TPTP Problem File: SEV623+1.p
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%------------------------------------------------------------------------------
% File : SEV623+1 : TPTP v9.3.1. Released v9.3.0.
% Domain : Set theory
% Problem : CoqHammer - HahnPath minus seq r
% 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 : HahnPath.minus.seq.r.p [Kal26]
% Status : Unknown
% Rating : 1.00 v9.3.0
% Syntax : Number of formulae : 2292 ( 594 unt; 0 def)
% Number of atoms : 8758 (1408 equ)
% Maximal formula atoms : 257 ( 3 avg)
% Number of connectives : 6550 ( 84 ~; 437 |; 663 &)
% ( 758 <=>;4608 =>; 0 <=; 0 <~>)
% Maximal formula depth : 258 ( 7 avg)
% Maximal term depth : 13 ( 1 avg)
% Number of predicates : 392 ( 391 usr; 0 prp; 1-11 aty)
% Number of functors : 1221 (1221 usr; 761 con; 0-10 aty)
% Number of variables : 7703 (7456 !; 247 ?)
% 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.Numbers.BinNums.N$34253',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__type__34256___24t(Vv__CANONICAL__0,Vv__CANONICAL__0)
=> ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> ( ( Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eN0
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_2434253___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 )
| ? [Vvar__0___24Anonymous__34254] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34254)
& Vv__CANONICAL__3 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__34254)
& c_24__case__Coq_2eNumbers_2eBinNums_2eN_2434253___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(c_24__let__4__P_27__34239___24a1(Vv__CANONICAL__0),happ(happ(Vv__CANONICAL__2,cCoq_2eNumbers_2eBinNums_2eN0),Vv__CANONICAL__1),c_24__let__5__f_27__34240___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2),Vvar__0___24Anonymous__34254) ) ) ) ) ).
fof('$_def_$_let_4_P\'_34239',axiom,
! [V0__P,V4__p] : c_24__let__4__P_27__34239___24a2(V0__P,V4__p) = happ(V0__P,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V4__p)) ).
fof('$_def_$_let_5_f\'_34240',axiom,
! [V0__P,V2__f,V5__p] : c_24__let__5__f_27__34240___24a3(V0__P,V2__f,V5__p) = happ(V2__f,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V5__p)) ).
fof('$_def_$_let_var_6_p_23043_23046',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23042] : c_24__let__var__6__p__23043__23046___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23042) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23042) ).
fof('$_def_$_let_var_6_p_23045_23047',axiom,
! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23044] : c_24__let__var__6__p__23045__23047___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23044) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23044) ).
fof('$_def_Coq.Arith.Compare_dec.le_gt_dec',axiom,
! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__gt__dec___24a2(V0__n,V1__m) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V0__n,V1__m) ).
fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__33049___24a1(V0__A)) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [Vvar__31393] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__31393)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__31393) ) ).
fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [Vvar__31394] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__31394)
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__31394) ) ).
fof('$_def_Coq.Init.Datatypes.IDProp',axiom,
( p(cCoq_2eInit_2eDatatypes_2eIDProp)
<=> ! [V0__A] :
( cProp___24t(V0__A)
=> ( p(V0__A)
=> p(V0__A) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.andb',axiom,
! [V0__b1,V1__b2] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
=> ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = V1__b2 )
| ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
& cCoq_2eInit_2eDatatypes_2eandb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).
fof('$_def_Coq.Init.Datatypes.app',axiom,
! [V0__A,V2__l,V3__m] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = V3__m )
| ? [Vvar__1___24Anonymous__3240] :
( t(Vvar__1___24Anonymous__3240,V0__A)
& ? [Vvar__2___24Anonymous__3241] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3241)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3240,Vvar__2___24Anonymous__3241)
& cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3240,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__3241,V3__m)) ) ) ) ) ) ).
fof('$_def_Coq.Init.Datatypes.length',axiom,
! [V0__A,V2__l] :
( cType___24t(V0__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
=> ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
| ? [Vvar__1___24Anonymous__3230] :
( t(Vvar__1___24Anonymous__3230,V0__A)
& ? [Vvar__2___24Anonymous__3231] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__3231)
& V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__3230,Vvar__2___24Anonymous__3231)
& cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__3231)) ) ) ) ) ) ).
fof('$_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__2893] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2893)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2893)
& cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__2893,V2__m)) ) ) ) ).
fof('$_def_Coq.Init.Nat.modulo',axiom,
! [V0__x,V1__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
=> ( ( V1__y = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2emodulo___24a2(V0__x,V1__y) = V1__y )
| ? [Vvar__0___24Anonymous__2903] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2903)
& V1__y = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2903)
& cCoq_2eInit_2eNat_2emodulo___24a2(V0__x,V1__y) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__2903,cCoq_2eInit_2eDatatypes_2esnd___24a3(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2edivmod___24a4(V0__x,Vvar__0___24Anonymous__2903,cCoq_2eInit_2eDatatypes_2eO,Vvar__0___24Anonymous__2903))) ) ) ) ).
fof('$_def_Coq.Init.Nat.pred',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = V0__n )
| ? [Vvar__0___24Anonymous__8768] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8768)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__8768)
& cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__8768 ) ) ) ).
fof('$_def_Coq.Init.Nat.sub',axiom,
! [V1__n,V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2898] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2898)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2898)
& ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
| ? [Vvar__0___24Anonymous__2901] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2901)
& V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2901)
& cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__2898,Vvar__0___24Anonymous__2901) ) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Init.Wf.well_founded',axiom,
! [V0__A,V1__R] :
( p(cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__R))
<=> ! [V2__a] :
( t(V2__a,V0__A)
=> cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__a) ) ) ).
fof('$_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__7530] :
( t(Vvar__1___24Anonymous__7530,V0__A)
& ? [Vvar__2___24Anonymous__7531] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7531)
& V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7530,Vvar__2___24Anonymous__7531)
& ( p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l))
<=> ( Vvar__1___24Anonymous__7530 = V2__a
| p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__7531)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.Lists.SetoidList.transpose',axiom,
! [V0__A,V1__B,V2__eqB,V3__f] :
( cCoq_2eLists_2eSetoidList_2etranspose___24a4(V0__A,V1__B,V2__eqB,V3__f)
<=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ! [V6__z] :
( t(V6__z,V1__B)
=> p(happ(happ(V2__eqB,happ(happ(V3__f,V4__x),happ(happ(V3__f,V5__y),V6__z))),happ(happ(V3__f,V5__y),happ(happ(V3__f,V4__x),V6__z)))) ) ) ) ) ).
fof('$_def_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
! [V0__A,V1__B] :
( cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V0__A,V1__B)
<=> ! [V2__R] :
( c_24__type__8654___24t(V0__A,V1__B,V2__R)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ? [V4__y] :
( t(V4__y,V1__B)
& p(happ(happ(V2__R,V3__x),V4__y)) ) )
=> ? [V4__f] :
( c_24__type__57___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('$_def_Coq.NArith.BinNat.N.le',axiom,
! [V0__x,V1__y] :
( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
<=> cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eGt ) ).
fof('$_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('$_def_Coq.NArith.BinNat.N.peano_rect',axiom,
! [V0__P,V1__f0,V2__f,V3__n] : cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__f0,V2__f,V3__n) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_2434253___24a4(V0__P,V1__f0,V2__f,V3__n) ).
fof('$_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__33029___24a1(V0__A)) ).
fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
| ? [Vvar__0___24Anonymous__31249] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__31249)
& V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__31249)
& cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__31249)) ) ) ) ).
fof('$_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('$_def_Coq.Relations.Relation_Definitions.commut',axiom,
! [V0__A,V1__R1,V2__R2] :
( cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3(V0__A,V1__R1,V2__R2)
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V4__y),V3__x))
=> ! [V6__z] :
( t(V6__z,V0__A)
=> ( p(happ(happ(V2__R2,V6__z),V4__y))
=> cCoq_2eInit_2eLogic_2eex2___24a3(V0__A,c_24__lam__32097___24a3(V0__A,V2__R2,V3__x),c_24__lam__32101___24a3(V0__A,V1__R1,V6__z)) ) ) ) ) ) ) ).
fof('$_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('$_def_Coq.Relations.Relation_Definitions.inclusion',axiom,
! [V0__A,V1__R1,V2__R2] :
( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2))
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__R1,V3__x),V4__y))
=> p(happ(happ(V2__R2,V3__x),V4__y)) ) ) ) ) ).
fof('$_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('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__90___24a1(V0__A) ).
fof('$_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)
<=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__R1,V2__R2))
& p(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.Sets.Relations_1.Relation',axiom,
! [V0__U] : cCoq_2eSets_2eRelations__1_2eRelation___24a1(V0__U) = c_24__type__90___24a1(V0__U) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [Vvar__36989] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__36989)
<=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__36989) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [Vvar__36946] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__36946)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__36946) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [Vvar__37055] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__37055)
<=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__37055) ) ).
fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [Vvar__37009] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__37009)
<=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__37009) ) ).
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__2987] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2987)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2987)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2991] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2991)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2991)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2987,Vvar__0___24Anonymous__2991)) )
| ? [Vvar__0___24Anonymous__2992] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2992)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2992)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2987,Vvar__0___24Anonymous__2992) ) ) ) ) )
| ? [Vvar__0___24Anonymous__2993] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2993)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2993)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
| ? [Vvar__0___24Anonymous__2997] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2997)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2997)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2997,Vvar__0___24Anonymous__2993) )
| ? [Vvar__0___24Anonymous__2998] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2998)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2998)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2993,Vvar__0___24Anonymous__2998)) ) ) ) ) ) ) ) ).
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__2421] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2421)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2421)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__2422] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2422)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2422)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
| ? [Vvar__0___24Anonymous__2423] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2423)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2423)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
| ? [Vvar__0___24Anonymous__2427] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2427)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2427)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__2423,Vvar__0___24Anonymous__2427) )
| ? [Vvar__0___24Anonymous__2428] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2428)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2428)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
| ? [Vvar__0___24Anonymous__2429] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2429)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2429)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__2433] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2433)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2433)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
| ? [Vvar__0___24Anonymous__2434] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2434)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2434)
& cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__2429,Vvar__0___24Anonymous__2434)) ) ) ) ) ) ) ) ).
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__3007] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3007)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3007)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3011] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3011)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3011)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3007,Vvar__0___24Anonymous__3011)) )
| ? [Vvar__0___24Anonymous__3012] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3012)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3012)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3007,Vvar__0___24Anonymous__3012)) ) ) ) ) )
| ? [Vvar__0___24Anonymous__3013] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3013)
& ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3013)
& ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3017] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3017)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3017)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3013,Vvar__0___24Anonymous__3017)) )
| ? [Vvar__0___24Anonymous__3018] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3018)
& V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3018)
& cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__3013,Vvar__0___24Anonymous__3018)) ) ) ) ) ) ) ) ).
fof('$_def_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
| ? [Vvar__0___24Anonymous__3020] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__3020)
& V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3020)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__3020)) ) ) ) ).
fof('$_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__3002] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3002)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3002)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3002) )
| ? [Vvar__0___24Anonymous__3003] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3003)
& V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__3003)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__3003) ) ) ) ).
