( happ(happ(V17__cleb,V25__x),V26__y) = cCoq_2eInit_2eDatatypes_2etrue
=> p(happ(happ(V8__rle,happ(V18__phi,V25__x)),happ(V18__phi,V26__y))) ) ) )
=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.Tauto.no_middle_eval_tt',axiom,
! [V0__Env] :
( cType___24t(V0__Env)
=> ! [V1__Term_27] :
( cType___24t(V1__Term_27)
=> ! [V2__Annot] :
( cType___24t(V2__Annot)
=> ! [V3__eval_27] :
( c_24__type__1196___24t(V0__Env,V1__Term_27,V3__eval_27)
=> ( ! [V4__env] :
( t(V4__env,V0__Env)
=> ! [V5__d] :
( t(V5__d,V1__Term_27)
=> ( p(happ(happ(V3__eval_27,V4__env),V5__d))
| ~ p(happ(happ(V3__eval_27,V4__env),V5__d)) ) ) )
=> ! [V5__env] :
( t(V5__env,V0__Env)
=> ! [V6__a] :
( cCoq_2eInit_2eDatatypes_2eprod___24t(V1__Term_27,V2__Annot,V6__a)
=> ( cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V5__env,V6__a)
| ~ cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V0__Env,V1__Term_27,V2__Annot,V3__eval_27,V5__env,V6__a) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_ind',axiom,
! [V0__P] :
( c_24__type__3530___24t(V0__P)
=> ( ! [V1__S] :
( cType___24t(V1__S)
=> ! [V2__x] :
( t(V2__x,V1__S)
=> ! [V3__y] :
( t(V3__y,V1__S)
=> p(happ(V0__P,c_24__prop__35139___24a3(V1__S,V2__x,V3__y))) ) ) )
=> ( ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> p(happ(V0__P,c_24__prop__35143___24a2(V2__x,V3__y))) ) )
=> ( ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ! [V4__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V4__s)
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V3__x,V4__s))) ) )
=> ( p(happ(V0__P,c_24True))
=> ( p(happ(V0__P,c_24False))
=> ( ! [V6__P] :
( cProp___24t(V6__P)
=> ! [V7__Q] :
( cProp___24t(V7__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V6__P)
=> ( p(happ(V0__P,V6__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__Q)
=> ( p(happ(V0__P,V7__Q))
=> p(happ(V0__P,c_24__prop__35148___24a2(V6__P,V7__Q))) ) ) ) ) ) )
=> ( ! [V7__P] :
( cProp___24t(V7__P)
=> ! [V8__Q] :
( cProp___24t(V8__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__P)
=> ( p(happ(V0__P,V7__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__Q)
=> ( p(happ(V0__P,V8__Q))
=> p(happ(V0__P,c_24__prop__35155___24a2(V7__P,V8__Q))) ) ) ) ) ) )
=> ( ! [V8__P] :
( cProp___24t(V8__P)
=> ! [V9__Q] :
( cProp___24t(V9__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__P)
=> ( p(happ(V0__P,V8__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__Q)
=> ( p(happ(V0__P,V9__Q))
=> p(happ(V0__P,c_24__prop__35162___24a2(V8__P,V9__Q))) ) ) ) ) ) )
=> ( ! [V9__P] :
( cProp___24t(V9__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__P)
=> ( p(happ(V0__P,V9__P))
=> p(happ(V0__P,c_24__prop__35170___24a1(V9__P))) ) ) )
=> ! [V10__P] :
( cProp___24t(V10__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V10__P)
=> p(happ(V0__P,V10__P)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_sind',axiom,
! [V0__P] :
( c_24__type__3530___24t(V0__P)
=> ( ! [V1__S] :
( cType___24t(V1__S)
=> ! [V2__x] :
( t(V2__x,V1__S)
=> ! [V3__y] :
( t(V3__y,V1__S)
=> p(happ(V0__P,c_24__prop__35174___24a3(V1__S,V2__x,V3__y))) ) ) )
=> ( ! [V2__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
=> ! [V3__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
=> p(happ(V0__P,c_24__prop__35178___24a2(V2__x,V3__y))) ) )
=> ( ! [V3__x] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V3__x)
=> ! [V4__s] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V4__s)
=> p(happ(V0__P,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V3__x,V4__s))) ) )
=> ( p(happ(V0__P,c_24True))
=> ( p(happ(V0__P,c_24False))
=> ( ! [V6__P] :
( cProp___24t(V6__P)
=> ! [V7__Q] :
( cProp___24t(V7__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V6__P)
=> ( p(happ(V0__P,V6__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__Q)
=> ( p(happ(V0__P,V7__Q))
=> p(happ(V0__P,c_24__prop__35183___24a2(V6__P,V7__Q))) ) ) ) ) ) )
=> ( ! [V7__P] :
( cProp___24t(V7__P)
=> ! [V8__Q] :
( cProp___24t(V8__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V7__P)
=> ( p(happ(V0__P,V7__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__Q)
=> ( p(happ(V0__P,V8__Q))
=> p(happ(V0__P,c_24__prop__35190___24a2(V7__P,V8__Q))) ) ) ) ) ) )
=> ( ! [V8__P] :
( cProp___24t(V8__P)
=> ! [V9__Q] :
( cProp___24t(V9__Q)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V8__P)
=> ( p(happ(V0__P,V8__P))
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__Q)
=> ( p(happ(V0__P,V9__Q))
=> p(happ(V0__P,c_24__prop__35197___24a2(V8__P,V9__Q))) ) ) ) ) ) )
=> ( ! [V9__P] :
( cProp___24t(V9__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V9__P)
=> ( p(happ(V0__P,V9__P))
=> p(happ(V0__P,c_24__prop__35205___24a1(V9__P))) ) ) )
=> ! [V10__P] :
( cProp___24t(V10__P)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V10__P)
=> p(happ(V0__P,V10__P)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetLogicalFacts.test_pull',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__Q)
=> ( ~ p(c_24True)
=> ( ~ p(c_24False)
=> ( ~ ~ p(V0__P)
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
=> ~ p(V2__R) )
=> ( ( ( p(V0__P)
& p(V1__Q) )
| ~ p(V2__R) )
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
| p(V2__R) )
=> ( ( p(V2__R)
| ~ ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V2__R)
| ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V0__P)
=> p(V2__R) )
=> ( ( ~ ( p(V2__R)
=> p(V0__P) )
& ~ ( p(V1__Q)
=> p(V2__R) ) )
=> ( ( ~ p(V0__P)
| ~ p(V2__R) )
=> ( ( p(V0__P)
& ~ p(V2__R) )
=> ( ( ~ p(V2__R)
& p(V0__P) )
=> p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetLogicalFacts.test_push',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ! [V2__R] :
( cProp___24t(V2__R)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
=> ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__Q)
=> ( ~ p(c_24True)
=> ( ~ p(c_24False)
=> ( ~ ~ p(V0__P)
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
=> ~ p(V2__R) )
=> ( ( ( p(V0__P)
& p(V1__Q) )
| ~ p(V2__R) )
=> ( ( ~ ( p(V0__P)
& p(V1__Q) )
| p(V2__R) )
=> ( ( p(V2__R)
| ~ ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V2__R)
| ( p(V0__P)
& p(V1__Q) ) )
=> ( ( ~ p(V0__P)
=> p(V2__R) )
=> ( ~ ( ( p(V2__R)
=> p(V0__P) )
| ( p(V1__Q)
=> p(V2__R) ) )
=> ( ~ ( p(V0__P)
& p(V2__R) )
=> ( ~ ( p(V0__P)
=> p(V2__R) )
=> p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA17',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_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA20',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_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).
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)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> 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.OMEGA7',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)
=> ! [V3__t] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)
=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.OMEGA8',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x)
=> ( 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.fast_OMEGA10',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k1)
=> ! [V6__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V6__k2)
=> ! [V7__P] :
( c_24__type__376___24t(V7__P)
=> ( p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V6__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l1,V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V6__k2)))))
=> p(happ(V7__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),V5__k1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V6__k2)))) ) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA11',axiom,
! [V0__v1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v1)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k1)
=> ! [V5__P] :
( c_24__type__376___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c1,V4__k1)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l1,V4__k1),V3__l2))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v1,V1__c1),V2__l1),V4__k1),V3__l2))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
! [V0__v2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
=> ! [V1__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
=> ! [V2__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
=> ! [V3__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
=> ! [V4__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
=> ! [V5__P] :
( c_24__type__376___24t(V5__P)
=> ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
=> p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__376___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
=> ! [V2__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
=> ! [V3__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
=> ! [V4__P] :
( c_24__type__376___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
=> ! [V2__c2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
=> ! [V3__l1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
=> ! [V4__l2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
=> ! [V5__k2] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
=> ! [V6__P] :
( c_24__type__376___24t(V6__P)
=> ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
=> p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_OMEGA16',axiom,
! [V0__v] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
=> ! [V1__c] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
=> ! [V2__l] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l)
=> ! [V3__k] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__k)
=> ! [V4__P] :
( c_24__type__376___24t(V4__P)
=> ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c,V3__k)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__l,V3__k))))
=> p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c),V2__l),V3__k))) ) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__376___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__376___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_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)
=> ! [V3__P] :
( c_24__type__376___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',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__P] :
( c_24__type__376___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__376___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',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__P] :
( c_24__type__376___24t(V3__P)
=> ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
=> p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__376___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor2',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__376___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__376___24t(V2__P)
=> ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__P] :
( c_24__type__376___24t(V2__P)
=> ( p(happ(V2__P,V1__y))
=> p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).
fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__P] :
( c_24__type__376___24t(V1__P)
=> ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
=> p(happ(V1__P,V0__x)) ) ) ) ).
fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ? [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
& cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0)) ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_1_neq_0',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ~ p(happ(happ(V9__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AF_AR',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFdiv_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ! [V12__q] :
( t(V12__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V11__p),V12__q)),happ(happ(V4__rmul,V11__p),happ(V8__rinv,V12__q)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.AFinv_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_1_neq_0',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ~ p(happ(happ(V9__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.F_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.Fdiv_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ! [V12__q] :
( t(V12__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V11__p),V12__q)),happ(happ(V4__rmul,V11__p),happ(V8__rinv,V12__q)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.Finv_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V11__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V11__p)),V11__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3_Reflexive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__60___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3_Symmetric',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__60___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.R_setoid3_Transitive',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__req] :
( c_24__type__60___24t(V0__R,V1__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V1__req)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V0__R,V1__req) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SF_1_neq_0',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__5967___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__3213___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> ~ p(happ(happ(V7__req,V2__rI),V1__rO)) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SF_SR',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__5967___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__3213___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SFdiv_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__5967___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__3213___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> ! [V9__p] :
( t(V9__p,V0__R)
=> ! [V10__q] :
( t(V10__q,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rdiv,V9__p),V10__q)),happ(happ(V4__rmul,V9__p),happ(V6__rinv,V10__q)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.SFinv_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__5967___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__3213___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req)
=> ! [V9__p] :
( t(V9__p,V0__R)
=> ( ~ p(happ(happ(V7__req,V9__p),V1__rO))
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(V6__rinv,V9__p)),V9__p)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.cross_product_eq',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V15__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V17__d),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b)))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V14__a),V15__b)),happ(happ(V7__rdiv,V16__c),V17__d))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.field_is_integral_domain',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r1] :
( t(V13__r1,V0__R)
=> ! [V14__r2] :
( t(V14__r2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__r1),V1__rO))
=> ( ~ p(happ(happ(V9__req,V14__r2),V1__rO))
=> ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V13__r1),V14__r2)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.gen_phiN_inj',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ( p(happ(happ(V9__req,happ(happ(V3__radd,V2__rI),V13__x)),happ(happ(V3__radd,V2__rI),V14__y)))
=> p(happ(happ(V9__req,V13__x),V14__y)) ) ) )
=> ( ! [V14__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__p)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V14__p)),V1__rO)) )
=> ! [V15__x] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V15__x)
=> ! [V16__y] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V16__y)
=> ( p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V15__x)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V16__y)))
=> V15__x = V16__y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.gen_phiPOS_discr_sgn',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ( ! [V13__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V13__p)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V13__p)),V1__rO)) )
=> ! [V14__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__x)
=> ! [V15__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V15__y)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V14__x)),happ(V6__ropp,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V15__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.gen_phiPOS_inj',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ( ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ( p(happ(happ(V9__req,happ(happ(V3__radd,V2__rI),V13__x)),happ(happ(V3__radd,V2__rI),V14__y)))
=> p(happ(happ(V9__req,V13__x),V14__y)) ) ) )
=> ( ! [V14__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__p)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V14__p)),V1__rO)) )
=> ! [V15__x] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V15__x)
=> ! [V16__y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V16__y)
=> ( p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V15__x)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V16__y)))
=> V15__x = V16__y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.gen_phiZ_inj',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ( ! [V13__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V13__p)
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V2__rI,V3__radd,V4__rmul,V13__p)),V1__rO)) )
=> ! [V14__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V14__x)
=> ! [V15__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V15__y)
=> ( p(happ(happ(V9__req,cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V6__ropp,V14__x)),cCoq_2esetoid__ring_2eInitialRing_2egen__phiZ___24a7(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V6__ropp,V15__y)))
=> V14__x = V15__y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_afield',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req)
=> ( ~ p(happ(happ(V9__req,V2__rI),V1__rO))
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__p),V13__q)),happ(happ(V4__rmul,V12__p),happ(V8__rinv,V13__q)))) ) )
=> ( ! [V13__p] :
( t(V13__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V13__p)),V13__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_field',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V9__req)
=> ( ~ p(happ(happ(V9__req,V2__rI),V1__rO))
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__p),V13__q)),happ(happ(V4__rmul,V12__p),happ(V8__rinv,V13__q)))) ) )
=> ( ! [V13__p] :
( t(V13__p,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(V8__rinv,V13__p)),V13__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.mk_sfield',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rdiv] :
( c_24__type__5967___24t(V0__R,V5__rdiv)
=> ! [V6__rinv] :
( c_24__type__3213___24t(V0__R,V6__rinv)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V7__req)
=> ( ~ p(happ(happ(V7__req,V2__rI),V1__rO))
=> ( ! [V10__p] :
( t(V10__p,V0__R)
=> ! [V11__q] :
( t(V11__q,V0__R)
=> p(happ(happ(V7__req,happ(happ(V5__rdiv,V10__p),V11__q)),happ(happ(V4__rmul,V10__p),happ(V6__rinv,V11__q)))) ) )
=> ( ! [V11__p] :
( t(V11__p,V0__R)
=> ( ~ p(happ(happ(V7__req,V11__p),V1__rO))
=> p(happ(happ(V7__req,happ(happ(V4__rmul,happ(V6__rinv,V11__p)),V11__p)),V2__rI)) ) )
=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rdiv,V6__rinv,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.pow_pos_div',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V15__p)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,happ(happ(V7__rdiv,V13__a),V14__b),V15__p)),happ(happ(V7__rdiv,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__a,V15__p)),cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V14__b,V15__p)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.pow_pos_nz',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__p] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V14__p)
=> ( ~ p(happ(happ(V9__req,V13__x),V1__rO))
=> ~ p(happ(happ(V9__req,cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V4__rmul,V13__x,V14__p)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.radd_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5967___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5967___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3213___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__60___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5967___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3213___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv2',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V16__d),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V3__radd,happ(happ(V7__rdiv,V13__a),V14__b)),happ(happ(V7__rdiv,V15__c),V16__d))),happ(happ(V7__rdiv,happ(happ(V3__radd,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V15__c),V14__b))),happ(happ(V4__rmul,V14__b),V16__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv2b',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ! [V17__e] :