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('$_def_Coq.micromega.Env.Env',axiom,
! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__34648___24a1(V0__D) ).
fof('$_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__23042] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23042)
& V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__23042)
& 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__23043__23046___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23042)),c_24__let__var__6__p__23043__23046___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23042))) )
| ? [Vvar__0___24Anonymous__23044] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__23044)
& V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__23044)
& 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__23045__23047___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23044)),c_24__let__var__6__p__23045__23047___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__23044)) )
| ( 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('$_def_hahn.HahnBase.Equality.sort',axiom,
! [V0__t] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V0__t)
=> ? [Vvar__0__sort__2979] :
( cType___24t(Vvar__0__sort__2979)
& ? [Vvar__1___24Anonymous__2980] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__2979,Vvar__1___24Anonymous__2980)
& ? [Vvar__2___24Anonymous__2981] :
( cType___24t(Vvar__2___24Anonymous__2981)
& V0__t = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__2979,Vvar__1___24Anonymous__2980,Vvar__2___24Anonymous__2981)
& chahn_2eHahnBase_2eEquality_2esort___24a1(V0__t) = Vvar__0__sort__2979 ) ) ) ) ).
fof('$_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('$_def_hahn.HahnDom.dom_cond',axiom,
! [V0__A,V1__r,V2__d,V3__e] :
( chahn_2eHahnDom_2edom__cond___24a4(V0__A,V1__r,V2__d,V3__e)
<=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V3__e)))),V2__d) ) ).
fof('$_def_hahn.HahnDom.doma',axiom,
! [V0__A,V1__r,V2__d] :
( p(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('$_def_hahn.HahnDom.domb',axiom,
! [V0__A,V1__r,V2__d] :
( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
<=> ! [V3__x] :
( t(V3__x,V0__A)
=> ! [V4__y] :
( t(V4__y,V0__A)
=> ( p(happ(happ(V1__r,V3__x),V4__y))
=> p(happ(V2__d,V4__y)) ) ) ) ) ).
fof('$_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__33165___24a2(V0__A,V1__P))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__33192___24a2(V0__A,V1__P)) ) ) ).
fof('$_def_hahn.HahnFuneq.funeq',axiom,
! [V0__A,V1__B,V2__f,V3__r] :
( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
<=> ! [V4__a] :
( t(V4__a,V0__A)
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(happ(V3__r,V4__a),V5__b))
=> happ(V2__f,V4__a) = happ(V2__f,V5__b) ) ) ) ) ).
fof('$_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__7313] :
( t(Vvar__1___24Anonymous__7313,V1__A)
& ? [Vvar__2___24Anonymous__7314] :
( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__7314)
& ( cType___24t(V1__A)
=> ( t(Vvar__1___24Anonymous__7313,V1__A)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__7314)
=> ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314)
& ( ( p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314)) = cCoq_2eInit_2eSpecif_2eleft___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314),c_24__prop__7330___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__7314) )
| ( ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314))
& cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314)) = cCoq_2eInit_2eSpecif_2eright___24a2(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314),c_24__prop__7342___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314))
& chahn_2eHahnList_2eundup___24a2(V1__A,V2__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__7313,chahn_2eHahnList_2eundup___24a2(V1__A,Vvar__2___24Anonymous__7314)) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.max_elt',axiom,
! [V0__A,V1__r,V2__a] :
( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a))
<=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(happ(happ(V1__r,V2__a),V3__b))
=> p(c_24False) ) ) ) ).
fof('$_def_hahn.HahnMaxElt.wmax_elt',axiom,
! [V0__A,V1__r,V2__a] :
( p(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('$_def_hahn.HahnRelationsBasic.acyclic',axiom,
! [V0__A,V1__r] :
( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r))
<=> p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r))) ) ).
fof('$_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('$_def_hahn.HahnRelationsBasic.eqv_dom_rel',axiom,
! [V0__A,V1__dom,V2__x,V3__y] :
( chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a4(V0__A,V1__dom,V2__x,V3__y)
<=> ( V2__x = V3__y
& p(cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__x,V1__dom)) ) ) ).
fof('$_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('$_def_hahn.HahnRelationsBasic.functional',axiom,
! [V0__A,V1__r] :
( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
<=> ! [V2__x] :
( t(V2__x,V0__A)
=> ! [V3__y] :
( t(V3__y,V0__A)
=> ! [V4__z] :
( t(V4__z,V0__A)
=> ( p(happ(happ(V1__r,V2__x),V3__y))
=> ( p(happ(happ(V1__r,V2__x),V4__z))
=> V3__y = V4__z ) ) ) ) ) ) ).
fof('$_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] :
( p(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('$_def_hahn.HahnRelationsBasic.is_total',axiom,
! [V0__A,V1__cond,V2__r] :
( p(chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r))
<=> ! [V3__a] :
( t(V3__a,V0__A)
=> ( p(happ(V1__cond,V3__a))
=> ! [V5__b] :
( t(V5__b,V0__A)
=> ( p(happ(V1__cond,V5__b))
=> ( V3__a != V5__b
=> ( p(happ(happ(V2__r,V3__a),V5__b))
| p(happ(happ(V2__r,V5__b),V3__a)) ) ) ) ) ) ) ) ).
fof('$_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__31589___24a1(V1__A)) )
| ? [Vvar__0___24Anonymous__31742] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31742)
& V3__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31742)
& 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__31742),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)
<=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r))
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r) ) ) ).
fof('$_def_hahn.HahnRelationsBasic.strict_total_order',axiom,
! [V0__A,V1__cond,V2__r] :
( chahn_2eHahnRelationsBasic_2estrict__total__order___24a3(V0__A,V1__cond,V2__r)
<=> ( chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2(V0__A,V2__r)
& p(chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__cond,V2__r)) ) ) ).
fof('$_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('$_def_hahn.HahnSets.set_bunion',axiom,
! [V0__A,V1__B,V2__s,V3__ss,V4__x] :
( chahn_2eHahnSets_2eset__bunion___24a5(V0__A,V1__B,V2__s,V3__ss,V4__x)
<=> ? [V5__y] :
( t(V5__y,V0__A)
& p(happ(V2__s,V5__y))
& p(happ(happ(V3__ss,V5__y),V4__x)) ) ) ).
fof('$_def_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_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$Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__2462,Vvar__1___24Anonymous__2463,Vvar__0__P__2464,Vvar__1___24Anonymous__2465] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__2462) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__2464) ).
fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__37000,Vvar__1___24Anonymous__37001,Vvar__2___24Anonymous__37002] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37000,Vvar__1___24Anonymous__37001,Vvar__2___24Anonymous__37002) ).
fof('$_discrim_Coq.Init.Byte.x00$Coq.Init.Byte.x01',axiom,
cCoq_2eInit_2eByte_2ex00 != cCoq_2eInit_2eByte_2ex01 ).
fof('$_discrim_Coq.Init.Datatypes.Eq$Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2eEq != cCoq_2eInit_2eDatatypes_2eLt ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__268] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__268) ).
fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3082,Vvar__1___24Anonymous__3083,Vvar__0__A__3084] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3082,Vvar__1___24Anonymous__3083) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3084) ).
fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__34478,Vvar__1__B__34479,Vvar__2___24Anonymous__34480,Vvar__0__A__34481,Vvar__1__B__34482,Vvar__2___24Anonymous__34483] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__34478,Vvar__1__B__34479,Vvar__2___24Anonymous__34480) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__34481,Vvar__1__B__34482,Vvar__2___24Anonymous__34483) ).
fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3126,Vvar__0__A__3127,Vvar__1___24Anonymous__3128,Vvar__2___24Anonymous__3129] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3126) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3127,Vvar__1___24Anonymous__3128,Vvar__2___24Anonymous__3129) ).
fof('$_discrim_Coq.Init.Datatypes.true$Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2etrue != cCoq_2eInit_2eDatatypes_2efalse ).
fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__34612] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__34612) ).
fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__34636,Vvar__0__d__34637] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__34636) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__34637) ).
fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__29673,Vvar__1__B__29674,Vvar__2___24Anonymous__29675,Vvar__0__A__29676,Vvar__1__B__29677,Vvar__2___24Anonymous__29678] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29673,Vvar__1__B__29674,Vvar__2___24Anonymous__29675) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29676,Vvar__1__B__29677) ).
fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2948,Vvar__1__B__2949,Vvar__2___24Anonymous__2950,Vvar__0__A__2951,Vvar__1__B__2952,Vvar__2___24Anonymous__2953] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2948,Vvar__1__B__2949) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2951,Vvar__1__B__2952) ).
fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3055] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3055) ).
fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__259] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__259) ).
fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__247,Vvar__0___24Anonymous__248] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__247) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__248) ).
fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__36993] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__36993) ).
fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__36852,Vvar__1___24Anonymous__36853] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36852,Vvar__1___24Anonymous__36853) ).
fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__35785,Vvar__1__lt__35786,Vvar__2__eq__35787,Vvar__3__x__35788,Vvar__4__y__35789,Vvar__5___24Anonymous__35790,Vvar__0__X__35791,Vvar__1__lt__35792,Vvar__2__eq__35793,Vvar__3__x__35794,Vvar__4__y__35795,Vvar__5___24Anonymous__35796] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__35785,Vvar__1__lt__35786,Vvar__2__eq__35787,Vvar__3__x__35788,Vvar__4__y__35789) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__35791,Vvar__1__lt__35792,Vvar__2__eq__35793,Vvar__3__x__35794,Vvar__4__y__35795) ).
fof('$_discrim_Coq.Structures.OrdersTac.OEQ$Coq.Structures.OrdersTac.OLT',axiom,
cCoq_2eStructures_2eOrdersTac_2eOEQ != cCoq_2eStructures_2eOrdersTac_2eOLT ).
fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__30774,Vvar__0__A__30775,Vvar__1__h__30776,Vvar__2__n__30777,Vvar__3___24Anonymous__30778] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__30774) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30775,Vvar__1__h__30776,Vvar__2__n__30777,Vvar__3___24Anonymous__30778) ).
fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__34774,Vvar__1___24Anonymous__34775,Vvar__0__C__34776,Vvar__1___24Anonymous__34777] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__34774,Vvar__1___24Anonymous__34775) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__34776,Vvar__1___24Anonymous__34777) ).
fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__3275,Vvar__1___24Anonymous__3276,Vvar__0__C__3277,Vvar__1___24Anonymous__3278,Vvar__2___24Anonymous__3279] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__3275,Vvar__1___24Anonymous__3276) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__3277,Vvar__1___24Anonymous__3278,Vvar__2___24Anonymous__3279) ).
fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__34825,Vvar__1___24Anonymous__34826] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__34825,Vvar__1___24Anonymous__34826) ).
fof('$_discrim_Coq.micromega.RMicromega.C0$Coq.micromega.RMicromega.C1',axiom,
cCoq_2emicromega_2eRMicromega_2eC0 != cCoq_2emicromega_2eRMicromega_2eC1 ).
fof('$_discrim_Coq.micromega.RingMicromega.Equal$Coq.micromega.RingMicromega.NonEqual',axiom,
cCoq_2emicromega_2eRingMicromega_2eEqual != cCoq_2emicromega_2eRingMicromega_2eNonEqual ).
fof('$_discrim_Coq.micromega.RingMicromega.OpEq$Coq.micromega.RingMicromega.OpNEq',axiom,
cCoq_2emicromega_2eRingMicromega_2eOpEq != cCoq_2emicromega_2eRingMicromega_2eOpNEq ).
fof('$_discrim_Coq.micromega.RingMicromega.PsatzIn$Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__16549,Vvar__1___24Anonymous__16550,Vvar__0__C__16551,Vvar__1___24Anonymous__16552] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__16549,Vvar__1___24Anonymous__16550) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__16551,Vvar__1___24Anonymous__16552) ).
fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__30050,Vvar__1__TX__30051,Vvar__2__AA__30052,Vvar__3__AF__30053,Vvar__0__TA__30054,Vvar__1__TX__30055,Vvar__2__AA__30056,Vvar__3__AF__30057] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30050,Vvar__1__TX__30051,Vvar__2__AA__30052,Vvar__3__AF__30053) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30054,Vvar__1__TX__30055,Vvar__2__AA__30056,Vvar__3__AF__30057) ).
fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__36878,Vvar__0__A__36879,Vvar__1___24Anonymous__36880] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__36878) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__36879,Vvar__1___24Anonymous__36880) ).
fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__31166,Vvar__1___24Anonymous__31167] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__31166,Vvar__1___24Anonymous__31167) ).
fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
! [Vvar__0__P__2470,Vvar__0__P__2471,Vvar__1___24Anonymous__2472,Vvar__1___24Anonymous__2473] :
( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__2470) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__2471)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__2470 = Vvar__0__P__2471 ) ) ).
fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
! [Vvar__0__P__2466,Vvar__0__P__2467,Vvar__1___24Anonymous__2468,Vvar__1___24Anonymous__2469] :
( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__2466) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__2467)
=> ( c_24Proof = c_24Proof
& Vvar__0__P__2466 = Vvar__0__P__2467 ) ) ).
fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
! [Vvar__0___24Anonymous__37003,Vvar__0___24Anonymous__37004,Vvar__1___24Anonymous__37005,Vvar__1___24Anonymous__37006,Vvar__2___24Anonymous__37007,Vvar__2___24Anonymous__37008] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37003,Vvar__1___24Anonymous__37005,Vvar__2___24Anonymous__37007) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__37004,Vvar__1___24Anonymous__37006,Vvar__2___24Anonymous__37008)
=> ( Vvar__2___24Anonymous__37007 = Vvar__2___24Anonymous__37008
& Vvar__1___24Anonymous__37005 = Vvar__1___24Anonymous__37006
& Vvar__0___24Anonymous__37003 = Vvar__0___24Anonymous__37004 ) ) ).
fof('$_inj_Coq.Init.Datatypes.None',axiom,
! [Vvar__0__A__3089,Vvar__0__A__3090] :
( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3089) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3090)
=> Vvar__0__A__3089 = Vvar__0__A__3090 ) ).
fof('$_inj_Coq.Init.Datatypes.S',axiom,
! [Vvar__0___24Anonymous__269,Vvar__0___24Anonymous__270] :
( cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__269) = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__270)
=> Vvar__0___24Anonymous__269 = Vvar__0___24Anonymous__270 ) ).
fof('$_inj_Coq.Init.Datatypes.Some',axiom,
! [Vvar__0__A__3085,Vvar__0__A__3086,Vvar__1___24Anonymous__3087,Vvar__1___24Anonymous__3088] :
( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3085,Vvar__1___24Anonymous__3087) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3086,Vvar__1___24Anonymous__3088)
=> ( Vvar__1___24Anonymous__3087 = Vvar__1___24Anonymous__3088
& Vvar__0__A__3085 = Vvar__0__A__3086 ) ) ).
fof('$_inj_Coq.Init.Datatypes.cons',axiom,
! [Vvar__0__A__3132,Vvar__0__A__3133,Vvar__1___24Anonymous__3134,Vvar__1___24Anonymous__3135,Vvar__2___24Anonymous__3136,Vvar__2___24Anonymous__3137] :
( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3132,Vvar__1___24Anonymous__3134,Vvar__2___24Anonymous__3136) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3133,Vvar__1___24Anonymous__3135,Vvar__2___24Anonymous__3137)
=> ( Vvar__2___24Anonymous__3136 = Vvar__2___24Anonymous__3137
& Vvar__1___24Anonymous__3134 = Vvar__1___24Anonymous__3135
& Vvar__0__A__3132 = Vvar__0__A__3133 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inl',axiom,
! [Vvar__0__A__34484,Vvar__0__A__34485,Vvar__1__B__34486,Vvar__1__B__34487,Vvar__2___24Anonymous__34488,Vvar__2___24Anonymous__34489] :
( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__34484,Vvar__1__B__34486,Vvar__2___24Anonymous__34488) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__34485,Vvar__1__B__34487,Vvar__2___24Anonymous__34489)
=> ( Vvar__2___24Anonymous__34488 = Vvar__2___24Anonymous__34489
& Vvar__1__B__34486 = Vvar__1__B__34487
& Vvar__0__A__34484 = Vvar__0__A__34485 ) ) ).
fof('$_inj_Coq.Init.Datatypes.inr',axiom,
! [Vvar__0__A__34490,Vvar__0__A__34491,Vvar__1__B__34492,Vvar__1__B__34493,Vvar__2___24Anonymous__34494,Vvar__2___24Anonymous__34495] :
( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__34490,Vvar__1__B__34492,Vvar__2___24Anonymous__34494) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__34491,Vvar__1__B__34493,Vvar__2___24Anonymous__34495)
=> ( Vvar__2___24Anonymous__34494 = Vvar__2___24Anonymous__34495
& Vvar__1__B__34492 = Vvar__1__B__34493
& Vvar__0__A__34490 = Vvar__0__A__34491 ) ) ).
fof('$_inj_Coq.Init.Datatypes.nil',axiom,
! [Vvar__0__A__3130,Vvar__0__A__3131] :
( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3130) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3131)
=> Vvar__0__A__3130 = Vvar__0__A__3131 ) ).
fof('$_inj_Coq.Init.Decimal.D0',axiom,
! [Vvar__0___24Anonymous__34613,Vvar__0___24Anonymous__34614] :
( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__34613) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__34614)
=> Vvar__0___24Anonymous__34613 = Vvar__0___24Anonymous__34614 ) ).
fof('$_inj_Coq.Init.Decimal.D1',axiom,
! [Vvar__0___24Anonymous__34615,Vvar__0___24Anonymous__34616] :
( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__34615) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__34616)
=> Vvar__0___24Anonymous__34615 = Vvar__0___24Anonymous__34616 ) ).
fof('$_inj_Coq.Init.Decimal.D2',axiom,
! [Vvar__0___24Anonymous__34617,Vvar__0___24Anonymous__34618] :
( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__34617) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__34618)
=> Vvar__0___24Anonymous__34617 = Vvar__0___24Anonymous__34618 ) ).
fof('$_inj_Coq.Init.Decimal.D3',axiom,
! [Vvar__0___24Anonymous__34619,Vvar__0___24Anonymous__34620] :
( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__34619) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__34620)
=> Vvar__0___24Anonymous__34619 = Vvar__0___24Anonymous__34620 ) ).
fof('$_inj_Coq.Init.Decimal.D4',axiom,
! [Vvar__0___24Anonymous__34621,Vvar__0___24Anonymous__34622] :
( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__34621) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__34622)
=> Vvar__0___24Anonymous__34621 = Vvar__0___24Anonymous__34622 ) ).
fof('$_inj_Coq.Init.Decimal.D5',axiom,
! [Vvar__0___24Anonymous__34623,Vvar__0___24Anonymous__34624] :
( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__34623) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__34624)
=> Vvar__0___24Anonymous__34623 = Vvar__0___24Anonymous__34624 ) ).
fof('$_inj_Coq.Init.Decimal.D6',axiom,
! [Vvar__0___24Anonymous__34625,Vvar__0___24Anonymous__34626] :
( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__34625) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__34626)
=> Vvar__0___24Anonymous__34625 = Vvar__0___24Anonymous__34626 ) ).
fof('$_inj_Coq.Init.Decimal.D7',axiom,
! [Vvar__0___24Anonymous__34627,Vvar__0___24Anonymous__34628] :
( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__34627) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__34628)
=> Vvar__0___24Anonymous__34627 = Vvar__0___24Anonymous__34628 ) ).
fof('$_inj_Coq.Init.Decimal.D8',axiom,
! [Vvar__0___24Anonymous__34629,Vvar__0___24Anonymous__34630] :
( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__34629) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__34630)
=> Vvar__0___24Anonymous__34629 = Vvar__0___24Anonymous__34630 ) ).
fof('$_inj_Coq.Init.Decimal.D9',axiom,
! [Vvar__0___24Anonymous__34631,Vvar__0___24Anonymous__34632] :
( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__34631) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__34632)
=> Vvar__0___24Anonymous__34631 = Vvar__0___24Anonymous__34632 ) ).
fof('$_inj_Coq.Init.Decimal.Neg',axiom,
! [Vvar__0__d__34640,Vvar__0__d__34641] :
( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__34640) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__34641)
=> Vvar__0__d__34640 = Vvar__0__d__34641 ) ).
fof('$_inj_Coq.Init.Decimal.Pos',axiom,
! [Vvar__0__d__34638,Vvar__0__d__34639] :
( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__34638) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__34639)
=> Vvar__0__d__34638 = Vvar__0__d__34639 ) ).
fof('$_inj_Coq.Init.Specif.exist',axiom,
! [Vvar__0__A__29594,Vvar__0__A__29595,Vvar__1__P__29596,Vvar__1__P__29597,Vvar__2__x__29598,Vvar__2__x__29599,Vvar__3___24Anonymous__29600,Vvar__3___24Anonymous__29601] :
( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__29594,Vvar__1__P__29596,Vvar__2__x__29598) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__29595,Vvar__1__P__29597,Vvar__2__x__29599)
=> ( c_24Proof = c_24Proof
& Vvar__2__x__29598 = Vvar__2__x__29599
& Vvar__1__P__29596 = Vvar__1__P__29597
& Vvar__0__A__29594 = Vvar__0__A__29595 ) ) ).