( t(V17__e,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V14__b),V17__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V16__d),V17__e)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V3__radd,happ(happ(V7__rdiv,V13__a),happ(happ(V4__rmul,V14__b),V17__e))),happ(happ(V7__rdiv,V15__c),happ(happ(V4__rmul,V16__d),V17__e)))),happ(happ(V7__rdiv,happ(happ(V3__radd,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V15__c),V14__b))),happ(happ(V4__rmul,V14__b),happ(happ(V4__rmul,V16__d),V17__e))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv3b',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V18__e)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V5__rsub,happ(happ(V7__rdiv,V14__a),happ(happ(V4__rmul,V15__b),V18__e))),happ(happ(V7__rdiv,V16__c),happ(happ(V4__rmul,V17__d),V18__e)))),happ(happ(V7__rdiv,happ(happ(V5__rsub,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V16__c),V15__b))),happ(happ(V4__rmul,V15__b),happ(happ(V4__rmul,V17__d),V18__e))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv4',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V16__d),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(happ(V7__rdiv,V13__a),V14__b)),happ(happ(V7__rdiv,V15__c),V16__d))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V13__a),V15__c)),happ(happ(V4__rmul,V14__b),V16__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv4b',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ! [V19__f] :
( t(V19__f,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V19__f)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V19__f)),happ(happ(V4__rmul,V15__b),V18__e))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V16__c),V18__e)),happ(happ(V4__rmul,V17__d),V19__f)))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V16__c)),happ(happ(V4__rmul,V15__b),V17__d)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv5',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> p(happ(happ(V9__req,happ(V6__ropp,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,happ(V6__ropp,V13__a)),V14__b))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv6',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> p(happ(happ(V9__req,happ(V8__rinv,happ(happ(V7__rdiv,V13__a),V14__b))),happ(happ(V7__rdiv,V14__b),V13__a))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv7',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ! [V15__c] :
( t(V15__c,V0__R)
=> ! [V16__d] :
( t(V16__d,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( ~ p(happ(happ(V9__req,V15__c),V1__rO))
=> ( ~ p(happ(happ(V9__req,V16__d),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,happ(happ(V7__rdiv,V13__a),V14__b)),happ(happ(V7__rdiv,V15__c),V16__d))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V13__a),V16__d)),happ(happ(V4__rmul,V14__b),V15__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv7b',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V14__a] :
( t(V14__a,V0__R)
=> ! [V15__b] :
( t(V15__b,V0__R)
=> ! [V16__c] :
( t(V16__c,V0__R)
=> ! [V17__d] :
( t(V17__d,V0__R)
=> ! [V18__e] :
( t(V18__e,V0__R)
=> ! [V19__f] :
( t(V19__f,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V15__b),V19__f)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V16__c),V18__e)),V1__rO))
=> ( ~ p(happ(happ(V9__req,happ(happ(V4__rmul,V17__d),V19__f)),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V18__e)),happ(happ(V4__rmul,V15__b),V19__f))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V16__c),V18__e)),happ(happ(V4__rmul,V17__d),V19__f)))),happ(happ(V7__rdiv,happ(happ(V4__rmul,V14__a),V17__d)),happ(happ(V4__rmul,V15__b),V16__c)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv8',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ! [V14__b] :
( t(V14__b,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__b),V1__rO))
=> ( p(happ(happ(V9__req,V13__a),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V13__a),V14__b)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_ext',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( ! [V12__p] :
( t(V12__p,V0__R)
=> ! [V13__q] :
( t(V13__q,V0__R)
=> ( p(happ(happ(V9__req,V12__p),V13__q))
=> p(happ(happ(V9__req,happ(V8__rinv,V12__p)),happ(V8__rinv,V13__q))) ) ) )
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5967___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3213___24a1(V0__R),V9__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V9__req,V9__req)),V7__rdiv) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_r_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V12__r] :
( t(V12__r,V0__R)
=> ( ~ p(happ(happ(V9__req,V12__r),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V7__rdiv,V12__r),V12__r)),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rdiv_simpl',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q] :
( t(V14__q,V0__R)
=> ( ~ p(happ(happ(V9__req,V14__q),V1__rO))
=> p(happ(happ(V9__req,happ(happ(V4__rmul,V14__q),happ(happ(V7__rdiv,V13__p),V14__q))),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ring_S_inj',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__x] :
( t(V13__x,V0__R)
=> ! [V14__y] :
( t(V14__y,V0__R)
=> ( p(happ(happ(V9__req,happ(happ(V3__radd,V2__rI),V13__x)),happ(happ(V3__radd,V2__rI),V14__y)))
=> p(happ(happ(V9__req,V13__x),V14__y)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rinv_nz',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__a] :
( t(V13__a,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__a),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V8__rinv,V13__a)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5967___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5967___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3213___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__60___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5967___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3213___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V2__rmul) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.rmul_reg_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__p] :
( t(V13__p,V0__R)
=> ! [V14__q1] :
( t(V14__q1,V0__R)
=> ! [V15__q2] :
( t(V15__q2,V0__R)
=> ( ~ p(happ(happ(V9__req,V13__p),V1__rO))
=> ( p(happ(happ(V9__req,happ(happ(V4__rmul,V13__p),V14__q1)),happ(happ(V4__rmul,V13__p),V15__q2)))
=> p(happ(happ(V9__req,V14__q1),V15__q2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext3_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5967___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5967___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3213___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__60___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3213___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_ext_Proper',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5967___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5967___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3213___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__60___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__3213___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req),V3__ropp) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Field_theory.ropp_neq_0',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__rdiv] :
( c_24__type__5967___24t(V0__R,V7__rdiv)
=> ! [V8__rinv] :
( c_24__type__3213___24t(V0__R,V8__rinv)
=> ! [V9__req] :
( c_24__type__60___24t(V0__R,V9__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V9__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V3__radd,V4__rmul,V6__ropp,V9__req)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__rdiv,V8__rinv,V9__req)
=> ! [V13__r] :
( t(V13__r,V0__R)
=> ( ~ p(happ(happ(V9__req,happ(V6__ropp,V2__rI)),V1__rO))
=> ( ~ p(happ(happ(V9__req,V13__r),V1__rO))
=> ~ p(happ(happ(V9__req,happ(V6__ropp,V13__r)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARadd_0_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),V1__rO)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARdistr_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> ! [V12__y] :
( t(V12__y,V0__R)
=> ! [V13__z] :
( t(V13__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V13__z),happ(happ(V3__radd,V11__x),V12__y))),happ(happ(V3__radd,happ(happ(V4__rmul,V13__z),V11__x)),happ(happ(V4__rmul,V13__z),V12__y)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_1_r',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V10__x] :
( t(V10__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V2__rI)),V10__x)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> ! [V11__z] :
( t(V11__z,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,V7__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> ! [V10__y] :
( t(V10__y,V0__R)
=> p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rO] :
( t(V1__rO,V0__R)
=> ! [V2__rI] :
( t(V2__rI,V0__R)
=> ! [V3__radd] :
( c_24__type__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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.Radd_ext',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__radd] :
( c_24__type__5967___24t(V0__R,V1__radd)
=> ! [V2__rmul] :
( c_24__type__5967___24t(V0__R,V2__rmul)
=> ! [V3__ropp] :
( c_24__type__3213___24t(V0__R,V3__ropp)
=> ! [V4__req] :
( c_24__type__60___24t(V0__R,V4__req)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V0__R,V1__radd,V2__rmul,V3__ropp,V4__req)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__5967___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__3213___24a1(V0__R),V4__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,V0__R,V4__req,V4__req)),V1__radd) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Ropp_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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___24t(V0__R,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)
=> ! [V9__x] :
( t(V9__x,V0__R)
=> p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(V6__ropp,V9__x))),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).
fof('Coq.setoid_ring.Ring_theory.Ropp_opp',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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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)
=> ! [V11__x] :
( t(V11__x,V0__R)
=> p(happ(happ(V7__req,happ(V6__ropp,happ(V6__ropp,V11__x))),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__10645___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__10645___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__10645___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__10659___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__10666___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__10670___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__5967___24t(V0__R,V3__radd)
=> ! [V4__rmul] :
( c_24__type__5967___24t(V0__R,V4__rmul)
=> ! [V5__rsub] :
( c_24__type__5967___24t(V0__R,V5__rsub)
=> ! [V6__ropp] :
( c_24__type__3213___24t(V0__R,V6__ropp)
=> ! [V7__req] :
( c_24__type__60___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__10645___24t(V0__R,V8__C,V11__cadd)
=> ! [V12__cmul] :
( c_24__type__10645___24t(V0__R,V8__C,V12__cmul)
=> ! [V13__csub] :
( c_24__type__10645___24t(V0__R,V8__C,V13__csub)
=> ! [V14__copp] :
( c_24__type__10659___24t(V0__R,V8__C,V14__copp)
=> ! [V15__ceqb] :
( c_24__type__10666___24t(V0__R,V8__C,V15__ceqb)
=> ! [V16__phi] :
( c_24__type__10670___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('Coq.setoid_ring.Ring_theory.rpow_pow_N',axiom,
! [V0__R] :
( cType___24t(V0__R)
=> ! [V1__rI] :
( t(V1__rI,V0__R)
=> ! [V2__rmul] :
( c_24__type__5967___24t(V0__R,V2__rmul)
=> ! [V3__req] :
( c_24__type__60___24t(V0__R,V3__req)
=> ! [V4__Cpow] :
( cType___24t(V4__Cpow)
=> ! [V5__Cp__phi] :
( c_24__type__32652___24t(V0__R,V4__Cpow,V5__Cp__phi)
=> ! [V6__rpow] :
( c_24__type__32659___24t(V0__R,V4__Cpow,V6__rpow)
=> ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V0__R,V1__rI,V2__rmul,V3__req,V4__Cpow,V5__Cp__phi,V6__rpow)
=> ! [V8__r] :
( t(V8__r,V0__R)
=> ! [V9__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V9__n)
=> p(happ(happ(V3__req,happ(happ(V6__rpow,V8__r),happ(V5__Cp__phi,V9__n))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V8__r,V9__n))) ) ) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_decomp_u_total',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__dom,V3__r_27)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V3__r_27,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27))) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_disj',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),c_24__lam__10___24a1(V0__A))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r) ) ) ) ).
fof('HahnAcyclic.acyclic_du',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__adom] :
( c_24__type__4___24t(V0__X,V3__adom)
=> ! [V4__bdom] :
( c_24__type__4___24t(V0__X,V4__bdom)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V1__r,V3__adom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V1__r,V4__bdom)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__bdom),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V2__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__adom)))))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)) ) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_pref_union',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__dom] :
( c_24__type__4___24t(V0__X,V3__dom)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V3__dom,V1__r)
=> ( ! [V7__x] :
( t(V7__x,V0__X)
=> ! [V8__y] :
( t(V8__y,V0__X)
=> ( p(happ(happ(V2__r_27,V7__x),V8__y))
=> ( p(happ(V3__dom,V7__x))
& ~ p(happ(V3__dom,V8__y)) ) ) ) )
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,cHahnAcyclic_2epref__union___24a3(V0__X,V1__r,V2__r_27)) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_rotl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('HahnAcyclic.acyclic_seqC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('HahnAcyclic.acyclic_seq_union_incompat',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27),c_24__lam__10___24a1(V0__A))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r_27_27,V2__r_27),c_24__lam__10___24a1(V0__A))
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)))) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_seq_via_expand_minus',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27))
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,V1__r)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27)))))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_specific_absorb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r))
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_ud',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__adom] :
( c_24__type__4___24t(V0__X,V3__adom)
=> ! [V4__bdom] :
( c_24__type__4___24t(V0__X,V4__bdom)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V2__r_27,V3__adom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V2__r_27,V4__bdom)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__bdom),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__adom))),V2__r_27))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)) ) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_union1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_union_total_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__dom,V1__r)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V3__r_27)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27))) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_union_total_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__dom,V3__r_27)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V3__r_27,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V3__r_27)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27))) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_ut',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27)
& chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_utd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r_27)
=> ! [V6__dom] :
( c_24__type__4___24t(V0__A,V6__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V6__dom,V3__r_27)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V3__r_27,V6__dom)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27)) ) ) ) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_utt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27)
& chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ) ) ).
fof('HahnAcyclic.acyclic_via_expand_minus',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,V1__r)))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r) ) ) ) ) ).
fof('HahnAcyclic.cycle_decomp_u1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)),V4__c,V4__c)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V4__c,V4__c)
| cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__b,V2__a) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.codom_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnDom.ct_doma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__d) ) ) ) ) ).
fof('hahn.HahnDom.ct_domb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__d) ) ) ) ) ).
fof('hahn.HahnDom.dom_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnDom.doma_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__4___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d),V2__r),V1__d) ) ) ) ).
fof('hahn.HahnDom.doma_implies',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__4___24t(V0__A,V3__d_27)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(happ(V2__d,V4__a))
=> p(happ(V3__d_27,V4__a)) ) )
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d_27) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domb_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__4___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d)),V1__d) ) ) ) ).
fof('hahn.HahnDom.domb_implies',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__4___24t(V0__A,V3__d_27)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ( p(happ(V2__d,V4__a))
=> p(happ(V3__d_27,V4__a)) ) )
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d_27) ) ) ) ) ) ) ).
fof('hahn.HahnDom.irr_dom',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__4___24t(V0__A,V3__d_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)))))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)),c_24__lam__10___24a1(V0__A))
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d))))
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27))))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.minus_doma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V3__d) ) ) ) ) ) ).
fof('hahn.HahnDom.minus_domb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V3__d) ) ) ) ) ) ).
fof('hahn.HahnDom.restr_doma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d,V1__r),V2__d) ) ) ) ).
fof('hahn.HahnDom.restr_doma_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__4___24t(V0__A,V3__d_27)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V3__d_27,V1__r),V2__d) ) ) ) ) ) ).
fof('hahn.HahnDom.restr_domb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d,V1__r),V2__d) ) ) ) ).
fof('hahn.HahnDom.restr_domb_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__4___24t(V0__A,V3__d_27)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V3__d_27,V1__r),V2__d) ) ) ) ) ) ).
fof('hahn.HahnDom.restr_eq_rel_doma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__f] :
( c_24__type__315___24t(V0__A,V1__B,V3__f)
=> ! [V4__d] :
( c_24__type__616___24t(V0__A,V1__B,V4__d)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V2__r,V4__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V3__f,V2__r),V4__d) ) ) ) ) ) ) ).
fof('hahn.HahnDom.restr_eq_rel_domb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__f] :
( c_24__type__315___24t(V0__A,V1__B,V3__f)
=> ! [V4__d] :
( c_24__type__616___24t(V0__A,V1__B,V4__d)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r,V4__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V3__f,V2__r),V4__d) ) ) ) ) ) ) ).
fof('hahn.HahnDom.seq_doma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__d) ) ) ) ) ) ).
fof('hahn.HahnDom.seq_domb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r_27,V3__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__d) ) ) ) ) ) ).
fof('hahn.HahnDom.step_dom',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__4___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__4___24t(V0__A,V3__d_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)))))
=> ! [V5__dd] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__dd)
=> ( V5__dd = chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d)))
=> ! [V7__de] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__de)
=> ( V7__de = chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)))
=> ! [V9__ed] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__ed)
=> ( V9__ed = chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d)))
=> ! [V11__ee] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V11__ee)
=> ( V11__ee = chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V5__dd,V7__de),V9__ed),V11__ee)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.union_doma',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__A,V2__r_27,V3__d)
=> chahn_2eHahnDom_2edoma___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__d) ) ) ) ) ) ) ).
fof('hahn.HahnDom.union_domb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r_27,V3__d)
=> chahn_2eHahnDom_2edomb___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__d) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_case_split',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__f] :
( c_24__type__4___24t(V0__A,V2__f)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__f,V1__r))
& ! [V3__x] :
( t(V3__x,V0__A)
=> ( ~ p(happ(V2__f,V3__x))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__x,V3__x)
=> p(c_24False) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__165___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),chahn_2eHahnRelationsBasic_2eacyclic___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.acyclic_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__165___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2eacyclic___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.acyclic_seqC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_eq',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__a] :
( t(V2__a,V0__B)
=> ! [V3__rr] :
( c_24__type__620___24t(V0__B,V1__A,V3__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,c_3d___24a2(V0__B,V2__a),V3__rr),happ(V3__rr,V2__a)) ) ) ) ) ).
fof('hahn.HahnEquational.clos_refl_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_trans_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_relf_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_trans_imm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__L)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,V4__L)
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( ! [V8__c] :
( t(V8__c,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V8__c))
=> ( p(happ(happ(V1__r,V8__c),V7__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V8__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_imm2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__L)
=> ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( ! [V7__c] :
( t(V7__c,V0__A)
=> ( p(happ(happ(V1__r,V5__a),V7__c))
=> ( p(happ(happ(V1__r,V7__c),V6__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V7__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V5__a),V6__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V5__a,V6__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_immediate1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V3__a,V4__b)
=> p(happ(happ(V1__r,V3__a),V4__b)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_immediate2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ! [V4__dom] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__dom)
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( p(happ(happ(V1__r,V5__a),V6__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__b,V4__dom)) ) ) )
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_trans_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.clos_trans_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.codom_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1735___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__4___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)),chahn_2eHahnRelationsBasic_2ecodom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.collect_rel_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.crE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),V1__r)) ) ) ).
fof('hahn.HahnEquational.cr_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cr_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cr_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.crs_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.cs_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ctEE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_24__lam__1892___24a1(V0__A),c_24__lam__1901___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.ct_begin',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.ct_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_imm1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__acts] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__acts)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),c_24__lam__329___24a2(V0__A,V4__acts))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_imm2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V4__acts] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__acts)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),c_24__lam__329___24a2(V0__A,V4__acts))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__r),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V6__k)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_ind_left_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__x] :
( c_24__type__60___24t(V0__A,V3__x)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( V3__x = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V4__r)
=> ! [V6__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V4__r),V6__r_27)
=> ( ! [V8__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V8__k),V6__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V8__k)),V6__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__x),V6__r_27) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V3__r),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__k,V3__r)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.ct_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_of_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_of_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V1__r) ) ) ) ).
fof('hahn.HahnEquational.ct_of_union_ct_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.ct_of_union_ct_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.ct_rotl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)),V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.ct_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_seq_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('hahn.HahnEquational.ct_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.ct_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.dom_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1735___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__4___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)),chahn_2eHahnRelationsBasic_2edom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__179___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1996___24a3(V0__A,V1__P,V3__Q)) ) ) ) ) ) ).
fof('hahn.HahnEquational.good_ctx_const',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1966___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.good_ctx_id',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1963___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1972___24a3(V0__A,V1__P,V3__r)) ) ) ) ) ).
fof('hahn.HahnEquational.good_ctx_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1978___24a3(V0__A,V1__P,V3__r)) ) ) ) ) ).
fof('hahn.HahnEquational.good_ctx_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__179___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__1987___24a3(V0__A,V1__P,V3__Q)) ) ) ) ) ) ).
fof('hahn.HahnEquational.immediate_clos_trans_elim',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a,V3__b)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V5__c] :
( t(V5__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V5__c)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V5__c,V3__b)
=> p(c_24False) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_ct_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),V2__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r))) ) ) ) ).
fof('hahn.HahnEquational.inclusion_ct_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom))) ) ) ) ).
fof('hahn.HahnEquational.inclusion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__170___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__165___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_r_t_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom),V1__r),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inclusion_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom)),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inclusion_step2_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_t_r_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_transpE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.interA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2),V3__r3),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('hahn.HahnEquational.interAC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__r_27_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__r_27_27))) ) ) ) ) ).
fof('hahn.HahnEquational.interC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r2,V1__r1)) ) ) ) ).
fof('hahn.HahnEquational.interK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.inter_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V1__r),V1__r) ) ) ) ) ).
fof('hahn.HahnEquational.inter_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ) ).
fof('hahn.HahnEquational.inter_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,c_24__lam__10___24a1(V0__A),V1__r),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.inter_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,c_24__lam__10___24a1(V0__A)),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.inter_inclusion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__i] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__i)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__i),V1__r) ) ) ) ).
fof('hahn.HahnEquational.inter_irrefl_equiv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),c_24__lam__10___24a1(V0__A))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ) ) ).
fof('hahn.HahnEquational.inter_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnEquational.inter_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__i] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__i)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__i)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__i),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__i)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__i)) ) ) ) ) ) ).
fof('hahn.HahnEquational.irreflexive_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__x)
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('hahn.HahnEquational.irreflexive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__165___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.irreflexive_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__165___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.is_total_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__4___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__4___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__equiv___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__x)
=> ! [V5__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V4__x,V5__y)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__x,V4__x)
<=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__y,V5__y) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.is_total_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1544___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__4___24a1(V0__A),c_24__type__165___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e)),chahn_2eHahnRelationsBasic_2eis__total___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.is_total_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__1544___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__4___24a1(V0__A),c_24__type__165___24a1(V0__A),cCoq_2eProgram_2eBasics_2eflip___24a4(c_24__type__4___24a1(V0__A),c_24__type__4___24a1(V0__A),cProp,chahn_2eHahnSets_2eset__subset___24a1(V0__A)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl)),chahn_2eHahnRelationsBasic_2eis__total___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.map_rel_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,V3__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V1__B,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,V3__r)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.minusK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V1__r),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.minus_absorb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),c_24__lam__10___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnEquational.minus_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,c_24__lam__10___24a1(V0__A),V1__r),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.minus_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,c_24__lam__10___24a1(V0__A)),V1__r) ) ) ).
fof('hahn.HahnEquational.minus_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__179___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eminus__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.minus_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__179___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eProgram_2eBasics_2eflip___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eminus__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.minus_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnEquational.minus_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r1,V3__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r2,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.pow_inclusion',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,V2__r,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V0__n),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V3__r_27,V0__n)) ) ) ) ) ) ).
fof('hahn.HahnEquational.pow_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,V1__n)),V2__r) ) ) ) ) ).
fof('hahn.HahnEquational.restrC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__4___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__4___24t(V0__A,V2__d_27)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d_27,V3__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__d_27,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.restr_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__4___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,V2__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r))) ) ) ) ).
fof('hahn.HahnEquational.restr_eq_elim',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__315___24t(V0__A,V2__B,V3__f)
=> ( ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
=> happ(V3__f,V4__x) = happ(V3__f,V5__y) ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r),V1__r) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_full',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,c_24__lam__312___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.restr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__4___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,V2__r)) ) ) ) ) ).
fof('hahn.HahnEquational.rtE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.rtEE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_24__lam__1892___24a1(V0__A),c_24__lam__1895___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.rt_begin',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)))) ) ) ).
fof('hahn.HahnEquational.rt_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_end',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r))) ) ) ).
fof('hahn.HahnEquational.rt_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__179___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A))),V4__r_27)
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V6__k)),V4__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r)),V4__r_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.rt_of_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_of_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_of_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_of_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.rt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.rt_seq_swap',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)))) ) ) ) ).
fof('hahn.HahnEquational.rt_unit',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnEquational.same_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_rel_Symmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_relation_exp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
<=> p(happ(happ(V2__r_27,V4__x),V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.same_relation_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_relation_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.same_relation_transpE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.seqA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r3),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('hahn.HahnEquational.seqA2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27,V4__x,V5__y)
<=> chahn_2eHahnRelationsBasic_2eseq___24a5(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27),V4__x,V5__y) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_bunion_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__P] :
( c_24__type__4___24t(V0__B,V2__P)
=> ! [V3__rr] :
( c_24__type__620___24t(V0__B,V1__A,V3__rr)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V4__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__P,V3__rr),V4__r),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__P,c_24__lam__1779___24a4(V0__B,V1__A,V3__rr,V4__r))) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_bunion_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V2__r)
=> ! [V3__P] :
( c_24__type__616___24t(V0__B,V1__A,V3__P)
=> ! [V4__rr] :
( c_24__type__620___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V1__A,V2__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V3__P,V4__rr)),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V3__P,c_24__lam__1791___24a4(V0__B,V1__A,V2__r,V4__rr))) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__doma] :
( c_24__type__4___24t(V0__A,V1__doma)
=> ! [V2__domb] :
( c_24__type__4___24t(V0__A,V2__domb)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__doma),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__domb)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__1800___24a3(V0__A,V1__doma,V2__domb))) ) ) ) ).
fof('hahn.HahnEquational.seq_eqvC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__doma] :
( c_24__type__4___24t(V0__A,V1__doma)
=> ! [V2__domb] :
( c_24__type__4___24t(V0__A,V2__domb)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__doma),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__domb)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__domb),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__doma))) ) ) ) ).
fof('hahn.HahnEquational.seq_eqvK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom)) ) ) ).
fof('hahn.HahnEquational.seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom),V1__r),c_24__lam__2040___24a3(V0__A,V1__r,V2__dom)) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom1] :
( c_24__type__4___24t(V0__A,V2__dom1)
=> ! [V3__dom2] :
( c_24__type__4___24t(V0__A,V3__dom2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__dom2))),c_24__lam__202___24a4(V0__A,V1__r,V2__dom1,V3__dom2)) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom)),c_24__lam__2029___24a3(V0__A,V1__r,V2__dom)) ) ) ) ).
fof('hahn.HahnEquational.seq_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,c_24__lam__10___24a1(V0__A),V1__r),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.seq_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,c_24__lam__10___24a1(V0__A)),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnEquational.seq_id_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.seq_id_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A))),V1__r) ) ) ).
fof('hahn.HahnEquational.seq_minus_transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r1,V3__r2),V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r1,V1__r),V3__r2),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r1,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r2,V1__r)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__179___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eseq___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.seq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__179___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2eseq___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.seq_pow_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V1__r,V2__n),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V1__r,V2__n))) ) ) ) ).
fof('hahn.HahnEquational.seq_rtE_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))) ) ) ) ).
fof('hahn.HahnEquational.seq_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V3__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.seq_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r1,V3__r2)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V3__r2))) ) ) ) ) ).
fof('hahn.HahnEquational.tot_ex',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__mo] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__mo)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__X,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V2__dom,V1__mo)
=> ! [V4__a] :
( t(V4__a,V0__X)
=> ! [V5__b] :
( t(V5__b,V0__X)
=> ( p(happ(V2__dom,V4__a))
=> ( p(happ(V2__dom,V5__b))
=> ( ~ p(happ(happ(V1__mo,V4__a),V5__b))
=> ( V4__a != V5__b
=> p(happ(happ(V1__mo,V5__b),V4__a)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.total_immediate_unique',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( c_24__type__60___24t(V0__A,V1__r)
=> ! [V2__P] :
( c_24__type__4___24t(V0__A,V2__P)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__P,V1__r)
=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ! [V6__c] :
( t(V6__c,V0__A)
=> ( p(happ(V2__P,V4__a))
=> ( p(happ(V2__P,V5__b))
=> ( p(happ(V2__P,V6__c))
=> ( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,V1__r,V4__a,V6__c)
=> ( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,V1__r,V5__b,V6__c)
=> V4__a = V5__b ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.trailing_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__e] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__e)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__e))) ) ) ) ) ) ).
fof('hahn.HahnEquational.transitive_more',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__x,V2__y)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__x)
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__y) ) ) ) ) ) ).
fof('hahn.HahnEquational.transitive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__165___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cProp,cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),c_3c_3d_3e),cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.transitive_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.transp_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.transp_inv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)),V1__r) ) ) ).
fof('hahn.HahnEquational.transp_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.unionA',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),V3__r3),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r2,V3__r3))) ) ) ) ) ).
fof('hahn.HahnEquational.unionAC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27_27))) ) ) ) ) ).
fof('hahn.HahnEquational.unionC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r2,V1__r1)) ) ) ) ).
fof('hahn.HahnEquational.unionK',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.union_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.union_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V1__r),V2__r_27) ) ) ) ) ).
fof('hahn.HahnEquational.union_false_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,c_24__lam__10___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.union_false_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,c_24__lam__10___24a1(V0__A)),V1__r) ) ) ).
fof('hahn.HahnEquational.union_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__179___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.union_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__176___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__179___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.union_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_inter_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_irreflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V4__t),V3__r))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__t,V3__r)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ! [V5__dom] :
( c_24__type__616___24t(V0__A,V1__B,V5__dom)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V5__dom,V3__r)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ! [V5__C] :
( cType___24t(V5__C)
=> ! [V6__dom] :
( c_24__type__2254___24t(V0__A,V1__B,V5__C,V6__dom)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V5__C,V6__dom,V3__r)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr_eq_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__t)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r)
=> ( chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t)
=> chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V3__r,V4__t)) ) ) ) ) ) ) ) ).
fof('hahn.HahnList.in_undup_iff',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( t(V1__x,V0__A)
=> ! [V2__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,chahn_2eHahnList_2eundup___24a2(V0__A,V2__l)))
<=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V1__x,V2__l)) ) ) ) ) ).
fof('hahn.HahnList.nodup_undup',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__l] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
=> cCoq_2eLists_2eList_2eNoDup___24a2(V0__A,chahn_2eHahnList_2eundup___24a2(V0__A,V1__l)) ) ) ).
fof('hahn.HahnMaxElt.max_elt_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__315___24t(V0__A,V3__B,V4__f)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),V2__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_seq1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_weaken',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),V1__r),c_24__lam__10___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__10___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__b] :
( t(V2__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),V1__r),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.seq_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),c_24__lam__10___24a1(V0__A)) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),c_24__lam__10___24a1(V0__A)) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),V1__r),c_24__lam__10___24a1(V0__A)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__10___24a1(V0__A)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),V1__r),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__b)
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ! [V6__y] :
( t(V6__y,V0__A)
=> ( p(happ(happ(V1__r,V5__x),V6__y))
=> V6__y = V3__b ) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_equiv_max_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_equiv_wmax_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_subset_max_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.set_subset_wmax_elt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V1__r),chahn_2eHahnMaxElt_2ewmax__elt___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnMaxElt.transp_seq_eqv_max',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.transp_seq_eqv_max_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))),c_24__lam__10___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__B] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__315___24t(V0__A,V3__B,V4__f)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),V2__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_seq1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_seq2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a)
=> ( chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a)
=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__a) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.Build_min_cycle_mod',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__667___24t(V0__X,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( V3__n != cCoq_2eInit_2eDatatypes_2eO
=> ( ! [V5__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__x)
=> happ(V2__f,V5__x) = happ(V2__f,cCoq_2eInit_2eNat_2emodulo___24a2(V5__x,V3__n)) )
=> ( ! [V6__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__i)
=> p(happ(happ(V1__r,happ(V2__f,V6__i)),happ(V2__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__i)))) )
=> ( ! [V7__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V7__i)
=> ! [V8__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V8__j)
=> ( p(happ(happ(V1__r,happ(V2__f,V7__i)),happ(V2__f,V8__j)))
=> cCoq_2eInit_2eNat_2emodulo___24a2(V8__j,V3__n) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V7__i),V3__n) ) ) )
=> chahn_2eHahnMinPath_2emin__cycle__mod___24a4(V0__X,V1__r,V2__f,V3__n) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.acyclic_no_min_cycle',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r)
<=> ~ ? [V2__f] :
( c_24__type__667___24t(V0__X,V2__f)
& ? [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
& chahn_2eHahnMinPath_2emin__cycle__mod___24a4(V0__X,V1__r,V2__f,V3__n) ) ) ) ) ) ).