fof('$_inj_Coq.Init.Specif.exist2',axiom,
! [Vvar__0__A__36781,Vvar__0__A__36782,Vvar__1__P__36783,Vvar__1__P__36784,Vvar__2__Q__36785,Vvar__2__Q__36786,Vvar__3__x__36787,Vvar__3__x__36788,Vvar__4___24Anonymous__36789,Vvar__4___24Anonymous__36790,Vvar__5___24Anonymous__36791,Vvar__5___24Anonymous__36792] :
( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__36781,Vvar__1__P__36783,Vvar__2__Q__36785,Vvar__3__x__36787) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__36782,Vvar__1__P__36784,Vvar__2__Q__36786,Vvar__3__x__36788)
=> ( c_24Proof = c_24Proof
& c_24Proof = c_24Proof
& Vvar__3__x__36787 = Vvar__3__x__36788
& Vvar__2__Q__36785 = Vvar__2__Q__36786
& Vvar__1__P__36783 = Vvar__1__P__36784
& Vvar__0__A__36781 = Vvar__0__A__36782 ) ) ).
fof('$_inj_Coq.Init.Specif.existT',axiom,
! [Vvar__0__A__29633,Vvar__0__A__29634,Vvar__1__P__29635,Vvar__1__P__29636,Vvar__2__x__29637,Vvar__2__x__29638,Vvar__3___24Anonymous__29639,Vvar__3___24Anonymous__29640] :
( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__29633,Vvar__1__P__29635,Vvar__2__x__29637,Vvar__3___24Anonymous__29639) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__29634,Vvar__1__P__29636,Vvar__2__x__29638,Vvar__3___24Anonymous__29640)
=> ( Vvar__3___24Anonymous__29639 = Vvar__3___24Anonymous__29640
& Vvar__2__x__29637 = Vvar__2__x__29638
& Vvar__1__P__29635 = Vvar__1__P__29636
& Vvar__0__A__29633 = Vvar__0__A__29634 ) ) ).
fof('$_inj_Coq.Init.Specif.existT2',axiom,
! [Vvar__0__A__36837,Vvar__0__A__36838,Vvar__1__P__36839,Vvar__1__P__36840,Vvar__2__Q__36841,Vvar__2__Q__36842,Vvar__3__x__36843,Vvar__3__x__36844,Vvar__4___24Anonymous__36845,Vvar__4___24Anonymous__36846,Vvar__5___24Anonymous__36847,Vvar__5___24Anonymous__36848] :
( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__36837,Vvar__1__P__36839,Vvar__2__Q__36841,Vvar__3__x__36843,Vvar__4___24Anonymous__36845,Vvar__5___24Anonymous__36847) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__36838,Vvar__1__P__36840,Vvar__2__Q__36842,Vvar__3__x__36844,Vvar__4___24Anonymous__36846,Vvar__5___24Anonymous__36848)
=> ( Vvar__5___24Anonymous__36847 = Vvar__5___24Anonymous__36848
& Vvar__4___24Anonymous__36845 = Vvar__4___24Anonymous__36846
& Vvar__3__x__36843 = Vvar__3__x__36844
& Vvar__2__Q__36841 = Vvar__2__Q__36842
& Vvar__1__P__36839 = Vvar__1__P__36840
& Vvar__0__A__36837 = Vvar__0__A__36838 ) ) ).
fof('$_inj_Coq.Init.Specif.inleft',axiom,
! [Vvar__0__A__29679,Vvar__0__A__29680,Vvar__1__B__29681,Vvar__1__B__29682,Vvar__2___24Anonymous__29683,Vvar__2___24Anonymous__29684] :
( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29679,Vvar__1__B__29681,Vvar__2___24Anonymous__29683) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29680,Vvar__1__B__29682,Vvar__2___24Anonymous__29684)
=> ( Vvar__2___24Anonymous__29683 = Vvar__2___24Anonymous__29684
& Vvar__1__B__29681 = Vvar__1__B__29682
& Vvar__0__A__29679 = Vvar__0__A__29680 ) ) ).
fof('$_inj_Coq.Init.Specif.inright',axiom,
! [Vvar__0__A__29685,Vvar__0__A__29686,Vvar__1__B__29687,Vvar__1__B__29688,Vvar__2___24Anonymous__29689,Vvar__2___24Anonymous__29690] :
( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29685,Vvar__1__B__29687) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29686,Vvar__1__B__29688)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__29687 = Vvar__1__B__29688
& Vvar__0__A__29685 = Vvar__0__A__29686 ) ) ).
fof('$_inj_Coq.Init.Specif.left',axiom,
! [Vvar__0__A__2954,Vvar__0__A__2955,Vvar__1__B__2956,Vvar__1__B__2957,Vvar__2___24Anonymous__2958,Vvar__2___24Anonymous__2959] :
( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2954,Vvar__1__B__2956) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2955,Vvar__1__B__2957)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2956 = Vvar__1__B__2957
& Vvar__0__A__2954 = Vvar__0__A__2955 ) ) ).
fof('$_inj_Coq.Init.Specif.right',axiom,
! [Vvar__0__A__2960,Vvar__0__A__2961,Vvar__1__B__2962,Vvar__1__B__2963,Vvar__2___24Anonymous__2964,Vvar__2___24Anonymous__2965] :
( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2960,Vvar__1__B__2962) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2961,Vvar__1__B__2963)
=> ( c_24Proof = c_24Proof
& Vvar__1__B__2962 = Vvar__1__B__2963
& Vvar__0__A__2960 = Vvar__0__A__2961 ) ) ).
fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
! [Vvar__0___24Anonymous__3056,Vvar__0___24Anonymous__3057] :
( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3056) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3057)
=> Vvar__0___24Anonymous__3056 = Vvar__0___24Anonymous__3057 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
! [Vvar__0___24Anonymous__262,Vvar__0___24Anonymous__263] :
( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__262) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__263)
=> Vvar__0___24Anonymous__262 = Vvar__0___24Anonymous__263 ) ).
fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
! [Vvar__0___24Anonymous__260,Vvar__0___24Anonymous__261] :
( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__260) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__261)
=> Vvar__0___24Anonymous__260 = Vvar__0___24Anonymous__261 ) ).
fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
! [Vvar__0___24Anonymous__249,Vvar__0___24Anonymous__250] :
( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__249) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__250)
=> Vvar__0___24Anonymous__249 = Vvar__0___24Anonymous__250 ) ).
fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
! [Vvar__0___24Anonymous__251,Vvar__0___24Anonymous__252] :
( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__251) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__252)
=> Vvar__0___24Anonymous__251 = Vvar__0___24Anonymous__252 ) ).
fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
! [Vvar__0___24Anonymous__36994,Vvar__0___24Anonymous__36995] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__36994) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__36995)
=> Vvar__0___24Anonymous__36994 = Vvar__0___24Anonymous__36995 ) ).
fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
! [Vvar__0__Qnum__32056,Vvar__0__Qnum__32057,Vvar__1__Qden__32058,Vvar__1__Qden__32059] :
( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__32056,Vvar__1__Qden__32058) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__32057,Vvar__1__Qden__32059)
=> ( Vvar__1__Qden__32058 = Vvar__1__Qden__32059
& Vvar__0__Qnum__32056 = Vvar__0__Qnum__32057 ) ) ).
fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
! [Vvar__0___24Anonymous__34439,Vvar__0___24Anonymous__34440,Vvar__1___24Anonymous__34441,Vvar__1___24Anonymous__34442,Vvar__2___24Anonymous__34443,Vvar__2___24Anonymous__34444,Vvar__3___24Anonymous__34445,Vvar__3___24Anonymous__34446,Vvar__4___24Anonymous__34447,Vvar__4___24Anonymous__34448,Vvar__5___24Anonymous__34449,Vvar__5___24Anonymous__34450,Vvar__6___24Anonymous__34451,Vvar__6___24Anonymous__34452,Vvar__7___24Anonymous__34453,Vvar__7___24Anonymous__34454] :
( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__34439,Vvar__1___24Anonymous__34441,Vvar__2___24Anonymous__34443,Vvar__3___24Anonymous__34445,Vvar__4___24Anonymous__34447,Vvar__5___24Anonymous__34449,Vvar__6___24Anonymous__34451,Vvar__7___24Anonymous__34453) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__34440,Vvar__1___24Anonymous__34442,Vvar__2___24Anonymous__34444,Vvar__3___24Anonymous__34446,Vvar__4___24Anonymous__34448,Vvar__5___24Anonymous__34450,Vvar__6___24Anonymous__34452,Vvar__7___24Anonymous__34454)
=> ( Vvar__7___24Anonymous__34453 = Vvar__7___24Anonymous__34454
& Vvar__6___24Anonymous__34451 = Vvar__6___24Anonymous__34452
& Vvar__5___24Anonymous__34449 = Vvar__5___24Anonymous__34450
& Vvar__4___24Anonymous__34447 = Vvar__4___24Anonymous__34448
& Vvar__3___24Anonymous__34445 = Vvar__3___24Anonymous__34446
& Vvar__2___24Anonymous__34443 = Vvar__2___24Anonymous__34444
& Vvar__1___24Anonymous__34441 = Vvar__1___24Anonymous__34442
& Vvar__0___24Anonymous__34439 = Vvar__0___24Anonymous__34440 ) ) ).
fof('$_inj_Coq.Strings.String.String',axiom,
! [Vvar__0___24Anonymous__36854,Vvar__0___24Anonymous__36855,Vvar__1___24Anonymous__36856,Vvar__1___24Anonymous__36857] :
( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36854,Vvar__1___24Anonymous__36856) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36855,Vvar__1___24Anonymous__36857)
=> ( Vvar__1___24Anonymous__36856 = Vvar__1___24Anonymous__36857
& Vvar__0___24Anonymous__36854 = Vvar__0___24Anonymous__36855 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
! [Vvar__0__X__35809,Vvar__0__X__35810,Vvar__1__lt__35811,Vvar__1__lt__35812,Vvar__2__eq__35813,Vvar__2__eq__35814,Vvar__3__x__35815,Vvar__3__x__35816,Vvar__4__y__35817,Vvar__4__y__35818,Vvar__5___24Anonymous__35819,Vvar__5___24Anonymous__35820] :
( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__35809,Vvar__1__lt__35811,Vvar__2__eq__35813,Vvar__3__x__35815,Vvar__4__y__35817) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__35810,Vvar__1__lt__35812,Vvar__2__eq__35814,Vvar__3__x__35816,Vvar__4__y__35818)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__35817 = Vvar__4__y__35818
& Vvar__3__x__35815 = Vvar__3__x__35816
& Vvar__2__eq__35813 = Vvar__2__eq__35814
& Vvar__1__lt__35811 = Vvar__1__lt__35812
& Vvar__0__X__35809 = Vvar__0__X__35810 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
! [Vvar__0__X__35821,Vvar__0__X__35822,Vvar__1__lt__35823,Vvar__1__lt__35824,Vvar__2__eq__35825,Vvar__2__eq__35826,Vvar__3__x__35827,Vvar__3__x__35828,Vvar__4__y__35829,Vvar__4__y__35830,Vvar__5___24Anonymous__35831,Vvar__5___24Anonymous__35832] :
( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__35821,Vvar__1__lt__35823,Vvar__2__eq__35825,Vvar__3__x__35827,Vvar__4__y__35829) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__35822,Vvar__1__lt__35824,Vvar__2__eq__35826,Vvar__3__x__35828,Vvar__4__y__35830)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__35829 = Vvar__4__y__35830
& Vvar__3__x__35827 = Vvar__3__x__35828
& Vvar__2__eq__35825 = Vvar__2__eq__35826
& Vvar__1__lt__35823 = Vvar__1__lt__35824
& Vvar__0__X__35821 = Vvar__0__X__35822 ) ) ).
fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
! [Vvar__0__X__35797,Vvar__0__X__35798,Vvar__1__lt__35799,Vvar__1__lt__35800,Vvar__2__eq__35801,Vvar__2__eq__35802,Vvar__3__x__35803,Vvar__3__x__35804,Vvar__4__y__35805,Vvar__4__y__35806,Vvar__5___24Anonymous__35807,Vvar__5___24Anonymous__35808] :
( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__35797,Vvar__1__lt__35799,Vvar__2__eq__35801,Vvar__3__x__35803,Vvar__4__y__35805) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__35798,Vvar__1__lt__35800,Vvar__2__eq__35802,Vvar__3__x__35804,Vvar__4__y__35806)
=> ( c_24Proof = c_24Proof
& Vvar__4__y__35805 = Vvar__4__y__35806
& Vvar__3__x__35803 = Vvar__3__x__35804
& Vvar__2__eq__35801 = Vvar__2__eq__35802
& Vvar__1__lt__35799 = Vvar__1__lt__35800
& Vvar__0__X__35797 = Vvar__0__X__35798 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
! [Vvar__0__A__30781,Vvar__0__A__30782,Vvar__1__h__30783,Vvar__1__h__30784,Vvar__2__n__30785,Vvar__2__n__30786,Vvar__3___24Anonymous__30787,Vvar__3___24Anonymous__30788] :
( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30781,Vvar__1__h__30783,Vvar__2__n__30785,Vvar__3___24Anonymous__30787) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30782,Vvar__1__h__30784,Vvar__2__n__30786,Vvar__3___24Anonymous__30788)
=> ( Vvar__3___24Anonymous__30787 = Vvar__3___24Anonymous__30788
& Vvar__2__n__30785 = Vvar__2__n__30786
& Vvar__1__h__30783 = Vvar__1__h__30784
& Vvar__0__A__30781 = Vvar__0__A__30782 ) ) ).
fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
! [Vvar__0__A__30779,Vvar__0__A__30780] :
( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__30779) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__30780)
=> Vvar__0__A__30779 = Vvar__0__A__30780 ) ).
fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
! [Vvar__0__C__34782,Vvar__0__C__34783,Vvar__1___24Anonymous__34784,Vvar__1___24Anonymous__34785] :
( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__34782,Vvar__1___24Anonymous__34784) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__34783,Vvar__1___24Anonymous__34785)
=> ( Vvar__1___24Anonymous__34784 = Vvar__1___24Anonymous__34785
& Vvar__0__C__34782 = Vvar__0__C__34783 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
! [Vvar__0__C__34786,Vvar__0__C__34787,Vvar__1___24Anonymous__34788,Vvar__1___24Anonymous__34789,Vvar__2___24Anonymous__34790,Vvar__2___24Anonymous__34791] :
( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__34786,Vvar__1___24Anonymous__34788,Vvar__2___24Anonymous__34790) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__34787,Vvar__1___24Anonymous__34789,Vvar__2___24Anonymous__34791)
=> ( Vvar__2___24Anonymous__34790 = Vvar__2___24Anonymous__34791
& Vvar__1___24Anonymous__34788 = Vvar__1___24Anonymous__34789
& Vvar__0__C__34786 = Vvar__0__C__34787 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
! [Vvar__0__C__34778,Vvar__0__C__34779,Vvar__1___24Anonymous__34780,Vvar__1___24Anonymous__34781] :
( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__34778,Vvar__1___24Anonymous__34780) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__34779,Vvar__1___24Anonymous__34781)
=> ( Vvar__1___24Anonymous__34780 = Vvar__1___24Anonymous__34781
& Vvar__0__C__34778 = Vvar__0__C__34779 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
! [Vvar__0__C__34798,Vvar__0__C__34799,Vvar__1___24Anonymous__34800,Vvar__1___24Anonymous__34801,Vvar__2___24Anonymous__34802,Vvar__2___24Anonymous__34803] :
( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__34798,Vvar__1___24Anonymous__34800,Vvar__2___24Anonymous__34802) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__34799,Vvar__1___24Anonymous__34801,Vvar__2___24Anonymous__34803)
=> ( Vvar__2___24Anonymous__34802 = Vvar__2___24Anonymous__34803
& Vvar__1___24Anonymous__34800 = Vvar__1___24Anonymous__34801
& Vvar__0__C__34798 = Vvar__0__C__34799 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
! [Vvar__0__C__34804,Vvar__0__C__34805,Vvar__1___24Anonymous__34806,Vvar__1___24Anonymous__34807] :
( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__34804,Vvar__1___24Anonymous__34806) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__34805,Vvar__1___24Anonymous__34807)
=> ( Vvar__1___24Anonymous__34806 = Vvar__1___24Anonymous__34807
& Vvar__0__C__34804 = Vvar__0__C__34805 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
! [Vvar__0__C__34808,Vvar__0__C__34809,Vvar__1___24Anonymous__34810,Vvar__1___24Anonymous__34811,Vvar__2___24Anonymous__34812,Vvar__2___24Anonymous__34813] :
( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__34808,Vvar__1___24Anonymous__34810,Vvar__2___24Anonymous__34812) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__34809,Vvar__1___24Anonymous__34811,Vvar__2___24Anonymous__34813)
=> ( Vvar__2___24Anonymous__34812 = Vvar__2___24Anonymous__34813
& Vvar__1___24Anonymous__34810 = Vvar__1___24Anonymous__34811
& Vvar__0__C__34808 = Vvar__0__C__34809 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
! [Vvar__0__C__34792,Vvar__0__C__34793,Vvar__1___24Anonymous__34794,Vvar__1___24Anonymous__34795,Vvar__2___24Anonymous__34796,Vvar__2___24Anonymous__34797] :
( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__34792,Vvar__1___24Anonymous__34794,Vvar__2___24Anonymous__34796) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__34793,Vvar__1___24Anonymous__34795,Vvar__2___24Anonymous__34797)
=> ( Vvar__2___24Anonymous__34796 = Vvar__2___24Anonymous__34797
& Vvar__1___24Anonymous__34794 = Vvar__1___24Anonymous__34795
& Vvar__0__C__34792 = Vvar__0__C__34793 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
! [Vvar__0__C__3290,Vvar__0__C__3291,Vvar__1___24Anonymous__3292,Vvar__1___24Anonymous__3293,Vvar__2___24Anonymous__3294,Vvar__2___24Anonymous__3295,Vvar__3___24Anonymous__3296,Vvar__3___24Anonymous__3297] :
( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__3290,Vvar__1___24Anonymous__3292,Vvar__2___24Anonymous__3294,Vvar__3___24Anonymous__3296) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__3291,Vvar__1___24Anonymous__3293,Vvar__2___24Anonymous__3295,Vvar__3___24Anonymous__3297)
=> ( Vvar__3___24Anonymous__3296 = Vvar__3___24Anonymous__3297
& Vvar__2___24Anonymous__3294 = Vvar__2___24Anonymous__3295
& Vvar__1___24Anonymous__3292 = Vvar__1___24Anonymous__3293
& Vvar__0__C__3290 = Vvar__0__C__3291 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
! [Vvar__0__C__3280,Vvar__0__C__3281,Vvar__1___24Anonymous__3282,Vvar__1___24Anonymous__3283] :
( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__3280,Vvar__1___24Anonymous__3282) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__3281,Vvar__1___24Anonymous__3283)
=> ( Vvar__1___24Anonymous__3282 = Vvar__1___24Anonymous__3283
& Vvar__0__C__3280 = Vvar__0__C__3281 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
! [Vvar__0__C__3284,Vvar__0__C__3285,Vvar__1___24Anonymous__3286,Vvar__1___24Anonymous__3287,Vvar__2___24Anonymous__3288,Vvar__2___24Anonymous__3289] :
( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__3284,Vvar__1___24Anonymous__3286,Vvar__2___24Anonymous__3288) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__3285,Vvar__1___24Anonymous__3287,Vvar__2___24Anonymous__3289)
=> ( Vvar__2___24Anonymous__3288 = Vvar__2___24Anonymous__3289
& Vvar__1___24Anonymous__3286 = Vvar__1___24Anonymous__3287
& Vvar__0__C__3284 = Vvar__0__C__3285 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
! [Vvar__0___24Anonymous__34831,Vvar__0___24Anonymous__34832,Vvar__1___24Anonymous__34833,Vvar__1___24Anonymous__34834] :
( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__34831,Vvar__1___24Anonymous__34833) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__34832,Vvar__1___24Anonymous__34834)
=> ( Vvar__1___24Anonymous__34833 = Vvar__1___24Anonymous__34834
& Vvar__0___24Anonymous__34831 = Vvar__0___24Anonymous__34832 ) ) ).
fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
! [Vvar__0___24Anonymous__34827,Vvar__0___24Anonymous__34828,Vvar__1___24Anonymous__34829,Vvar__1___24Anonymous__34830] :
( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__34827,Vvar__1___24Anonymous__34829) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__34828,Vvar__1___24Anonymous__34830)
=> ( Vvar__1___24Anonymous__34829 = Vvar__1___24Anonymous__34830
& Vvar__0___24Anonymous__34827 = Vvar__0___24Anonymous__34828 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
! [Vvar__0__r__35975,Vvar__0__r__35976] :
( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__35975) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__35976)
=> Vvar__0__r__35975 = Vvar__0__r__35976 ) ).
fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
! [Vvar__0__r1__35963,Vvar__0__r1__35964,Vvar__1__r2__35965,Vvar__1__r2__35966] :
( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__35963,Vvar__1__r2__35965) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__35964,Vvar__1__r2__35966)
=> ( Vvar__1__r2__35965 = Vvar__1__r2__35966
& Vvar__0__r1__35963 = Vvar__0__r1__35964 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
! [Vvar__0__r1__35967,Vvar__0__r1__35968,Vvar__1__r2__35969,Vvar__1__r2__35970] :
( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__35967,Vvar__1__r2__35969) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__35968,Vvar__1__r2__35970)
=> ( Vvar__1__r2__35969 = Vvar__1__r2__35970
& Vvar__0__r1__35967 = Vvar__0__r1__35968 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
! [Vvar__0__r__35977,Vvar__0__r__35978] :
( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__35977) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__35978)
=> Vvar__0__r__35977 = Vvar__0__r__35978 ) ).
fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
! [Vvar__0__r1__35959,Vvar__0__r1__35960,Vvar__1__r2__35961,Vvar__1__r2__35962] :
( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__35959,Vvar__1__r2__35961) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__35960,Vvar__1__r2__35962)
=> ( Vvar__1__r2__35961 = Vvar__1__r2__35962
& Vvar__0__r1__35959 = Vvar__0__r1__35960 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
! [Vvar__0__r1__35971,Vvar__0__r1__35972,Vvar__1__z__35973,Vvar__1__z__35974] :
( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__35971,Vvar__1__z__35973) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__35972,Vvar__1__z__35974)
=> ( Vvar__1__z__35973 = Vvar__1__z__35974
& Vvar__0__r1__35971 = Vvar__0__r1__35972 ) ) ).
fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
! [Vvar__0__r__35955,Vvar__0__r__35956] :
( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__35955) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__35956)
=> Vvar__0__r__35955 = Vvar__0__r__35956 ) ).
fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
! [Vvar__0__r__35957,Vvar__0__r__35958] :
( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__35957) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__35958)
=> Vvar__0__r__35957 = Vvar__0__r__35958 ) ).
fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
! [Vvar__0__T__32409,Vvar__0__T__32410,Vvar__1__Flhs__32411,Vvar__1__Flhs__32412,Vvar__2__Fop__32413,Vvar__2__Fop__32414,Vvar__3__Frhs__32415,Vvar__3__Frhs__32416] :
( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__32409,Vvar__1__Flhs__32411,Vvar__2__Fop__32413,Vvar__3__Frhs__32415) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__32410,Vvar__1__Flhs__32412,Vvar__2__Fop__32414,Vvar__3__Frhs__32416)
=> ( Vvar__3__Frhs__32415 = Vvar__3__Frhs__32416
& Vvar__2__Fop__32413 = Vvar__2__Fop__32414
& Vvar__1__Flhs__32411 = Vvar__1__Flhs__32412
& Vvar__0__T__32409 = Vvar__0__T__32410 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
! [Vvar__0__C__16573,Vvar__0__C__16574,Vvar__1___24Anonymous__16575,Vvar__1___24Anonymous__16576,Vvar__2___24Anonymous__16577,Vvar__2___24Anonymous__16578] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__16573,Vvar__1___24Anonymous__16575,Vvar__2___24Anonymous__16577) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__16574,Vvar__1___24Anonymous__16576,Vvar__2___24Anonymous__16578)
=> ( Vvar__2___24Anonymous__16577 = Vvar__2___24Anonymous__16578
& Vvar__1___24Anonymous__16575 = Vvar__1___24Anonymous__16576
& Vvar__0__C__16573 = Vvar__0__C__16574 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
! [Vvar__0__C__16579,Vvar__0__C__16580,Vvar__1___24Anonymous__16581,Vvar__1___24Anonymous__16582] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__16579,Vvar__1___24Anonymous__16581) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__16580,Vvar__1___24Anonymous__16582)
=> ( Vvar__1___24Anonymous__16581 = Vvar__1___24Anonymous__16582
& Vvar__0__C__16579 = Vvar__0__C__16580 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
! [Vvar__0__C__16553,Vvar__0__C__16554,Vvar__1___24Anonymous__16555,Vvar__1___24Anonymous__16556] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__16553,Vvar__1___24Anonymous__16555) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__16554,Vvar__1___24Anonymous__16556)
=> ( Vvar__1___24Anonymous__16555 = Vvar__1___24Anonymous__16556
& Vvar__0__C__16553 = Vvar__0__C__16554 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
! [Vvar__0__C__16561,Vvar__0__C__16562,Vvar__1___24Anonymous__16563,Vvar__1___24Anonymous__16564,Vvar__2___24Anonymous__16565,Vvar__2___24Anonymous__16566] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__16561,Vvar__1___24Anonymous__16563,Vvar__2___24Anonymous__16565) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__16562,Vvar__1___24Anonymous__16564,Vvar__2___24Anonymous__16566)
=> ( Vvar__2___24Anonymous__16565 = Vvar__2___24Anonymous__16566
& Vvar__1___24Anonymous__16563 = Vvar__1___24Anonymous__16564
& Vvar__0__C__16561 = Vvar__0__C__16562 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
! [Vvar__0__C__16567,Vvar__0__C__16568,Vvar__1___24Anonymous__16569,Vvar__1___24Anonymous__16570,Vvar__2___24Anonymous__16571,Vvar__2___24Anonymous__16572] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__16567,Vvar__1___24Anonymous__16569,Vvar__2___24Anonymous__16571) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__16568,Vvar__1___24Anonymous__16570,Vvar__2___24Anonymous__16572)
=> ( Vvar__2___24Anonymous__16571 = Vvar__2___24Anonymous__16572
& Vvar__1___24Anonymous__16569 = Vvar__1___24Anonymous__16570
& Vvar__0__C__16567 = Vvar__0__C__16568 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
! [Vvar__0__C__16557,Vvar__0__C__16558,Vvar__1___24Anonymous__16559,Vvar__1___24Anonymous__16560] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__16557,Vvar__1___24Anonymous__16559) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__16558,Vvar__1___24Anonymous__16560)
=> ( Vvar__1___24Anonymous__16559 = Vvar__1___24Anonymous__16560
& Vvar__0__C__16557 = Vvar__0__C__16558 ) ) ).
fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
! [Vvar__0__C__16583,Vvar__0__C__16584] :
( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__16583) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__16584)
=> Vvar__0__C__16583 = Vvar__0__C__16584 ) ).
fof('$_inj_Coq.micromega.Tauto.A',axiom,
! [Vvar__0__TA__30084,Vvar__0__TA__30085,Vvar__1__TX__30086,Vvar__1__TX__30087,Vvar__2__AA__30088,Vvar__2__AA__30089,Vvar__3__AF__30090,Vvar__3__AF__30091,Vvar__4___24Anonymous__30092,Vvar__4___24Anonymous__30093,Vvar__5___24Anonymous__30094,Vvar__5___24Anonymous__30095] :
( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__30084,Vvar__1__TX__30086,Vvar__2__AA__30088,Vvar__3__AF__30090,Vvar__4___24Anonymous__30092,Vvar__5___24Anonymous__30094) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__30085,Vvar__1__TX__30087,Vvar__2__AA__30089,Vvar__3__AF__30091,Vvar__4___24Anonymous__30093,Vvar__5___24Anonymous__30095)
=> ( Vvar__5___24Anonymous__30094 = Vvar__5___24Anonymous__30095
& Vvar__4___24Anonymous__30092 = Vvar__4___24Anonymous__30093
& Vvar__3__AF__30090 = Vvar__3__AF__30091
& Vvar__2__AA__30088 = Vvar__2__AA__30089
& Vvar__1__TX__30086 = Vvar__1__TX__30087
& Vvar__0__TA__30084 = Vvar__0__TA__30085 ) ) ).
fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
! [Vvar__0__TA__30096,Vvar__0__TA__30097,Vvar__1__TX__30098,Vvar__1__TX__30099,Vvar__2__AA__30100,Vvar__2__AA__30101,Vvar__3__AF__30102,Vvar__3__AF__30103,Vvar__4___24Anonymous__30104,Vvar__4___24Anonymous__30105,Vvar__5___24Anonymous__30106,Vvar__5___24Anonymous__30107] :
( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__30096,Vvar__1__TX__30098,Vvar__2__AA__30100,Vvar__3__AF__30102,Vvar__4___24Anonymous__30104,Vvar__5___24Anonymous__30106) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__30097,Vvar__1__TX__30099,Vvar__2__AA__30101,Vvar__3__AF__30103,Vvar__4___24Anonymous__30105,Vvar__5___24Anonymous__30107)
=> ( Vvar__5___24Anonymous__30106 = Vvar__5___24Anonymous__30107
& Vvar__4___24Anonymous__30104 = Vvar__4___24Anonymous__30105
& Vvar__3__AF__30102 = Vvar__3__AF__30103
& Vvar__2__AA__30100 = Vvar__2__AA__30101
& Vvar__1__TX__30098 = Vvar__1__TX__30099
& Vvar__0__TA__30096 = Vvar__0__TA__30097 ) ) ).
fof('$_inj_Coq.micromega.Tauto.D',axiom,
! [Vvar__0__TA__30108,Vvar__0__TA__30109,Vvar__1__TX__30110,Vvar__1__TX__30111,Vvar__2__AA__30112,Vvar__2__AA__30113,Vvar__3__AF__30114,Vvar__3__AF__30115,Vvar__4___24Anonymous__30116,Vvar__4___24Anonymous__30117,Vvar__5___24Anonymous__30118,Vvar__5___24Anonymous__30119] :
( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__30108,Vvar__1__TX__30110,Vvar__2__AA__30112,Vvar__3__AF__30114,Vvar__4___24Anonymous__30116,Vvar__5___24Anonymous__30118) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__30109,Vvar__1__TX__30111,Vvar__2__AA__30113,Vvar__3__AF__30115,Vvar__4___24Anonymous__30117,Vvar__5___24Anonymous__30119)
=> ( Vvar__5___24Anonymous__30118 = Vvar__5___24Anonymous__30119
& Vvar__4___24Anonymous__30116 = Vvar__4___24Anonymous__30117
& Vvar__3__AF__30114 = Vvar__3__AF__30115
& Vvar__2__AA__30112 = Vvar__2__AA__30113
& Vvar__1__TX__30110 = Vvar__1__TX__30111
& Vvar__0__TA__30108 = Vvar__0__TA__30109 ) ) ).
fof('$_inj_Coq.micromega.Tauto.FF',axiom,
! [Vvar__0__TA__30066,Vvar__0__TA__30067,Vvar__1__TX__30068,Vvar__1__TX__30069,Vvar__2__AA__30070,Vvar__2__AA__30071,Vvar__3__AF__30072,Vvar__3__AF__30073] :
( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30066,Vvar__1__TX__30068,Vvar__2__AA__30070,Vvar__3__AF__30072) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__30067,Vvar__1__TX__30069,Vvar__2__AA__30071,Vvar__3__AF__30073)
=> ( Vvar__3__AF__30072 = Vvar__3__AF__30073
& Vvar__2__AA__30070 = Vvar__2__AA__30071
& Vvar__1__TX__30068 = Vvar__1__TX__30069
& Vvar__0__TA__30066 = Vvar__0__TA__30067 ) ) ).