fof('hahn.HahnMinPath.get_first_nat',axiom,
! [V0__P] :
( c_24__type__258___24t(V0__P)
=> ( ? [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
& p(happ(V0__P,V1__m))
& ! [V2__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__k)
=> ( p(happ(V0__P,V2__k))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__k)) ) ) )
| ! [V1__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
=> ~ p(happ(V0__P,V1__k)) ) ) ) ).
fof('hahn.HahnMinPath.get_max_bounded_nat',axiom,
! [V0__P] :
( c_24__type__258___24t(V0__P)
=> ! [V1__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
=> ! [V2__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V1__x,V2__n))
=> ( p(happ(V0__P,V1__x))
=> ? [V5__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
& p(cCoq_2eInit_2ePeano_2ele___24a2(V5__m,V2__n))
& p(happ(V0__P,V5__m))
& ! [V6__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__k)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(V6__k,V2__n))
=> ( p(happ(V0__P,V6__k))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V6__k,V5__m)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.min_cycle',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__dom] :
( c_24__type__4___24t(V0__X,V3__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V3__dom,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r))
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27))
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,c_24__lam__18___24a2(V0__X,V3__dom),V1__r))
& ! [V8__x] :
( t(V8__x,V0__X)
=> ( p(happ(happ(V1__r,V8__x),V8__x))
=> ( p(happ(V3__dom,V8__x))
=> p(c_24False) ) ) )
& ! [V8__c1] :
( t(V8__c1,V0__X)
=> ! [V9__b1] :
( t(V9__b1,V0__X)
=> ( p(happ(happ(V1__r,V8__c1),V9__b1))
=> ! [V11__b2] :
( t(V11__b2,V0__X)
=> ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__X,V2__r_27,V9__b1,V11__b2)
=> ! [V13__c2] :
( t(V13__c2,V0__X)
=> ( p(happ(happ(V1__r,V11__b2),V13__c2))
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,c_24__lam__22___24a2(V0__X,V3__dom),V1__r),V13__c2,V8__c1)
=> ( p(happ(V3__dom,V9__b1))
=> ( p(happ(V3__dom,V11__b2))
=> ( ~ p(happ(V3__dom,V8__c1))
=> ( ~ p(happ(V3__dom,V13__c2))
=> p(c_24False) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.min_cycle1',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__X,V3__d)
=> ! [V4__nd] :
( c_24__type__4___24t(V0__X,V4__nd)
=> ( V4__nd = c_24__lam__974___24a2(V0__X,V3__d)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V3__d,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r))
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27))
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r)
<=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__nd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__nd))))
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__d))))
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__nd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__X,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__nd),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__nd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__nd)))))))))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.min_cycle_nodup',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__667___24t(V0__X,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( chahn_2eHahnMinPath_2emin__cycle__mod___24a4(V0__X,V1__r,V2__f,V3__n)
=> ! [V5__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__i)
=> ! [V6__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__j)
=> ( happ(V2__f,V5__i) = happ(V2__f,V6__j)
=> cCoq_2eInit_2eNat_2emodulo___24a2(V5__i,V3__n) = cCoq_2eInit_2eNat_2emodulo___24a2(V6__j,V3__n) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.min_cycle_wlog',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__667___24t(V0__X,V2__f)
=> ! [V3__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
=> ( chahn_2eHahnMinPath_2emin__cycle__mod___24a4(V0__X,V1__r,V2__f,V3__n)
=> ! [V5__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__i)
=> ! [V6__P] :
( c_24__type__4___24t(V0__X,V6__P)
=> ( p(happ(V6__P,happ(V2__f,V5__i)))
=> ? [V8__f] :
( c_24__type__667___24t(V0__X,V8__f)
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2429___24a4(V0__X,V1__r,V3__n,V8__f))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2436___24a3(V0__X,V6__P,V8__f)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.path_minimize',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__X)
=> ! [V3__b] :
( t(V3__b,V0__X)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,V1__r,V2__a,V3__b)
=> ? [V5__f] :
( c_24__type__667___24t(V0__X,V5__f)
& ? [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__674___24a3(V0__X,V2__a,V5__f))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__681___24a4(V0__X,V3__b,V5__f,V6__n))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__699___24a4(V0__X,V1__r,V5__f,V6__n))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__741___24a4(V0__X,V1__r,V5__f,V6__n)) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.clos_trans_imm',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V1__r)
=> ! [V4__L] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__X,V4__L)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(V0__X,V4__L)
=> ! [V6__a] :
( t(V6__a,V0__X)
=> ! [V7__b] :
( t(V7__b,V0__X)
=> ( ! [V8__c] :
( t(V8__c,V0__X)
=> ( p(happ(happ(V1__r,V6__a),V8__c))
=> ( p(happ(happ(V1__r,V8__c),V7__b))
=> p(cCoq_2eLists_2eList_2eIn___24a3(V0__X,V8__c,V4__L)) ) ) )
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__X,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.clos_trans_immediate1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V3__a,V4__b)
=> p(happ(happ(V1__r,V3__a),V4__b)) ) ) ) ) ) ) ).
fof('hahn.HahnPath.clos_trans_immediate2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ! [V4__dom] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__dom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,c_24__lam__329___24a2(V0__A,V4__dom))
=> ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),V6__a,V7__b) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.clos_trans_restr_trans_cycle',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__f] :
( c_24__type__4___24t(V0__X,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ! [V5__y] :
( t(V5__y,V0__X)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,V3__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),V4__x,V5__y)
=> ( p(happ(happ(V1__r,V5__y),V4__x))
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,V3__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),V4__x,V4__x) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.clos_trans_restr_trans_mid',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__f] :
( c_24__type__4___24t(V0__X,V3__f)
=> ! [V4__x] :
( t(V4__x,V0__X)
=> ! [V5__y] :
( t(V5__y,V0__X)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,V3__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),V4__x,V5__y)
=> ! [V7__z] :
( t(V7__z,V0__X)
=> ( p(happ(happ(V1__r,V5__y),V7__z))
=> ! [V9__w] :
( t(V9__w,V0__X)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,V3__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),V7__z,V9__w)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,V3__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),V4__x,V9__w) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.clos_trans_rotl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)),V2__r_27))) ) ) ) ).
fof('hahn.HahnPath.ct_ct_disj',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),c_24__lam__10___24a1(V0__A))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),c_24__lam__10___24a1(V0__A)) ) ) ) ).
fof('hahn.HahnPath.ct_inclusion_from_rt_inclusion1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ! [V4__d_27] :
( c_24__type__4___24t(V0__A,V4__d_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.ct_inclusion_from_rt_inclusion2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__d] :
( c_24__type__4___24t(V0__A,V3__d)
=> ! [V4__d_27] :
( c_24__type__4___24t(V0__A,V4__d_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d_27)))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d_27))) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.ct_minus_transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V1__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnPath.ct_no_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),c_24__lam__10___24a1(V0__A))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V1__r) ) ) ) ).
fof('hahn.HahnPath.ct_unionE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))))) ) ) ) ).
fof('hahn.HahnPath.ct_union_singl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))))) ) ) ) ) ).
fof('hahn.HahnPath.immediate_clos_trans_elim',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( chahn_2eHahnRelationsBasic_2eimmediate___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__a,V3__b)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
& ! [V5__c] :
( t(V5__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V5__c)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V5__c,V3__b)
=> p(c_24False) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.inclusion_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r1)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V3__r2)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r1,V3__r2)) ) ) ) ) ) ) ).
fof('hahn.HahnPath.inclusion_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r1)
=> ! [V3__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r2)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r2)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r1)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r1,V3__r2)) ) ) ) ) ) ) ).
fof('hahn.HahnPath.irreflexive_disj',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),c_24__lam__10___24a1(V0__A))
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnPath.minus_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V1__r))) ) ) ) ) ).
fof('hahn.HahnPath.minus_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27)) ) ) ) ) ).
fof('hahn.HahnPath.path_absorb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V1__r)
| cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnPath.path_absorb1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnPath.path_absorb2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnPath.path_absorb_lt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V1__r)
| cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27) )
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))) ) ) ) ) ) ).
fof('hahn.HahnPath.path_absorb_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V1__r)
| cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27) )
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27))) ) ) ) ) ) ).
fof('hahn.HahnPath.path_decomp_u_total',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__dom] :
( c_24__type__4___24t(V0__A,V2__dom)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__dom,V3__r_27)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__A,V3__r_27,V2__dom)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27)))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V3__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))))) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.path_specific_absorb',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)))) ) ) ) ) ) ).
fof('hahn.HahnPath.path_tur',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__adom] :
( c_24__type__4___24t(V0__X,V3__adom)
=> ! [V4__bdom] :
( c_24__type__4___24t(V0__X,V4__bdom)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V1__r)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V2__r_27,V3__adom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V2__r_27,V4__bdom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__adom)),V2__r_27)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__bdom),V1__r))))) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.path_tur2',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__adom] :
( c_24__type__4___24t(V0__X,V3__adom)
=> ! [V4__bdom] :
( c_24__type__4___24t(V0__X,V4__bdom)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V1__r,V3__adom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V1__r,V4__bdom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V2__r_27,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__adom))),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__bdom),V2__r_27)))))) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.path_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)))) ) ) ) ).
fof('hahn.HahnPath.path_union1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))))))) ) ) ) ).
fof('hahn.HahnPath.path_union2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))))) ) ) ) ).
fof('hahn.HahnPath.path_ur',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__adom] :
( c_24__type__4___24t(V0__X,V3__adom)
=> ! [V4__bdom] :
( c_24__type__4___24t(V0__X,V4__bdom)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V2__r_27,V3__adom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V2__r_27,V4__bdom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__adom)),V2__r_27)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__bdom),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r)))))) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.path_ur2',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__adom] :
( c_24__type__4___24t(V0__X,V3__adom)
=> ! [V4__bdom] :
( c_24__type__4___24t(V0__X,V4__bdom)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V1__r,V3__adom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V1__r,V4__bdom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V2__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V2__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V3__adom))),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__X,V4__bdom),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V2__r_27))))))) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.path_ut',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnPath.path_ut2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)))))) ) ) ) ) ).
fof('hahn.HahnPath.path_ut_first',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)))))) ) ) ) ).
fof('hahn.HahnPath.path_ut_last',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r))))) ) ) ) ).
fof('hahn.HahnPath.path_utd',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ! [V4__dom] :
( c_24__type__4___24t(V0__X,V4__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V4__dom,V2__r_27)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V2__r_27,V4__dom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V2__r_27,V4__dom)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,V1__r)))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,V1__r))))) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.path_utd_helper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ! [V4__dom] :
( c_24__type__4___24t(V0__X,V4__dom)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V4__dom,V2__r_27)
=> ( chahn_2eHahnDom_2edoma___24a3(V0__X,V2__r_27,V4__dom)
=> ( chahn_2eHahnDom_2edomb___24a3(V0__X,V2__r_27,V4__dom)
=> ! [V8__x] :
( t(V8__x,V0__X)
=> ! [V9__y] :
( t(V9__y,V0__X)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,c_24__lam__2460___24a3(V0__X,V1__r,V2__r_27),V8__x,V9__y)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,V1__r,V8__x,V9__y)
| ? [V11__z] :
( t(V11__z,V0__X)
& ? [V12__w] :
( t(V12__w,V0__X)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__X,V1__r,V8__x,V11__z)
& p(happ(happ(V2__r_27,V11__z),V12__w))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__X,V1__r,V12__w,V9__y) ) )
| ? [V11__z] :
( t(V11__z,V0__X)
& ? [V12__w] :
( t(V12__w,V0__X)
& p(happ(happ(V2__r_27,V11__z),V12__w))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__X,V1__r,V12__w,V11__z) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnPath.pathp_unc',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V1__r),c_24__lam__10___24a1(V0__X))
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,V2__r_27),c_24__lam__10___24a1(V0__X))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__X,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,V1__r))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,V1__r)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27))))) ) ) ) ) ) ).
fof('hahn.HahnPath.rt_unionE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27))))) ) ) ) ).
fof('hahn.HahnPath.seq_ct_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))) ) ) ) ).
fof('hahn.HahnPath.seq_ct_absorb_lt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27))))) ) ) ) ) ).
fof('hahn.HahnPath.seq_ct_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27)))) ) ) ) ).
fof('hahn.HahnPath.seq_ct_absorb_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnPath.seq_rt_absorb_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))) ) ) ) ).
fof('hahn.HahnPath.seq_rt_absorb_lt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27))))) ) ) ) ) ).
fof('hahn.HahnPath.seq_rt_absorb_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27)))) ) ) ) ).
fof('hahn.HahnPath.seq_rt_absorb_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27)))) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.acyclic_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_transE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b)
<=> ( V2__a = V3__b
| cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_trans_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__a,V4__b)
=> ( ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> p(happ(happ(V2__r_27,V6__a),V7__b)) ) ) )
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V2__r_27,V3__a,V4__b) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_refl_trans_of_transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__x,V4__y)
<=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V3__x,V4__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__f] :
( c_24__type__315___24t(V0__A,V2__B,V3__f)
=> ( ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V1__r,V4__a),V5__b))
=> happ(V3__f,V4__a) = happ(V3__f,V5__b) ) ) )
=> ! [V5__a] :
( t(V5__a,V0__A)
=> ! [V6__b] :
( t(V6__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V5__a,V6__b)
=> happ(V3__f,V5__a) = happ(V3__f,V6__b) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_in_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__a] :
( t(V3__a,V0__A)
=> ! [V4__b] :
( t(V4__b,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__a,V4__b)
=> ( ! [V6__a] :
( t(V6__a,V0__A)
=> ! [V7__b] :
( t(V7__b,V0__A)
=> ( p(happ(happ(V1__r,V6__a),V7__b))
=> p(happ(happ(V2__r_27,V6__a),V7__b)) ) ) )
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V2__r_27,V3__a,V4__b) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_clos_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__x,V3__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_clos_trans1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,c_24__lam__2633___24a3(V0__A,V1__r,V2__r_27),V3__x,V4__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,c_24__lam__2460___24a3(V0__A,V1__r,V2__r_27),V3__x,V4__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__x,V4__y)
<=> p(happ(happ(V1__r,V3__x),V4__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_of_transitiveD',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__x,V4__y)
=> p(happ(happ(V1__r,V3__x),V4__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_restrD',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V3__x,V4__y)
=> ( p(happ(V1__dom,V3__x))
& p(happ(V1__dom,V4__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.clos_trans_restr_eqD',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V4__x,V5__y)
=> happ(V2__f,V4__x) = happ(V2__f,V5__y) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.eq_in_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.eq_in_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_inter_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.immediateE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eimmediate___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r))) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_bunion_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__P] :
( c_24__type__643___24t(V0__A,V1__B,V3__P)
=> ! [V4__rr] :
( c_24__type__2600___24t(V0__A,V1__B,V4__rr)
=> ( ! [V5__x] :
( t(V5__x,V1__B)
=> ( p(happ(V3__P,V5__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V4__rr,V5__x),V2__r_27) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V1__B,V0__A,V3__P,V4__rr),V2__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_bunion_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__x] :
( t(V3__x,V1__B)
=> ! [V4__P] :
( c_24__type__643___24t(V0__A,V1__B,V4__P)
=> ! [V5__rr] :
( c_24__type__2600___24t(V0__A,V1__B,V5__rr)
=> ( p(happ(V4__P,V3__x))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,happ(V5__rr,V3__x))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V1__B,V0__A,V4__P,V5__rr)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_cr_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_id_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_id_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__312___24a1(V0__A)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r_27)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l1_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_l2_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__s_27,V3__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_minus_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_r_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_r_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V1__r) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V2__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V3__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_eq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__r,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r),V4__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_restr_rel_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,V3__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r),V3__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_rt_rt2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V3__s),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V3__r_27_27) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_seq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__t] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__t)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__t)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__t) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_step_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind_left',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_t',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_t_t2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__r_27_27) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_mon',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ! [V4__s_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__s_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V3__s),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V4__s_27)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
| cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27) )
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r1_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_union_r2_search',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__r_27_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__r_27_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_inclusion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r)
=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_restr_eq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_seqC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.irreflexive_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27))
<=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
& chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.is_total_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,V2__r)
=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.r_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V2__x) ) ) ) ).
fof('hahn.HahnRelationsBasic.r_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V0__A,V1__r,V2__x,V3__y) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_union_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.reflexive_union_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,V2__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.restr_eq_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__315___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.rt_t_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V3__b,V4__c)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V4__c) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.same_relation_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,V1__r) ) ) ).
fof('hahn.HahnRelationsBasic.strict_partial_order_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_rt_step',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ? [V4__z] :
( t(V4__z,V0__A)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V2__x,V4__z)
& p(happ(happ(V1__r,V4__z),V3__y)) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_rt_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ! [V4__c] :
( t(V4__c,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V3__b)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V3__b,V4__c)
=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__a,V4__c) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.t_step_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,V1__r,V2__x,V3__y)
<=> ? [V4__z] :
( t(V4__z,V0__A)
& p(happ(happ(V1__r,V2__x),V4__z))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V0__A,V1__r,V4__z,V3__y) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.trans_irr_acyclic',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.trans_irr_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V0__A,V1__r) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__4___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__dom,V2__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.transitive_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnRelationsBasic.upward_closed_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__P] :
( c_24__type__4___24t(V0__A,V2__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__P) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.upward_closed_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__P] :
( c_24__type__4___24t(V0__A,V2__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V2__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),V2__P) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.upward_closed_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ! [V3__P] :
( c_24__type__4___24t(V0__A,V3__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V1__r,V3__P)
=> ( chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,V2__r_27,V3__P)
=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__P) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.hahn_inclusion_exp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( p(happ(happ(V1__r,V4__x),V5__y))
=> p(happ(happ(V2__r_27,V4__x),V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V1__r),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.rewrite_trans_seq_cr_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),V1__r) ) ) ) ).
fof('hahn.HahnRewrite.seq2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r)
=> ! [V5__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V5__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V5__s)) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3)),V4__r)
=> ! [V6__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V6__s))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V6__s)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq4',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V4__r4))),V5__r)
=> ! [V7__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V7__s)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r,V7__s)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq5',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V5__r5)))),V6__r)
=> ! [V8__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V8__s))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r,V8__s)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.seq6',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r6] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r6)
=> ! [V7__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V6__r6))))),V7__r)
=> ! [V9__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__s)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r6,V9__s)))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V7__r,V9__s)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2),V3__r)
=> ! [V5__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V5__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V5__s)) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,V3__r3)),V4__r)
=> ! [V6__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V6__s))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V6__s)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin4',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,V4__r4))),V5__r)
=> ! [V7__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V7__s)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r,V7__s)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin5',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,V5__r5)))),V6__r)
=> ! [V8__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V8__s))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r,V8__s)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.sin6',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r1)
=> ! [V2__r2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r2)
=> ! [V3__r3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r3)
=> ! [V4__r4] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__r4)
=> ! [V5__r5] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r5)
=> ! [V6__r6] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__r6)
=> ! [V7__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V7__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,V6__r6))))),V7__r)
=> ! [V9__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V9__s)
=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r2,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r3,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r4,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V5__r5,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__r6,V9__s)))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V7__r,V9__s)) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnRewrite.transitiveI',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r),V1__r)
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ) ).
fof('hahn.HahnSets.set_equiv_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(c_24__type__4___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)) ) ).
fof('$adef_hahn.HahnSets.set_equiv_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__equiv,V_24X1) = chahn_2eHahnSets_2eset__equiv___24a1(V_24X1) ).
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('$adef_$_prop_16117_$a1',axiom,
! [V_24X1] : happ(c_24__prop__16117,V_24X1) = c_24__prop__16117___24a1(V_24X1) ).
fof('$adef_Coq.Init.Peano.le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1373_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1373,V_24X1),V_24X2),V_24X3) = c_24__lam__1373___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('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.TT_$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('$adef_Coq.Relations.Relation_Operators.transp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1987_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1987,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1987___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_hahn.HahnSets.set_full_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnSets_2eset__full,V_24X1),V_24X2))
<=> chahn_2eHahnSets_2eset__full___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_2460_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2460,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2460___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_1956_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1956,V_24X1),V_24X2),V_24X3) = c_24__lam__1956___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_let_2_s_1217_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__2__s__1217,V_24X1),V_24X2) = c_24__let__2__s__1217___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2436_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__2436,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__2436___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_974_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__974,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__974___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_2429_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2429,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2429___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnSets.set_collect_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnSets_2eset__collect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnSets_2eset__collect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Program.Basics.flip_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2eflip,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eProgram_2eBasics_2eflip___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_33572_$a1',axiom,
! [V_24X1] : happ(c_24__prop__33572,V_24X1) = c_24__prop__33572___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_Coq.Lists.List.Exists_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eExists,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eExists___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.NPEequiv_$a15',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] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eNPEequiv,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2eNPEequiv___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op2_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__op2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2eacyclic___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Logic.ex2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eLogic_2eex2,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eLogic_2eex2___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.immediate_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eimmediate___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_15958_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__15958,V_24X1),V_24X2) = c_24__lam__15958___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35190_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35190,V_24X1),V_24X2) = c_24__prop__35190___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_lam_1948_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1948,V_24X1),V_24X2) = c_24__lam__1948___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35205_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35205,V_24X1) = c_24__prop__35205___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.is_total_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eis__total,V_24X1) = chahn_2eHahnRelationsBasic_2eis__total___24a1(V_24X1) ).
fof('$adef_$_lam_1915_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1915,V_24X1),V_24X2) = c_24__lam__1915___24a2(V_24X1,V_24X2) ).
fof('$adef_$_let_11_subst_l_28561_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__28561,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__28561___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$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('$adef_$_lam_1972_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1972,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1972___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_1800_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1800,V_24X1),V_24X2),V_24X3) = c_24__lam__1800___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Logic.ex_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eLogic_2eex,V_24X1),V_24X2))
<=> cCoq_2eInit_2eLogic_2eex___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_35143_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35143,V_24X1),V_24X2) = c_24__prop__35143___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1892_$a1',axiom,
! [V_24X1] : happ(c_24__lam__1892,V_24X1) = c_24__lam__1892___24a1(V_24X1) ).
fof('$adef_$_lam_1779_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1779,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1779___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnSets.set_subset_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__subset,V_24X1) = chahn_2eHahnSets_2eset__subset___24a1(V_24X1) ).
fof('$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_hahn.HahnBase.Equality.class_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eEquality_2eclass,V_24X1) = chahn_2eHahnBase_2eEquality_2eclass___24a1(V_24X1) ).
fof('$adef_$_lam_674_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__674,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__674___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_hahn.HahnRelationsBasic.eq_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eeq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2eeq__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_prop_14165_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__14165,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__14165___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_14918_$a1',axiom,
! [V_24X1] : happ(c_24__prop__14918,V_24X1) = c_24__prop__14918___24a1(V_24X1) ).
fof('$adef_$_lam_28448_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__28448,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__28448___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.BinList.nth_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eBinList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eBinList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_2029_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2029,V_24X1),V_24X2),V_24X3) = c_24__lam__2029___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_prop_11782_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__11782,V_24X1),V_24X2) = c_24__prop__11782___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_28448_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__28448,V_24X1),V_24X2),V_24X3) = c_24__lam__28448___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1978_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1978,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1978___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Logic.False_rec_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eLogic_2eFalse__rec,V_24X1) = cCoq_2eInit_2eLogic_2eFalse__rec___24a1(V_24X1) ).
fof('$adef_hahn.HahnMaxElt.max_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnMaxElt_2emax__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.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_$_lam_329_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__329,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__329___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_$_lam_28464_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__28464,V_24X1),V_24X2),V_24X3) = c_24__lam__28464___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.strict_partial_order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2estrict__partial__order,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V_24X1,V_24X2) ) ).
fof('$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.micromega.Tauto.eval_f_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__f,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2emicromega_2eTauto_2eeval__f___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$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_hahn.HahnSets.set_disjoint_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__disjoint,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__disjoint___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_prop_11776_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__11776,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__11776___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Tauto.eval_tt_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eeval__tt,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2emicromega_2eTauto_2eeval__tt___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sig_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnMaxElt.wmax_elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1),V_24X2) = chahn_2eHahnMaxElt_2ewmax__elt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_35041_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__35041,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__35041___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_14917_$a1',axiom,
! [V_24X1] : happ(c_24__prop__14917,V_24X1) = c_24__prop__14917___24a1(V_24X1) ).
fof('$adef_$_prop_33563_$a1',axiom,
! [V_24X1] : happ(c_24__prop__33563,V_24X1) = c_24__prop__33563___24a1(V_24X1) ).
fof('$adef_$_lam_28633_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__28633,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__28633___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_$_prop_35148_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35148,V_24X1),V_24X2) = c_24__prop__35148___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.dom_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2edom__rel,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2edom__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2etransp___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_28456_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__28456,V_24X1),V_24X2),V_24X3) = c_24__lam__28456___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_22276_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__22276,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__22276___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnAcyclic.pref_union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cHahnAcyclic_2epref__union,V_24X1),V_24X2),V_24X3) = cHahnAcyclic_2epref__union___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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_hahn.HahnList.undup_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnList_2eundup,V_24X1),V_24X2) = chahn_2eHahnList_2eundup___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).
fof('$adef_Coq.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_hahn.HahnRelationsBasic.strict_total_order_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2estrict__total__order,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2estrict__total__order___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.clos_sym_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__sym,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__sym___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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_$_prop_16215_$a1',axiom,
! [V_24X1] : happ(c_24__prop__16215,V_24X1) = c_24__prop__16215___24a1(V_24X1) ).
fof('$adef_$_lam_15963_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__15963,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__15963___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_lam_202_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__202,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__202___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_35041_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__35041,V_24X1),V_24X2),V_24X3) = c_24__lam__35041___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_1948_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1948,V_24X1),V_24X2),V_24X3) = c_24__lam__1948___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_570_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__570,V_24X1),V_24X2) = c_24__prop__570___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_741_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__741,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__741___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V_24X1,V_24X2) ).
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_1987_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1987,V_24X1),V_24X2),V_24X3) = c_24__lam__1987___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a1(V_24X1) ).
fof('$adef_$_lam_3076_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__3076,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__3076___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.PCond_$a15',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] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ePCond,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15))
<=> cCoq_2esetoid__ring_2eField__theory_2ePCond___24a15(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.opp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_14675_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__14675,V_24X1),V_24X2) = c_24__lam__14675___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2eseq___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_14667_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__14667,V_24X1),V_24X2) = c_24__lam__14667___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.codom_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_2040_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2040,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2040___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_14675_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__14675,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__14675___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnBase.eq_op_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eeq__op,V_24X1) = chahn_2eHahnBase_2eeq__op___24a1(V_24X1) ).
fof('$adef_$_prop_22272_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__22272,V_24X1),V_24X2),V_24X3) = c_24__prop__22272___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.minus_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eminus__rel,V_24X1) = chahn_2eHahnRelationsBasic_2eminus__rel___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.codom_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2ecodom__rel___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Classes.RelationClasses.Transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eTransitive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_$_prop_14166_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__14166,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__14166___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_12917_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__12917,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__12917___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_prop_35227_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35227,V_24X1),V_24X2) = c_24__prop__35227___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.minus_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eminus__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2eminus__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.commut_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ecommut,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Arith.Between.between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnMaxElt.max_elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1),V_24X2) = chahn_2eHahnMaxElt_2emax__elt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1915_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1915,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1915___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_$_prop_33570_$a1',axiom,
! [V_24X1] : happ(c_24__prop__33570,V_24X1) = c_24__prop__33570___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).
fof('$adef_hahn.HahnBase.NW_$a1',axiom,
! [V_24X1] :
( p(happ(chahn_2eHahnBase_2eNW,V_24X1))
<=> chahn_2eHahnBase_2eNW___24a1(V_24X1) ) ).
fof('$adef_hahn.HahnRelationsBasic.dom_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2edom__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2edom__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_33568_$a1',axiom,
! [V_24X1] : happ(c_24__prop__33568,V_24X1) = c_24__prop__33568___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalRelReification_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalRelReification__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalRelReification__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_1942_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__1942,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__1942___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.restr_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnSets.set_subset_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__subset,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__subset___24a3(V_24X1,V_24X2,V_24X3) ) ).
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('$adef_hahn.HahnRelationsBasic.irreflexive_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1) = chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V_24X1) ).
fof('$adef_$_lam_1791_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__1791,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__1791___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_2299_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__2299,V_24X1),V_24X2),V_24X3) = c_24__prop__2299___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).
fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2040_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2040,V_24X1),V_24X2),V_24X3) = c_24__lam__2040___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35178_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35178,V_24X1),V_24X2) = c_24__prop__35178___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.CompareSpec_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpec,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.irreflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2eirreflexive___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('$adef_$_lam_1996_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1996,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1996___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_2029_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2029,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2029___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnRelationsBasic.bunion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2ebunion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_14667_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__14667,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__14667___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_3160_$a1',axiom,
! [V_24X1] : happ(c_24__lam__3160,V_24X1) = c_24__lam__3160___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.Morphisms.respectful_$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('$adef_$_lam_2460_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2460,V_24X1),V_24X2),V_24X3) = c_24__lam__2460___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_28633_$a12',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__28633,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__28633___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).
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('$adef_$_prop_35155_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35155,V_24X1),V_24X2) = c_24__prop__35155___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_union_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnSets_2eset__union,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnSets_2eset__union___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1966_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1966,V_24X1),V_24X2),V_24X3) = c_24__lam__1966___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnSets.set_compl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__compl,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__compl___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_11781_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__11781,V_24X1),V_24X2),V_24X3) = c_24__prop__11781___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Init.Datatypes.list_rect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rect,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rect___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_1892_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__1892,V_24X1),V_24X2))
<=> c_24__lam__1892___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnBase.Equality.Pack_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnBase_2eEquality_2ePack,V_24X1),V_24X2),V_24X3) = chahn_2eHahnBase_2eEquality_2ePack___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_699_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__699,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__699___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_prop_1238_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1238,V_24X1),V_24X2) = c_24__prop__1238___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_14691_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__14691,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__14691___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1901_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1901,V_24X1),V_24X2),V_24X3) = c_24__lam__1901___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.singl_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2esingl__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2esingl__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_prop_1233_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1233,V_24X1),V_24X2) = c_24__prop__1233___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35197_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35197,V_24X1),V_24X2) = c_24__prop__35197___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_14691_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__14691,V_24X1),V_24X2) = c_24__lam__14691___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_329_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__329,V_24X1),V_24X2) = c_24__lam__329___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_378_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__378,V_24X1),V_24X2) = c_24__prop__378___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Between.in_int_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ein__int,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eBetween_2ein__int___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.map_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2emap__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
<=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__right,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__right___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
<=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.minus_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2eminus__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1) = chahn_2eHahnRelationsBasic_2eacyclic___24a1(V_24X1) ).
fof('$adef_$_lam_2633_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2633,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2633___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_22265_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__22265,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__22265___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_22_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__22,V_24X1),V_24X2) = c_24__lam__22___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.codom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2ecodom__rel___24a1(V_24X1) ).
fof('$adef_$_lam_1942_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1942,V_24X1),V_24X2) = c_24__lam__1942___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_1791_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1791,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1791___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_14683_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__14683,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__14683___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1(V_24X1) ).
fof('$adef_$_fix_15285_1_add_carry_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__fix__15285__1__add__carry,V_24X1),V_24X2) = c_24__fix__15285__1__add__carry___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_map_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnSets_2eset__map,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnSets_2eset__map___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_28456_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__28456,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__28456___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnEquational.good_ctx_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnEquational_2egood__ctx,V_24X1),V_24X2))
<=> chahn_2eHahnEquational_2egood__ctx___24a2(V_24X1,V_24X2) ) ).
fof('$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_hahn.HahnMaxElt.wmax_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnMaxElt_2ewmax__elt___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cCoq_2eRelations_2eRelation__Operators_2eunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.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_$_lam_741_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__741,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__741___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_Coq.setoid_ring.Field_theory.rsplit_left_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__left,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__left___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_28472_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__28472,V_24X1),V_24X2),V_24X3) = c_24__lam__28472___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2757_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2757,V_24X1),V_24X2),V_24X3) = c_24__lam__2757___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.inter_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2einter__rel___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('$adef_hahn.HahnRelationsBasic.is_total_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2eis__total,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2eis__total___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.list_rec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elist__rec,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elist__rec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1963_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1963,V_24X1),V_24X2) = c_24__lam__1963___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.map_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2emap__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$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.micromega.Tauto.cnf_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).
fof('$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.Init.Specif.exist_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_11778_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__11778,V_24X1),V_24X2),V_24X3) = c_24__prop__11778___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_22265_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__22265,V_24X1),V_24X2) = c_24__lam__22265___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_15977_$a1',axiom,
! [V_24X1] : happ(c_24__prop__15977,V_24X1) = c_24__prop__15977___24a1(V_24X1) ).
fof('$adef_$_let_var_6_p_7704_7706_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__7704__7706,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__7704__7706___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_312_$a1',axiom,
! [V_24X1] : happ(c_24__lam__312,V_24X1) = c_24__lam__312___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).
fof('$adef_$_lam_18_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__18,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__18___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_hahn.HahnRelationsBasic.singl_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2esingl__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnSets.set_empty_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnSets_2eset__empty,V_24X1),V_24X2))
<=> chahn_2eHahnSets_2eset__empty___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.collect_rel_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2ecollect__rel___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
<=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.same_relation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_$_lam_1895_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1895,V_24X1),V_24X2),V_24X3) = c_24__lam__1895___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Definitions.equiv_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequiv,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.pair_$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('$adef_$_lam_15963_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__15963,V_24X1),V_24X2) = c_24__lam__15963___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_10_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__10,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__10___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_11777_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__11777,V_24X1),V_24X2),V_24X3) = c_24__prop__11777___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Logic.ClassicalDescription.excluded_middle_informative_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative,V_24X1) = cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(V_24X1) ).
fof('$adef_$_prop_35139_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35139,V_24X1),V_24X2),V_24X3) = c_24__prop__35139___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.cnf_tt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.inter_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEeval_$a14',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEeval,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14) = cCoq_2esetoid__ring_2eRing__polynom_2ePEeval___24a14(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14) ).
fof('$adef_Coq.Init.Specif.absurd_set_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eabsurd__set,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eabsurd__set___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('$adef_$_lam_3244_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__3244,V_24X1),V_24X2) = c_24__lam__3244___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.ChoiceFacts.ConstructiveDefiniteDescription_on_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on,V_24X1) = cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on___24a1(V_24X1) ).
fof('$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_hahn.HahnRelationsBasic.immediate_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eimmediate___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_681_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__681,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__681___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Arith.Wf_nat.has_unique_least_element_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eArith_2eWf__nat_2ehas__unique__least__element,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eArith_2eWf__nat_2ehas__unique__least__element___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_3160_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__3160,V_24X1),V_24X2) = c_24__lam__3160___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnBase.Equality.sort_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eEquality_2esort,V_24X1) = chahn_2eHahnBase_2eEquality_2esort___24a1(V_24X1) ).
fof('$adef_$_lam_312_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__312,V_24X1),V_24X2))
<=> c_24__lam__312___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_681_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__681,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__681___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_2757_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__2757,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__2757___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1373_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1373,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1373___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.Bool.Bool.ReflectF_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).
fof('$adef_Coq.Arith.Compare_dec.le_gt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__gt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1800_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__1800,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__1800___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_hahn.HahnRelationsBasic.restr_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2erestr__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_inter_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnSets_2eset__inter,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnSets_2eset__inter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Logic.unique_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eunique,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eunique___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.right_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
<=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).
fof('$adef_$_lam_18_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__18,V_24X1),V_24X2) = c_24__lam__18___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_571_$a1',axiom,
! [V_24X1] : happ(c_24__prop__571,V_24X1) = c_24__prop__571___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.cross_rel_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecross__rel,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2ecross__rel___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Gt.gt_not_le_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eGt_2egt__not__le,V_24X1),V_24X2) = cCoq_2eArith_2eGt_2egt__not__le___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2436_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2436,V_24X1),V_24X2),V_24X3) = c_24__lam__2436___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_35174_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35174,V_24X1),V_24X2),V_24X3) = c_24__prop__35174___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Arith.Compare_dec.le_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.restr_subset_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2erestr__subset,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2erestr__subset___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_prop_16049_$a1',axiom,
! [V_24X1] : happ(c_24__prop__16049,V_24X1) = c_24__prop__16049___24a1(V_24X1) ).
fof('$adef_Coq.Lists.SetoidList.removeA_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eremoveA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eSetoidList_2eremoveA___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_prop_14164_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__14164,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__14164___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_2311_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__2311,V_24X1),V_24X2),V_24X3) = c_24__prop__2311___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.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_$_prop_35162_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35162,V_24X1),V_24X2) = c_24__prop__35162___24a2(V_24X1,V_24X2) ).
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('$adef_hahn.HahnRelationsBasic.pow_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2epow__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2epow__rel___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('$adef_Coq.Relations.Relation_Definitions.same_relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2esame__relation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalFacts.Minimal_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eClassicalFacts_2eMinimal,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eClassicalFacts_2eMinimal___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eeqv__rel___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('$adef_$_prop_33567_$a1',axiom,
! [V_24X1] : happ(c_24__prop__33567,V_24X1) = c_24__prop__33567___24a1(V_24X1) ).
fof('$adef_hahn.HahnDom.doma_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnDom_2edoma,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnDom_2edoma___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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.Logic.ClassicalFacts.Minimization_Property_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property,V_24X1))
<=> cCoq_2eLogic_2eClassicalFacts_2eMinimization__Property___24a1(V_24X1) ) ).
fof('$adef_$_lam_28472_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__28472,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__28472___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_12917_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__12917,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__12917___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnRelationsBasic_2eseq___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.ZArith.Znat.neq_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnat_2eneq,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnat_2eneq___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.dom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2edom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2edom__rel___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.InitialRing.gen_phiN_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiN___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Definitions.inclusion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_1978_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1978,V_24X1),V_24X2),V_24X3) = c_24__lam__1978___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_11779_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__11779,V_24X1),V_24X2),V_24X3) = c_24__prop__11779___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.bunion_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> chahn_2eHahnRelationsBasic_2ebunion___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Lists.SetoidList.equivlistA_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eequivlistA,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2eequivlistA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eunion,V_24X1),V_24X2),V_24X3) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_2429_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2429,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2429___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_Coq.Lists.List.filter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2efilter,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2efilter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Sorting.Permutation.Permutation_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eSorting_2ePermutation_2ePermutation,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eSorting_2ePermutation_2ePermutation___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_prop_13059_$a1',axiom,
! [V_24X1] : happ(c_24__prop__13059,V_24X1) = c_24__prop__13059___24a1(V_24X1) ).
fof('$adef_$_lam_699_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__699,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__699___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__refl,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__refl___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$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('$adef_$_lam_1963_$a1',axiom,
! [V_24X1] : happ(c_24__lam__1963,V_24X1) = c_24__lam__1963___24a1(V_24X1) ).
fof('$adef_$_lam_3244_$a1',axiom,
! [V_24X1] : happ(c_24__lam__3244,V_24X1) = c_24__lam__3244___24a1(V_24X1) ).
fof('$adef_hahn.HahnBase.Equality.op_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnBase_2eEquality_2eop,V_24X1),V_24X2) = chahn_2eHahnBase_2eEquality_2eop___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Lists.List.fold_right_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_569_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__569,V_24X1),V_24X2) = c_24__prop__569___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_1956_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1956,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1956___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnMinPath.min_cycle_mod_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnMinPath_2emin__cycle__mod,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnMinPath_2emin__cycle__mod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_1966_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1966,V_24X1),V_24X2) = c_24__lam__1966___24a2(V_24X1,V_24X2) ).
fof('$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_$_prop_35170_$a1',axiom,
! [V_24X1] : happ(c_24__prop__35170,V_24X1) = c_24__prop__35170___24a1(V_24X1) ).
fof('$adef_hahn.HahnFuneq.funeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnFuneq_2efuneq,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnFuneq_2efuneq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
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('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_1895_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1895,V_24X1),V_24X2) = c_24__lam__1895___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.clos_sym_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eclos__sym,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).
fof('$adef_$_lam_1779_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__1779,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__1779___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_674_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__674,V_24X1),V_24X2),V_24X3) = c_24__lam__674___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_15958_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__15958,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__15958___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Lists.List.NoDup_$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('$adef_hahn.HahnSets.set_equiv_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnSets_2eset__equiv,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnSets_2eset__equiv___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_1901_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__1901,V_24X1),V_24X2) = c_24__lam__1901___24a2(V_24X1,V_24X2) ).
fof('$adef_$_case_Coq.Init.Specif.sumbool$1224_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumbool_241224,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eSpecif_2esumbool_241224___24a2(V_24X1,V_24X2) ).
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('$adef_$_prop_14199_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__14199,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__14199___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.semi_field_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_hahn.HahnSets.set_minus_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnSets_2eset__minus,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnSets_2eset__minus___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnDom.domb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnDom_2edomb,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnDom_2edomb___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_1972_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1972,V_24X1),V_24X2),V_24X3) = c_24__lam__1972___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_10_$a1',axiom,
! [V_24X1] : happ(c_24__lam__10,V_24X1) = c_24__lam__10___24a1(V_24X1) ).
fof('$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_$_lam_2633_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2633,V_24X1),V_24X2),V_24X3) = c_24__lam__2633___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_974_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__974,V_24X1),V_24X2) = c_24__lam__974___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_28464_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__28464,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__28464___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1) = chahn_2eHahnRelationsBasic_2eseq___24a1(V_24X1) ).
fof('$adef_$_lam_1996_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__1996,V_24X1),V_24X2),V_24X3) = c_24__lam__1996___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_1234_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__1234,V_24X1),V_24X2) = c_24__prop__1234___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_35183_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__35183,V_24X1),V_24X2) = c_24__prop__35183___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_22_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__22,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__22___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_HahnAcyclic.pref_union_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(cHahnAcyclic_2epref__union,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> cHahnAcyclic_2epref__union___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
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('$adef_hahn.HahnRelationsBasic.collect_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).
fof('$adef_$_let_var_6_p_7702_7705_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__7702__7705,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__7702__7705___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.Init.Specif.right_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eright___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
<=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Classes.RelationClasses.PreOrder_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2ePreOrder,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).
fof('$adef_Coq.setoid_ring.Field_theory.rsplit_common_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2ersplit__common,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2ersplit__common___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_14683_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__14683,V_24X1),V_24X2) = c_24__lam__14683___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_3076_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__3076,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__3076___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Lists.List.In_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnRelationsBasic.upward_closed_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(chahn_2eHahnRelationsBasic_2eupward__closed,V_24X1),V_24X2),V_24X3))
<=> chahn_2eHahnRelationsBasic_2eupward__closed___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_prop_11780_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__11780,V_24X1),V_24X2),V_24X3) = c_24__prop__11780___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_22276_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__22276,V_24X1),V_24X2) = c_24__lam__22276___24a2(V_24X1,V_24X2) ).
fof('$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_hahn.HahnRelationsBasic.functional_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(chahn_2eHahnRelationsBasic_2efunctional,V_24X1),V_24X2))
<=> chahn_2eHahnRelationsBasic_2efunctional___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.gt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_202_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__202,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__202___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_case_Coq.Init.Datatypes.prod$32394_$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_2432394,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_2432394___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).
fof('$tdef_$_type_19202',axiom,
! [V_24Y] :
( c_24__type__19202___24t(V_24Y)
<=> t(V_24Y,c_24__type__19202) ) ).
fof('$tdef_$_type_2254',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__2254___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__2254___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_205',axiom,
! [V_24Y] :
( c_24__type__205___24t(V_24Y)
<=> t(V_24Y,c_24__type__205) ) ).
fof('$tdef_$_type_10905',axiom,
! [V_24Y] :
( c_24__type__10905___24t(V_24Y)
<=> t(V_24Y,c_24__type__10905) ) ).
fof('$tdef_$_type_2513',axiom,
! [V_24Y] :
( c_24__type__2513___24t(V_24Y)
<=> t(V_24Y,c_24__type__2513) ) ).
fof('$tdef_$_type_30421',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__30421___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__30421___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_19908',axiom,
! [V_24Y] :
( c_24__type__19908___24t(V_24Y)
<=> t(V_24Y,c_24__type__19908) ) ).
fof('$tdef_$_type_27091',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__27091___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__27091___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_8851',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8851___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__8851___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_9429',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9429___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9429___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22792',axiom,
! [V_24Y] :
( c_24__type__22792___24t(V_24Y)
<=> t(V_24Y,c_24__type__22792) ) ).
fof('$tdef_$_type_32596',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32596___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32596___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_225',axiom,
! [V_24Y] :
( c_24__type__225___24t(V_24Y)
<=> t(V_24Y,c_24__type__225) ) ).
fof('$tdef_$_type_13071',axiom,
! [V_24Y] :
( c_24__type__13071___24t(V_24Y)
<=> t(V_24Y,c_24__type__13071) ) ).
fof('$tdef_$_type_10670',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10670___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10670___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19185',axiom,
! [V_24Y] :
( c_24__type__19185___24t(V_24Y)
<=> t(V_24Y,c_24__type__19185) ) ).
fof('$tdef_$_type_14420',axiom,
! [V_24Y] :
( c_24__type__14420___24t(V_24Y)
<=> t(V_24Y,c_24__type__14420) ) ).
fof('$tdef_$_type_7716',axiom,
! [V_24Y] :
( c_24__type__7716___24t(V_24Y)
<=> t(V_24Y,c_24__type__7716) ) ).
fof('$tdef_$_type_8725',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8725___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__8725___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_3061',axiom,
! [V_24Y] :
( c_24__type__3061___24t(V_24Y)
<=> t(V_24Y,c_24__type__3061) ) ).
fof('$tdef_$_type_455',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__455___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__455___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_6416',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__6416___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__6416___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_3362',axiom,
! [V_24Y] :
( c_24__type__3362___24t(V_24Y)
<=> t(V_24Y,c_24__type__3362) ) ).
fof('$tdef_$_type_13479',axiom,
! [V_24Y] :
( c_24__type__13479___24t(V_24Y)
<=> t(V_24Y,c_24__type__13479) ) ).
fof('$tdef_$_type_13329',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13329___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13329___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1146',axiom,
! [V_24Y] :
( c_24__type__1146___24t(V_24Y)
<=> t(V_24Y,c_24__type__1146) ) ).
fof('$tdef_$_type_374',axiom,
! [V_24Y] :
( c_24__type__374___24t(V_24Y)
<=> t(V_24Y,c_24__type__374) ) ).
fof('$tdef_$_type_4728',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__4728___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__4728___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_4460',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__4460___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__4460___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_353',axiom,
! [V_24Y] :
( c_24__type__353___24t(V_24Y)
<=> t(V_24Y,c_24__type__353) ) ).
fof('$tdef_$_type_5289',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__5289___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__5289___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25384',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__25384___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__25384___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('$tdef_hahn.HahnBase.Equality.axiom',axiom,
! [V_24X1,V_24X2,V_24Y] :
( chahn_2eHahnBase_2eEquality_2eaxiom___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2eaxiom___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.Init.Datatypes.bool',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ebool) ) ).
fof('$tdef_$_type_14144',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14144___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14144___24a2(V_24X1,V_24X2)) ) ).
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_$_type_31060',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31060___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31060___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_5861',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5861___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__5861___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Logic.ChoiceFacts.ConstructiveDefiniteDescription_on',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eLogic_2eChoiceFacts_2eConstructiveDefiniteDescription__on___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8905',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8905___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__8905___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_788',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__788___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__788___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_8360',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8360___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__8360___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_4553',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__4553___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__4553___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_7928',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__7928___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__7928___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_37',axiom,
! [V_24Y] :
( c_24__type__37___24t(V_24Y)
<=> t(V_24Y,c_24__type__37) ) ).
fof('$tdef_$_type_33615',axiom,
! [V_24Y] :
( c_24__type__33615___24t(V_24Y)
<=> t(V_24Y,c_24__type__33615) ) ).
fof('$tdef_$_type_13338',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__13338___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__13338___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_14080',axiom,
! [V_24Y] :
( c_24__type__14080___24t(V_24Y)
<=> t(V_24Y,c_24__type__14080) ) ).
fof('$tdef_$_type_26399',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26399___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26399___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_22021',axiom,
! [V_24Y] :
( c_24__type__22021___24t(V_24Y)
<=> t(V_24Y,c_24__type__22021) ) ).
fof('$tdef_$_type_15674',axiom,
! [V_24Y] :
( c_24__type__15674___24t(V_24Y)
<=> t(V_24Y,c_24__type__15674) ) ).
fof('$tdef_$_type_4',axiom,
! [V_24X1,V_24Y] :
( c_24__type__4___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__4___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31681',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31681___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31681___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_249',axiom,
! [V_24Y] :
( c_24__type__249___24t(V_24Y)
<=> t(V_24Y,c_24__type__249) ) ).
fof('$tdef_$_type_1565',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1565___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1565___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12739',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__12739___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__12739___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$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_586',axiom,
! [V_24Y] :
( c_24__type__586___24t(V_24Y)
<=> t(V_24Y,c_24__type__586) ) ).
fof('$tdef_$_type_405',axiom,
! [V_24X1,V_24Y] :
( c_24__type__405___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__405___24a1(V_24X1)) ) ).
fof('$tdef_$_type_21923',axiom,
! [V_24Y] :
( c_24__type__21923___24t(V_24Y)
<=> t(V_24Y,c_24__type__21923) ) ).
fof('$tdef_$_type_33598',axiom,
! [V_24Y] :
( c_24__type__33598___24t(V_24Y)
<=> t(V_24Y,c_24__type__33598) ) ).
fof('$tdef_$_type_28765',axiom,
! [V_24Y] :
( c_24__type__28765___24t(V_24Y)
<=> t(V_24Y,c_24__type__28765) ) ).
fof('$tdef_$_type_14263',axiom,
! [V_24Y] :
( c_24__type__14263___24t(V_24Y)
<=> t(V_24Y,c_24__type__14263) ) ).
fof('$tdef_$_type_3213',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3213___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3213___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32560',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32560___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32560___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
! [V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).
fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).
fof('$tdef_hahn.HahnBase.Equality.mixin_of',axiom,
! [V_24X1,V_24Y] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2emixin__of___24a1(V_24X1)) ) ).
fof('$tdef_$_type_68',axiom,
! [V_24Y] :
( c_24__type__68___24t(V_24Y)
<=> t(V_24Y,c_24__type__68) ) ).
fof('$tdef_$_type_14747',axiom,
! [V_24Y] :
( c_24__type__14747___24t(V_24Y)
<=> t(V_24Y,c_24__type__14747) ) ).
fof('$tdef_$_type_12774',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12774___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12774___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32640',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32640___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32640___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$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_$_type_34',axiom,
! [V_24Y] :
( c_24__type__34___24t(V_24Y)
<=> t(V_24Y,c_24__type__34) ) ).
fof('$tdef_$_type_12694',axiom,
! [V_24Y] :
( c_24__type__12694___24t(V_24Y)
<=> t(V_24Y,c_24__type__12694) ) ).
fof('$tdef_$_type_14162',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14162___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14162___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31468',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__31468___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__31468___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_9537',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9537___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9537___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_15658',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15658___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15658___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_498',axiom,
! [V_24Y] :
( c_24__type__498___24t(V_24Y)
<=> t(V_24Y,c_24__type__498) ) ).
fof('$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_33580',axiom,
! [V_24Y] :
( c_24__type__33580___24t(V_24Y)
<=> t(V_24Y,c_24__type__33580) ) ).
fof('$tdef_$_type_2642',axiom,
! [V_24Y] :
( c_24__type__2642___24t(V_24Y)
<=> t(V_24Y,c_24__type__2642) ) ).
fof('$tdef_$_type_7967',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__7967___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__7967___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_26076',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__26076___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__26076___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_30013',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__30013___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__30013___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_46',axiom,
! [V_24Y] :
( c_24__type__46___24t(V_24Y)
<=> t(V_24Y,c_24__type__46) ) ).
fof('$tdef_$_type_1142',axiom,
! [V_24Y] :
( c_24__type__1142___24t(V_24Y)
<=> t(V_24Y,c_24__type__1142) ) ).
fof('$tdef_$_type_165',axiom,
! [V_24X1,V_24Y] :
( c_24__type__165___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__165___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1254',axiom,
! [V_24Y] :
( c_24__type__1254___24t(V_24Y)
<=> t(V_24Y,c_24__type__1254) ) ).
fof('$tdef_$_type_11937',axiom,
! [V_24Y] :
( c_24__type__11937___24t(V_24Y)
<=> t(V_24Y,c_24__type__11937) ) ).
fof('$tdef_$_type_170',axiom,
! [V_24X1,V_24Y] :
( c_24__type__170___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__170___24a1(V_24X1)) ) ).
fof('$tdef_$_type_179',axiom,
! [V_24X1,V_24Y] :
( c_24__type__179___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__179___24a1(V_24X1)) ) ).
fof('$tdef_$_type_6618',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__6618___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__6618___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_30847',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__30847___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__30847___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_10666',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10666___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10666___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.setoid_ring.Field_theory.FExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1)) ) ).
fof('$tdef_$_type_40',axiom,
! [V_24Y] :
( c_24__type__40___24t(V_24Y)
<=> t(V_24Y,c_24__type__40) ) ).
fof('$tdef_$_type_22270',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22270___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22270___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24692',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__24692___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__24692___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_Coq.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_256',axiom,
! [V_24Y] :
( c_24__type__256___24t(V_24Y)
<=> t(V_24Y,c_24__type__256) ) ).
fof('$tdef_$_type_217',axiom,
! [V_24Y] :
( c_24__type__217___24t(V_24Y)
<=> t(V_24Y,c_24__type__217) ) ).
fof('$tdef_$_type_2649',axiom,
! [V_24Y] :
( c_24__type__2649___24t(V_24Y)
<=> t(V_24Y,c_24__type__2649) ) ).
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_$_type_19356',axiom,
! [V_24Y] :
( c_24__type__19356___24t(V_24Y)
<=> t(V_24Y,c_24__type__19356) ) ).
fof('$tdef_$_type_5371',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5371___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5371___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.sig',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_19913',axiom,
! [V_24X1,V_24Y] :
( c_24__type__19913___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__19913___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16934',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__16934___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__16934___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_27737',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__27737___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__27737___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_4635',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__4635___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__4635___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2313',axiom,
! [V_24Y] :
( c_24__type__2313___24t(V_24Y)
<=> t(V_24Y,c_24__type__2313) ) ).
fof('$tdef_$_type_33565',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33565___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33565___24a1(V_24X1)) ) ).
fof('$tdef_$_type_12686',axiom,
! [V_24Y] :
( c_24__type__12686___24t(V_24Y)
<=> t(V_24Y,c_24__type__12686) ) ).
fof('$tdef_$_type_30226',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__30226___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__30226___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_9399',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9399___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9399___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_4928',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__4928___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__4928___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_25038',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__25038___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__25038___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('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_14742',axiom,
! [V_24Y] :
( c_24__type__14742___24t(V_24Y)
<=> t(V_24Y,c_24__type__14742) ) ).
fof('$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_16922',axiom,
! [V_24X1,V_24Y] :
( c_24__type__16922___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__16922___24a1(V_24X1)) ) ).
fof('$tdef_$_type_16919',axiom,
! [V_24Y] :
( c_24__type__16919___24t(V_24Y)
<=> t(V_24Y,c_24__type__16919) ) ).
fof('$tdef_$_type_12689',axiom,
! [V_24Y] :
( c_24__type__12689___24t(V_24Y)
<=> t(V_24Y,c_24__type__12689) ) ).
fof('$tdef_$_type_9453',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9453___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9453___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_369',axiom,
! [V_24Y] :
( c_24__type__369___24t(V_24Y)
<=> t(V_24Y,c_24__type__369) ) ).
fof('$tdef_$_type_1095',axiom,
! [V_24Y] :
( c_24__type__1095___24t(V_24Y)
<=> t(V_24Y,c_24__type__1095) ) ).
fof('$tdef_$_type_1027',axiom,
! [V_24Y] :
( c_24__type__1027___24t(V_24Y)
<=> t(V_24Y,c_24__type__1027) ) ).
fof('$tdef_$_type_14185',axiom,
! [V_24Y] :
( c_24__type__14185___24t(V_24Y)
<=> t(V_24Y,c_24__type__14185) ) ).
fof('$tdef_$_type_3330',axiom,
! [V_24Y] :
( c_24__type__3330___24t(V_24Y)
<=> t(V_24Y,c_24__type__3330) ) ).
fof('$tdef_$_type_138',axiom,
! [V_24Y] :
( c_24__type__138___24t(V_24Y)
<=> t(V_24Y,c_24__type__138) ) ).
fof('$tdef_$_type_8297',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8297___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__8297___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_25730',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__25730___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__25730___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_23677',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__23677___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__23677___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_3172',axiom,
! [V_24Y] :
( c_24__type__3172___24t(V_24Y)
<=> t(V_24Y,c_24__type__3172) ) ).
fof('$tdef_$_type_315',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__315___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__315___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_2318',axiom,
! [V_24Y] :
( c_24__type__2318___24t(V_24Y)
<=> t(V_24Y,c_24__type__2318) ) ).
fof('$tdef_$_type_2578',axiom,
! [V_24Y] :
( c_24__type__2578___24t(V_24Y)
<=> t(V_24Y,c_24__type__2578) ) ).
fof('$tdef_$_type_620',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__620___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__620___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_10659',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10659___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10659___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_24346',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__24346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__24346___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_14829',axiom,
! [V_24Y] :
( c_24__type__14829___24t(V_24Y)
<=> t(V_24Y,c_24__type__14829) ) ).
fof('$tdef_$_type_5962',axiom,
! [V_24Y] :
( c_24__type__5962___24t(V_24Y)
<=> t(V_24Y,c_24__type__5962) ) ).
fof('$tdef_$_type_10622',axiom,
! [V_24X1,V_24Y] :
( c_24__type__10622___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__10622___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1127',axiom,
! [V_24Y] :
( c_24__type__1127___24t(V_24Y)
<=> t(V_24Y,c_24__type__1127) ) ).
fof('$tdef_$_type_2543',axiom,
! [V_24Y] :
( c_24__type__2543___24t(V_24Y)
<=> t(V_24Y,c_24__type__2543) ) ).
fof('$tdef_$_type_1735',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1735___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1735___24a1(V_24X1)) ) ).
fof('$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_8234',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8234___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__8234___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_13309',axiom,
! [V_24Y] :
( c_24__type__13309___24t(V_24Y)
<=> t(V_24Y,c_24__type__13309) ) ).
fof('$tdef_$_type_3177',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3177___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3177___24a1(V_24X1)) ) ).
fof('$tdef_$_type_29294',axiom,
! [V_24Y] :
( c_24__type__29294___24t(V_24Y)
<=> t(V_24Y,c_24__type__29294) ) ).
fof('$tdef_$_type_2600',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2600___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2600___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_12393',axiom,
! [V_24Y] :
( c_24__type__12393___24t(V_24Y)
<=> t(V_24Y,c_24__type__12393) ) ).
fof('$tdef_$_type_33632',axiom,
! [V_24Y] :
( c_24__type__33632___24t(V_24Y)
<=> t(V_24Y,c_24__type__33632) ) ).
fof('$tdef_$_type_307',axiom,
! [V_24Y] :
( c_24__type__307___24t(V_24Y)
<=> t(V_24Y,c_24__type__307) ) ).
fof('$tdef_$_type_19188',axiom,
! [V_24Y] :
( c_24__type__19188___24t(V_24Y)
<=> t(V_24Y,c_24__type__19188) ) ).
fof('$tdef_$_type_643',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__643___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__643___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32281',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32281___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32281___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_7011',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__7011___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__7011___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_15952',axiom,
! [V_24X1,V_24Y] :
( c_24__type__15952___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__15952___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3256',axiom,
! [V_24Y] :
( c_24__type__3256___24t(V_24Y)
<=> t(V_24Y,c_24__type__3256) ) ).
fof('$tdef_$_type_35223',axiom,
! [V_24Y] :
( c_24__type__35223___24t(V_24Y)
<=> t(V_24Y,c_24__type__35223) ) ).
fof('$tdef_$_type_2563',axiom,
! [V_24Y] :
( c_24__type__2563___24t(V_24Y)
<=> t(V_24Y,c_24__type__2563) ) ).
fof('$tdef_$_type_1177',axiom,
! [V_24Y] :
( c_24__type__1177___24t(V_24Y)
<=> t(V_24Y,c_24__type__1177) ) ).
fof('$tdef_$_type_23331',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__23331___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__23331___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_10901',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10901___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10901___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_5897',axiom,
! [V_24Y] :
( c_24__type__5897___24t(V_24Y)
<=> t(V_24Y,c_24__type__5897) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_$_type_5798',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5798___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__5798___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_hahn.HahnBase.Equality.sort',axiom,
! [V_24X1,V_24Y] :
( chahn_2eHahnBase_2eEquality_2esort___24t(V_24X1,V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2esort___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8414',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8414___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__8414___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_32659',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32659___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32659___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31273',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__31273___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__31273___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_12820',axiom,
! [V_24Y] :
( c_24__type__12820___24t(V_24Y)
<=> t(V_24Y,c_24__type__12820) ) ).
fof('$tdef_$_type_8968',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8968___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__8968___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_27414',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__27414___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__27414___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_1117',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1117___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1117___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6809',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__6809___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__6809___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32407',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32407___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32407___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_653',axiom,
! [V_24Y] :
( c_24__type__653___24t(V_24Y)
<=> t(V_24Y,c_24__type__653) ) ).
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_$_type_13057',axiom,
! [V_24Y] :
( c_24__type__13057___24t(V_24Y)
<=> t(V_24Y,c_24__type__13057) ) ).
fof('$tdef_$_type_14197',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14197___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14197___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33682',axiom,
! [V_24Y] :
( c_24__type__33682___24t(V_24Y)
<=> t(V_24Y,c_24__type__33682) ) ).
fof('$tdef_$_type_3449',axiom,
! [V_24Y] :
( c_24__type__3449___24t(V_24Y)
<=> t(V_24Y,c_24__type__3449) ) ).
fof('$tdef_$_type_341',axiom,
! [V_24Y] :
( c_24__type__341___24t(V_24Y)
<=> t(V_24Y,c_24__type__341) ) ).
fof('$tdef_$_type_62',axiom,
! [V_24Y] :
( c_24__type__62___24t(V_24Y)
<=> t(V_24Y,c_24__type__62) ) ).
fof('$tdef_$_type_35050',axiom,
! [V_24Y] :
( c_24__type__35050___24t(V_24Y)
<=> t(V_24Y,c_24__type__35050) ) ).
fof('$tdef_$_type_12697',axiom,
! [V_24Y] :
( c_24__type__12697___24t(V_24Y)
<=> t(V_24Y,c_24__type__12697) ) ).
fof('$tdef_$_type_28527',axiom,
! [V_24Y] :
( c_24__type__28527___24t(V_24Y)
<=> t(V_24Y,c_24__type__28527) ) ).
fof('$tdef_$_type_176',axiom,
! [V_24X1,V_24Y] :
( c_24__type__176___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__176___24a1(V_24X1)) ) ).
fof('$tdef_$_type_17295',axiom,
! [V_24Y] :
( c_24__type__17295___24t(V_24Y)
<=> t(V_24Y,c_24__type__17295) ) ).
fof('$tdef_$_type_60',axiom,
! [V_24X1,V_24Y] :
( c_24__type__60___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__60___24a1(V_24X1)) ) ).
fof('$tdef_$_type_15633',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__15633___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__15633___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_1544',axiom,
! [V_24X1,V_24Y] :
( c_24__type__1544___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__1544___24a1(V_24X1)) ) ).
fof('$tdef_$_type_8477',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8477___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8477___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_33659',axiom,
! [V_24Y] :
( c_24__type__33659___24t(V_24Y)
<=> t(V_24Y,c_24__type__33659) ) ).
fof('$tdef_$_type_2523',axiom,
! [V_24Y] :
( c_24__type__2523___24t(V_24Y)
<=> t(V_24Y,c_24__type__2523) ) ).
fof('$tdef_$_type_16875',axiom,
! [V_24Y] :
( c_24__type__16875___24t(V_24Y)
<=> t(V_24Y,c_24__type__16875) ) ).
fof('$tdef_$_type_14892',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__14892___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__14892___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_32239',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32239___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32239___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_13399',axiom,
! [V_24X1,V_24Y] :
( c_24__type__13399___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__13399___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1196',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__1196___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__1196___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_4192',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__4192___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__4192___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_376',axiom,
! [V_24Y] :
( c_24__type__376___24t(V_24Y)
<=> t(V_24Y,c_24__type__376) ) ).
fof('$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_667',axiom,
! [V_24X1,V_24Y] :
( c_24__type__667___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__667___24a1(V_24X1)) ) ).
fof('$tdef_$_type_483',axiom,
! [V_24Y] :
( c_24__type__483___24t(V_24Y)
<=> t(V_24Y,c_24__type__483) ) ).
fof('$tdef_$_type_28535',axiom,
! [V_24Y] :
( c_24__type__28535___24t(V_24Y)
<=> t(V_24Y,c_24__type__28535) ) ).
fof('$tdef_$_type_32189',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32189___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32189___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_14728',axiom,
! [V_24Y] :
( c_24__type__14728___24t(V_24Y)
<=> t(V_24Y,c_24__type__14728) ) ).
fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_1068',axiom,
! [V_24Y] :
( c_24__type__1068___24t(V_24Y)
<=> t(V_24Y,c_24__type__1068) ) ).
fof('$tdef_Coq.micromega.Tauto.cnf',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2emicromega_2eTauto_2ecnf___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15663',axiom,
! [V_24Y] :
( c_24__type__15663___24t(V_24Y)
<=> t(V_24Y,c_24__type__15663) ) ).
fof('$tdef_$_type_34411',axiom,
! [V_24Y] :
( c_24__type__34411___24t(V_24Y)
<=> t(V_24Y,c_24__type__34411) ) ).
fof('$tdef_$_type_3155',axiom,
! [V_24Y] :
( c_24__type__3155___24t(V_24Y)
<=> t(V_24Y,c_24__type__3155) ) ).
fof('$tdef_$_type_12813',axiom,
! [V_24Y] :
( c_24__type__12813___24t(V_24Y)
<=> t(V_24Y,c_24__type__12813) ) ).
fof('$tdef_$_type_588',axiom,
! [V_24Y] :
( c_24__type__588___24t(V_24Y)
<=> t(V_24Y,c_24__type__588) ) ).
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_$_type_3261',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3261___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3261___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33803',axiom,
! [V_24Y] :
( c_24__type__33803___24t(V_24Y)
<=> t(V_24Y,c_24__type__33803) ) ).
fof('$tdef_$_type_1256',axiom,
! [V_24Y] :
( c_24__type__1256___24t(V_24Y)
<=> t(V_24Y,c_24__type__1256) ) ).
fof('$tdef_$_type_12100',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12100___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12100___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_hahn.HahnBase.Equality.type',axiom,
! [V_24Y] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2etype) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_$_type_33561',axiom,
! [V_24Y] :
( c_24__type__33561___24t(V_24Y)
<=> t(V_24Y,c_24__type__33561) ) ).
fof('$tdef_$_type_295',axiom,
! [V_24Y] :
( c_24__type__295___24t(V_24Y)
<=> t(V_24Y,c_24__type__295) ) ).
fof('$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_4285',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__4285___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__4285___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_280',axiom,
! [V_24Y] :
( c_24__type__280___24t(V_24Y)
<=> t(V_24Y,c_24__type__280) ) ).
fof('$tdef_$_type_1959',axiom,
! [V_24Y] :
( c_24__type__1959___24t(V_24Y)
<=> t(V_24Y,c_24__type__1959) ) ).
fof('$tdef_$_type_32139',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32139___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32139___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_5681',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5681___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__5681___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_15148',axiom,
! [V_24Y] :
( c_24__type__15148___24t(V_24Y)
<=> t(V_24Y,c_24__type__15148) ) ).
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_$_type_22028',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__22028___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__22028___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_11150',axiom,
! [V_24Y] :
( c_24__type__11150___24t(V_24Y)
<=> t(V_24Y,c_24__type__11150) ) ).
fof('$tdef_$_type_14153',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__14153___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__14153___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_578',axiom,
! [V_24Y] :
( c_24__type__578___24t(V_24Y)
<=> t(V_24Y,c_24__type__578) ) ).
fof('$tdef_$_type_1046',axiom,
! [V_24Y] :
( c_24__type__1046___24t(V_24Y)
<=> t(V_24Y,c_24__type__1046) ) ).
fof('$tdef_$_type_26745',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__26745___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__26745___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_14441',axiom,
! [V_24Y] :
( c_24__type__14441___24t(V_24Y)
<=> t(V_24Y,c_24__type__14441) ) ).
fof('$tdef_$_type_5114',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5114___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5114___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_6708',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6708___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6708___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.setoid_ring.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_9486',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9486___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9486___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_29800',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__29800___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__29800___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_12783',axiom,
! [V_24Y] :
( c_24__type__12783___24t(V_24Y)
<=> t(V_24Y,c_24__type__12783) ) ).
fof('$tdef_$_type_3471',axiom,
! [V_24Y] :
( c_24__type__3471___24t(V_24Y)
<=> t(V_24Y,c_24__type__3471) ) ).
fof('$tdef_$_type_3089',axiom,
! [V_24Y] :
( c_24__type__3089___24t(V_24Y)
<=> t(V_24Y,c_24__type__3089) ) ).
fof('$tdef_$_type_3530',axiom,
! [V_24Y] :
( c_24__type__3530___24t(V_24Y)
<=> t(V_24Y,c_24__type__3530) ) ).
fof('$tdef_$_type_31876',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__31876___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__31876___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_28515',axiom,
! [V_24Y] :
( c_24__type__28515___24t(V_24Y)
<=> t(V_24Y,c_24__type__28515) ) ).
fof('$tdef_$_type_16873',axiom,
! [V_24Y] :
( c_24__type__16873___24t(V_24Y)
<=> t(V_24Y,c_24__type__16873) ) ).
fof('$tdef_$_type_576',axiom,
! [V_24Y] :
( c_24__type__576___24t(V_24Y)
<=> t(V_24Y,c_24__type__576) ) ).
fof('$tdef_$_type_24023',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__24023___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__24023___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_2673',axiom,
! [V_24Y] :
( c_24__type__2673___24t(V_24Y)
<=> t(V_24Y,c_24__type__2673) ) ).
fof('$tdef_$_type_1236',axiom,
! [V_24Y] :
( c_24__type__1236___24t(V_24Y)
<=> t(V_24Y,c_24__type__1236) ) ).
fof('$tdef_$_type_6517',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__6517___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__6517___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32516',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32516___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32516___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_10645',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__10645___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__10645___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7889',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__7889___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__7889___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_28',axiom,
! [V_24Y] :
( c_24__type__28___24t(V_24Y)
<=> t(V_24Y,c_24__type__28) ) ).
fof('$tdef_$_type_15964',axiom,
! [V_24Y] :
( c_24__type__15964___24t(V_24Y)
<=> t(V_24Y,c_24__type__15964) ) ).
fof('$tdef_$_type_14226',axiom,
! [V_24Y] :
( c_24__type__14226___24t(V_24Y)
<=> t(V_24Y,c_24__type__14226) ) ).
fof('$tdef_$_type_5021',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__5021___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__5021___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_258',axiom,
! [V_24Y] :
( c_24__type__258___24t(V_24Y)
<=> t(V_24Y,c_24__type__258) ) ).
fof('$tdef_$_type_1180',axiom,
! [V_24Y] :
( c_24__type__1180___24t(V_24Y)
<=> t(V_24Y,c_24__type__1180) ) ).
fof('$tdef_$_type_4378',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__4378___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__4378___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_418',axiom,
! [V_24Y] :
( c_24__type__418___24t(V_24Y)
<=> t(V_24Y,c_24__type__418) ) ).
fof('$tdef_$_type_28083',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y] :
( c_24__type__28083___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22,V_24Y)
<=> t(V_24Y,c_24__type__28083___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).
fof('$tdef_$_type_32331',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
( c_24__type__32331___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
<=> t(V_24Y,c_24__type__32331___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).
fof('$tdef_$_type_285',axiom,
! [V_24Y] :
( c_24__type__285___24t(V_24Y)
<=> t(V_24Y,c_24__type__285) ) ).
fof('$tdef_$_type_8788',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__8788___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__8788___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_9369',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9369___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9369___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_5618',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5618___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__5618___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_616',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__616___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__616___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_15974',axiom,
! [V_24Y] :
( c_24__type__15974___24t(V_24Y)
<=> t(V_24Y,c_24__type__15974) ) ).
fof('$tdef_$_type_5744',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__5744___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__5744___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_14267',axiom,
! [V_24Y] :
( c_24__type__14267___24t(V_24Y)
<=> t(V_24Y,c_24__type__14267) ) ).
fof('$tdef_$_type_9315',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9315___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9315___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32764',axiom,
! [V_24Y] :
( c_24__type__32764___24t(V_24Y)
<=> t(V_24Y,c_24__type__32764) ) ).
fof('$tdef_$_type_15677',axiom,
! [V_24Y] :
( c_24__type__15677___24t(V_24Y)
<=> t(V_24Y,c_24__type__15677) ) ).
fof('$tdef_$_type_30634',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y] :
( c_24__type__30634___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24Y)
<=> t(V_24Y,c_24__type__30634___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).
fof('$tdef_$_type_3233',axiom,
! [V_24Y] :
( c_24__type__3233___24t(V_24Y)
<=> t(V_24Y,c_24__type__3233) ) ).
fof('$tdef_$_type_5967',axiom,
! [V_24X1,V_24Y] :
( c_24__type__5967___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__5967___24a1(V_24X1)) ) ).
fof('$tdef_$_type_13083',axiom,
! [V_24Y] :
( c_24__type__13083___24t(V_24Y)
<=> t(V_24Y,c_24__type__13083) ) ).
fof('$tdef_$_type_488',axiom,
! [V_24Y] :
( c_24__type__488___24t(V_24Y)
<=> t(V_24Y,c_24__type__488) ) ).
fof('$tdef_$_type_20063',axiom,
! [V_24X1,V_24Y] :
( c_24__type__20063___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__20063___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32652',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__32652___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__32652___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_6910',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__6910___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__6910___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33795',axiom,
! [V_24Y] :
( c_24__type__33795___24t(V_24Y)
<=> t(V_24Y,c_24__type__33795) ) ).
fof('$tdef_$_type_19193',axiom,
! [V_24Y] :
( c_24__type__19193___24t(V_24Y)
<=> t(V_24Y,c_24__type__19193) ) ).
fof('$tdef_$_type_5464',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5464___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5464___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_12076',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__12076___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__12076___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_21991',axiom,
! [V_24Y] :
( c_24__type__21991___24t(V_24Y)
<=> t(V_24Y,c_24__type__21991) ) ).
fof('$tdef_$_type_5196',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__5196___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__5196___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_9345',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9345___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9345___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9510',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__9510___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__9510___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_1006',axiom,
! [V_24Y] :
( c_24__type__1006___24t(V_24Y)
<=> t(V_24Y,c_24__type__1006) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__r_27)
=> ! [V3__dom] :
( c_24__type__4___24t(V0__X,V3__dom)
=> ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,V1__r)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V1__r)
=> ( chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V3__dom,V1__r)
=> ( ! [V7__x] :
( t(V7__x,V0__X)
=> ! [V8__y] :
( t(V8__y,V0__X)
=> ( p(happ(happ(V2__r_27,V7__x),V8__y))
=> ( p(happ(V3__dom,V7__x))
& ~ p(happ(V3__dom,V8__y)) ) ) ) )
=> ! [V8__x] :
( t(V8__x,V0__X)
=> ! [V9__y] :
( t(V9__y,V0__X)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__X,cHahnAcyclic_2epref__union___24a3(V0__X,V1__r,V2__r_27),V8__x,V9__y)
=> ( p(happ(V3__dom,V9__y))
=> p(happ(happ(V1__r,V8__x),V9__y)) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------