fof('$_inj_Coq.micromega.Tauto.I',axiom,
! [Vvar__0__TA__30130,Vvar__0__TA__30131,Vvar__1__TX__30132,Vvar__1__TX__30133,Vvar__2__AA__30134,Vvar__2__AA__30135,Vvar__3__AF__30136,Vvar__3__AF__30137,Vvar__4___24Anonymous__30138,Vvar__4___24Anonymous__30139,Vvar__5___24Anonymous__30140,Vvar__5___24Anonymous__30141,Vvar__6___24Anonymous__30142,Vvar__6___24Anonymous__30143] :
( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__30130,Vvar__1__TX__30132,Vvar__2__AA__30134,Vvar__3__AF__30136,Vvar__4___24Anonymous__30138,Vvar__5___24Anonymous__30140,Vvar__6___24Anonymous__30142) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__30131,Vvar__1__TX__30133,Vvar__2__AA__30135,Vvar__3__AF__30137,Vvar__4___24Anonymous__30139,Vvar__5___24Anonymous__30141,Vvar__6___24Anonymous__30143)
=> ( Vvar__6___24Anonymous__30142 = Vvar__6___24Anonymous__30143
& Vvar__5___24Anonymous__30140 = Vvar__5___24Anonymous__30141
& Vvar__4___24Anonymous__30138 = Vvar__4___24Anonymous__30139
& Vvar__3__AF__30136 = Vvar__3__AF__30137
& Vvar__2__AA__30134 = Vvar__2__AA__30135
& Vvar__1__TX__30132 = Vvar__1__TX__30133
& Vvar__0__TA__30130 = Vvar__0__TA__30131 ) ) ).
fof('$_inj_Coq.micromega.Tauto.N',axiom,
! [Vvar__0__TA__30120,Vvar__0__TA__30121,Vvar__1__TX__30122,Vvar__1__TX__30123,Vvar__2__AA__30124,Vvar__2__AA__30125,Vvar__3__AF__30126,Vvar__3__AF__30127,Vvar__4___24Anonymous__30128,Vvar__4___24Anonymous__30129] :
( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__30120,Vvar__1__TX__30122,Vvar__2__AA__30124,Vvar__3__AF__30126,Vvar__4___24Anonymous__30128) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__30121,Vvar__1__TX__30123,Vvar__2__AA__30125,Vvar__3__AF__30127,Vvar__4___24Anonymous__30129)
=> ( Vvar__4___24Anonymous__30128 = Vvar__4___24Anonymous__30129
& Vvar__3__AF__30126 = Vvar__3__AF__30127
& Vvar__2__AA__30124 = Vvar__2__AA__30125
& Vvar__1__TX__30122 = Vvar__1__TX__30123
& Vvar__0__TA__30120 = Vvar__0__TA__30121 ) ) ).
fof('$_inj_Coq.micromega.Tauto.TT',axiom,
! [Vvar__0__TA__30058,Vvar__0__TA__30059,Vvar__1__TX__30060,Vvar__1__TX__30061,Vvar__2__AA__30062,Vvar__2__AA__30063,Vvar__3__AF__30064,Vvar__3__AF__30065] :
( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30058,Vvar__1__TX__30060,Vvar__2__AA__30062,Vvar__3__AF__30064) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__30059,Vvar__1__TX__30061,Vvar__2__AA__30063,Vvar__3__AF__30065)
=> ( Vvar__3__AF__30064 = Vvar__3__AF__30065
& Vvar__2__AA__30062 = Vvar__2__AA__30063
& Vvar__1__TX__30060 = Vvar__1__TX__30061
& Vvar__0__TA__30058 = Vvar__0__TA__30059 ) ) ).
fof('$_inj_Coq.micromega.Tauto.X',axiom,
! [Vvar__0__TA__30074,Vvar__0__TA__30075,Vvar__1__TX__30076,Vvar__1__TX__30077,Vvar__2__AA__30078,Vvar__2__AA__30079,Vvar__3__AF__30080,Vvar__3__AF__30081,Vvar__4___24Anonymous__30082,Vvar__4___24Anonymous__30083] :
( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__30074,Vvar__1__TX__30076,Vvar__2__AA__30078,Vvar__3__AF__30080,Vvar__4___24Anonymous__30082) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__30075,Vvar__1__TX__30077,Vvar__2__AA__30079,Vvar__3__AF__30081,Vvar__4___24Anonymous__30083)
=> ( Vvar__4___24Anonymous__30082 = Vvar__4___24Anonymous__30083
& Vvar__3__AF__30080 = Vvar__3__AF__30081
& Vvar__2__AA__30078 = Vvar__2__AA__30079
& Vvar__1__TX__30076 = Vvar__1__TX__30077
& Vvar__0__TA__30074 = Vvar__0__TA__30075 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
! [Vvar__0__A__36887,Vvar__0__A__36888,Vvar__1___24Anonymous__36889,Vvar__1___24Anonymous__36890,Vvar__2___24Anonymous__36891,Vvar__2___24Anonymous__36892,Vvar__3___24Anonymous__36893,Vvar__3___24Anonymous__36894] :
( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__36887,Vvar__1___24Anonymous__36889,Vvar__2___24Anonymous__36891,Vvar__3___24Anonymous__36893) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__36888,Vvar__1___24Anonymous__36890,Vvar__2___24Anonymous__36892,Vvar__3___24Anonymous__36894)
=> ( Vvar__3___24Anonymous__36893 = Vvar__3___24Anonymous__36894
& Vvar__2___24Anonymous__36891 = Vvar__2___24Anonymous__36892
& Vvar__1___24Anonymous__36889 = Vvar__1___24Anonymous__36890
& Vvar__0__A__36887 = Vvar__0__A__36888 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
! [Vvar__0__A__36883,Vvar__0__A__36884,Vvar__1___24Anonymous__36885,Vvar__1___24Anonymous__36886] :
( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__36883,Vvar__1___24Anonymous__36885) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__36884,Vvar__1___24Anonymous__36886)
=> ( Vvar__1___24Anonymous__36885 = Vvar__1___24Anonymous__36886
& Vvar__0__A__36883 = Vvar__0__A__36884 ) ) ).
fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
! [Vvar__0__A__36881,Vvar__0__A__36882] :
( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__36881) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__36882)
=> Vvar__0__A__36881 = Vvar__0__A__36882 ) ).
fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
! [Vvar__0___24Anonymous__31172,Vvar__0___24Anonymous__31173,Vvar__1___24Anonymous__31174,Vvar__1___24Anonymous__31175] :
( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__31172,Vvar__1___24Anonymous__31174) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__31173,Vvar__1___24Anonymous__31175)
=> ( Vvar__1___24Anonymous__31174 = Vvar__1___24Anonymous__31175
& Vvar__0___24Anonymous__31172 = Vvar__0___24Anonymous__31173 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
! [Vvar__0___24Anonymous__31176,Vvar__0___24Anonymous__31177,Vvar__1___24Anonymous__31178,Vvar__1___24Anonymous__31179,Vvar__2___24Anonymous__31180,Vvar__2___24Anonymous__31181] :
( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__31176,Vvar__1___24Anonymous__31178,Vvar__2___24Anonymous__31180) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__31177,Vvar__1___24Anonymous__31179,Vvar__2___24Anonymous__31181)
=> ( Vvar__2___24Anonymous__31180 = Vvar__2___24Anonymous__31181
& Vvar__1___24Anonymous__31178 = Vvar__1___24Anonymous__31179
& Vvar__0___24Anonymous__31176 = Vvar__0___24Anonymous__31177 ) ) ).
fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
! [Vvar__0___24Anonymous__31168,Vvar__0___24Anonymous__31169,Vvar__1___24Anonymous__31170,Vvar__1___24Anonymous__31171] :
( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__31168,Vvar__1___24Anonymous__31170) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__31169,Vvar__1___24Anonymous__31171)
=> ( Vvar__1___24Anonymous__31170 = Vvar__1___24Anonymous__31171
& Vvar__0___24Anonymous__31168 = Vvar__0___24Anonymous__31169 ) ) ).
fof('$_inj_hahn.HahnBase.Equality.Pack',axiom,
! [Vvar__0__sort__36951,Vvar__0__sort__36952,Vvar__1___24Anonymous__36953,Vvar__1___24Anonymous__36954,Vvar__2___24Anonymous__36955,Vvar__2___24Anonymous__36956] :
( chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__36951,Vvar__1___24Anonymous__36953,Vvar__2___24Anonymous__36955) = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__36952,Vvar__1___24Anonymous__36954,Vvar__2___24Anonymous__36956)
=> ( Vvar__2___24Anonymous__36955 = Vvar__2___24Anonymous__36956
& Vvar__1___24Anonymous__36953 = Vvar__1___24Anonymous__36954
& Vvar__0__sort__36951 = Vvar__0__sort__36952 ) ) ).
fof('$_inversion_Coq.Arith.Even.even',axiom,
! [Vvar__0___24Anonymous__34859] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__34859)
=> ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__34859)
=> ( Vvar__0___24Anonymous__34859 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0__n__34861] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__34861)
& cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__34861)
& Vvar__0___24Anonymous__34859 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__34861) ) ) ) ) ).
fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
! [Vvar__0__P__2452,Vvar__1___24Anonymous__2453,VX2454] :
( cProp___24t(Vvar__0__P__2452)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__2453)
=> ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__2452,Vvar__1___24Anonymous__2453,VX2454)
=> ( ( p(Vvar__0__P__2452)
& Vvar__1___24Anonymous__2453 = cCoq_2eInit_2eDatatypes_2etrue
& VX2454 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__2452) )
| ( ~ p(Vvar__0__P__2452)
& Vvar__1___24Anonymous__2453 = cCoq_2eInit_2eDatatypes_2efalse
& VX2454 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__2452) ) ) ) ) ) ).
fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [VX36996] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX36996)
=> ( VX36996 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
| ? [Vvar__0___24Anonymous__36997] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__36997)
& ? [Vvar__1___24Anonymous__36998] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__36998)
& ? [Vvar__2___24Anonymous__36999] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__36999)
& VX36996 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__36997,Vvar__1___24Anonymous__36998,Vvar__2___24Anonymous__36999) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Byte.byte',axiom,
! [VX34455] :
( cCoq_2eInit_2eByte_2ebyte___24t(VX34455)
=> ( VX34455 = cCoq_2eInit_2eByte_2ex00
| VX34455 = cCoq_2eInit_2eByte_2ex01
| VX34455 = cCoq_2eInit_2eByte_2ex02
| VX34455 = cCoq_2eInit_2eByte_2ex03
| VX34455 = cCoq_2eInit_2eByte_2ex04
| VX34455 = cCoq_2eInit_2eByte_2ex05
| VX34455 = cCoq_2eInit_2eByte_2ex06
| VX34455 = cCoq_2eInit_2eByte_2ex07
| VX34455 = cCoq_2eInit_2eByte_2ex08
| VX34455 = cCoq_2eInit_2eByte_2ex09
| VX34455 = cCoq_2eInit_2eByte_2ex0a
| VX34455 = cCoq_2eInit_2eByte_2ex0b
| VX34455 = cCoq_2eInit_2eByte_2ex0c
| VX34455 = cCoq_2eInit_2eByte_2ex0d
| VX34455 = cCoq_2eInit_2eByte_2ex0e
| VX34455 = cCoq_2eInit_2eByte_2ex0f
| VX34455 = cCoq_2eInit_2eByte_2ex10
| VX34455 = cCoq_2eInit_2eByte_2ex11
| VX34455 = cCoq_2eInit_2eByte_2ex12
| VX34455 = cCoq_2eInit_2eByte_2ex13
| VX34455 = cCoq_2eInit_2eByte_2ex14
| VX34455 = cCoq_2eInit_2eByte_2ex15
| VX34455 = cCoq_2eInit_2eByte_2ex16
| VX34455 = cCoq_2eInit_2eByte_2ex17
| VX34455 = cCoq_2eInit_2eByte_2ex18
| VX34455 = cCoq_2eInit_2eByte_2ex19
| VX34455 = cCoq_2eInit_2eByte_2ex1a
| VX34455 = cCoq_2eInit_2eByte_2ex1b
| VX34455 = cCoq_2eInit_2eByte_2ex1c
| VX34455 = cCoq_2eInit_2eByte_2ex1d
| VX34455 = cCoq_2eInit_2eByte_2ex1e
| VX34455 = cCoq_2eInit_2eByte_2ex1f
| VX34455 = cCoq_2eInit_2eByte_2ex20
| VX34455 = cCoq_2eInit_2eByte_2ex21
| VX34455 = cCoq_2eInit_2eByte_2ex22
| VX34455 = cCoq_2eInit_2eByte_2ex23
| VX34455 = cCoq_2eInit_2eByte_2ex24
| VX34455 = cCoq_2eInit_2eByte_2ex25
| VX34455 = cCoq_2eInit_2eByte_2ex26
| VX34455 = cCoq_2eInit_2eByte_2ex27
| VX34455 = cCoq_2eInit_2eByte_2ex28
| VX34455 = cCoq_2eInit_2eByte_2ex29
| VX34455 = cCoq_2eInit_2eByte_2ex2a
| VX34455 = cCoq_2eInit_2eByte_2ex2b
| VX34455 = cCoq_2eInit_2eByte_2ex2c
| VX34455 = cCoq_2eInit_2eByte_2ex2d
| VX34455 = cCoq_2eInit_2eByte_2ex2e
| VX34455 = cCoq_2eInit_2eByte_2ex2f
| VX34455 = cCoq_2eInit_2eByte_2ex30
| VX34455 = cCoq_2eInit_2eByte_2ex31
| VX34455 = cCoq_2eInit_2eByte_2ex32
| VX34455 = cCoq_2eInit_2eByte_2ex33
| VX34455 = cCoq_2eInit_2eByte_2ex34
| VX34455 = cCoq_2eInit_2eByte_2ex35
| VX34455 = cCoq_2eInit_2eByte_2ex36
| VX34455 = cCoq_2eInit_2eByte_2ex37
| VX34455 = cCoq_2eInit_2eByte_2ex38
| VX34455 = cCoq_2eInit_2eByte_2ex39
| VX34455 = cCoq_2eInit_2eByte_2ex3a
| VX34455 = cCoq_2eInit_2eByte_2ex3b
| VX34455 = cCoq_2eInit_2eByte_2ex3c
| VX34455 = cCoq_2eInit_2eByte_2ex3d
| VX34455 = cCoq_2eInit_2eByte_2ex3e
| VX34455 = cCoq_2eInit_2eByte_2ex3f
| VX34455 = cCoq_2eInit_2eByte_2ex40
| VX34455 = cCoq_2eInit_2eByte_2ex41
| VX34455 = cCoq_2eInit_2eByte_2ex42
| VX34455 = cCoq_2eInit_2eByte_2ex43
| VX34455 = cCoq_2eInit_2eByte_2ex44
| VX34455 = cCoq_2eInit_2eByte_2ex45
| VX34455 = cCoq_2eInit_2eByte_2ex46
| VX34455 = cCoq_2eInit_2eByte_2ex47
| VX34455 = cCoq_2eInit_2eByte_2ex48
| VX34455 = cCoq_2eInit_2eByte_2ex49
| VX34455 = cCoq_2eInit_2eByte_2ex4a
| VX34455 = cCoq_2eInit_2eByte_2ex4b
| VX34455 = cCoq_2eInit_2eByte_2ex4c
| VX34455 = cCoq_2eInit_2eByte_2ex4d
| VX34455 = cCoq_2eInit_2eByte_2ex4e
| VX34455 = cCoq_2eInit_2eByte_2ex4f
| VX34455 = cCoq_2eInit_2eByte_2ex50
| VX34455 = cCoq_2eInit_2eByte_2ex51
| VX34455 = cCoq_2eInit_2eByte_2ex52
| VX34455 = cCoq_2eInit_2eByte_2ex53
| VX34455 = cCoq_2eInit_2eByte_2ex54
| VX34455 = cCoq_2eInit_2eByte_2ex55
| VX34455 = cCoq_2eInit_2eByte_2ex56
| VX34455 = cCoq_2eInit_2eByte_2ex57
| VX34455 = cCoq_2eInit_2eByte_2ex58
| VX34455 = cCoq_2eInit_2eByte_2ex59
| VX34455 = cCoq_2eInit_2eByte_2ex5a
| VX34455 = cCoq_2eInit_2eByte_2ex5b
| VX34455 = cCoq_2eInit_2eByte_2ex5c
| VX34455 = cCoq_2eInit_2eByte_2ex5d
| VX34455 = cCoq_2eInit_2eByte_2ex5e
| VX34455 = cCoq_2eInit_2eByte_2ex5f
| VX34455 = cCoq_2eInit_2eByte_2ex60
| VX34455 = cCoq_2eInit_2eByte_2ex61
| VX34455 = cCoq_2eInit_2eByte_2ex62
| VX34455 = cCoq_2eInit_2eByte_2ex63
| VX34455 = cCoq_2eInit_2eByte_2ex64
| VX34455 = cCoq_2eInit_2eByte_2ex65
| VX34455 = cCoq_2eInit_2eByte_2ex66
| VX34455 = cCoq_2eInit_2eByte_2ex67
| VX34455 = cCoq_2eInit_2eByte_2ex68
| VX34455 = cCoq_2eInit_2eByte_2ex69
| VX34455 = cCoq_2eInit_2eByte_2ex6a
| VX34455 = cCoq_2eInit_2eByte_2ex6b
| VX34455 = cCoq_2eInit_2eByte_2ex6c
| VX34455 = cCoq_2eInit_2eByte_2ex6d
| VX34455 = cCoq_2eInit_2eByte_2ex6e
| VX34455 = cCoq_2eInit_2eByte_2ex6f
| VX34455 = cCoq_2eInit_2eByte_2ex70
| VX34455 = cCoq_2eInit_2eByte_2ex71
| VX34455 = cCoq_2eInit_2eByte_2ex72
| VX34455 = cCoq_2eInit_2eByte_2ex73
| VX34455 = cCoq_2eInit_2eByte_2ex74
| VX34455 = cCoq_2eInit_2eByte_2ex75
| VX34455 = cCoq_2eInit_2eByte_2ex76
| VX34455 = cCoq_2eInit_2eByte_2ex77
| VX34455 = cCoq_2eInit_2eByte_2ex78
| VX34455 = cCoq_2eInit_2eByte_2ex79
| VX34455 = cCoq_2eInit_2eByte_2ex7a
| VX34455 = cCoq_2eInit_2eByte_2ex7b
| VX34455 = cCoq_2eInit_2eByte_2ex7c
| VX34455 = cCoq_2eInit_2eByte_2ex7d
| VX34455 = cCoq_2eInit_2eByte_2ex7e
| VX34455 = cCoq_2eInit_2eByte_2ex7f
| VX34455 = cCoq_2eInit_2eByte_2ex80
| VX34455 = cCoq_2eInit_2eByte_2ex81
| VX34455 = cCoq_2eInit_2eByte_2ex82
| VX34455 = cCoq_2eInit_2eByte_2ex83
| VX34455 = cCoq_2eInit_2eByte_2ex84
| VX34455 = cCoq_2eInit_2eByte_2ex85
| VX34455 = cCoq_2eInit_2eByte_2ex86
| VX34455 = cCoq_2eInit_2eByte_2ex87
| VX34455 = cCoq_2eInit_2eByte_2ex88
| VX34455 = cCoq_2eInit_2eByte_2ex89
| VX34455 = cCoq_2eInit_2eByte_2ex8a
| VX34455 = cCoq_2eInit_2eByte_2ex8b
| VX34455 = cCoq_2eInit_2eByte_2ex8c
| VX34455 = cCoq_2eInit_2eByte_2ex8d
| VX34455 = cCoq_2eInit_2eByte_2ex8e
| VX34455 = cCoq_2eInit_2eByte_2ex8f
| VX34455 = cCoq_2eInit_2eByte_2ex90
| VX34455 = cCoq_2eInit_2eByte_2ex91
| VX34455 = cCoq_2eInit_2eByte_2ex92
| VX34455 = cCoq_2eInit_2eByte_2ex93
| VX34455 = cCoq_2eInit_2eByte_2ex94
| VX34455 = cCoq_2eInit_2eByte_2ex95
| VX34455 = cCoq_2eInit_2eByte_2ex96
| VX34455 = cCoq_2eInit_2eByte_2ex97
| VX34455 = cCoq_2eInit_2eByte_2ex98
| VX34455 = cCoq_2eInit_2eByte_2ex99
| VX34455 = cCoq_2eInit_2eByte_2ex9a
| VX34455 = cCoq_2eInit_2eByte_2ex9b
| VX34455 = cCoq_2eInit_2eByte_2ex9c
| VX34455 = cCoq_2eInit_2eByte_2ex9d
| VX34455 = cCoq_2eInit_2eByte_2ex9e
| VX34455 = cCoq_2eInit_2eByte_2ex9f
| VX34455 = cCoq_2eInit_2eByte_2exa0
| VX34455 = cCoq_2eInit_2eByte_2exa1
| VX34455 = cCoq_2eInit_2eByte_2exa2
| VX34455 = cCoq_2eInit_2eByte_2exa3
| VX34455 = cCoq_2eInit_2eByte_2exa4
| VX34455 = cCoq_2eInit_2eByte_2exa5
| VX34455 = cCoq_2eInit_2eByte_2exa6
| VX34455 = cCoq_2eInit_2eByte_2exa7
| VX34455 = cCoq_2eInit_2eByte_2exa8
| VX34455 = cCoq_2eInit_2eByte_2exa9
| VX34455 = cCoq_2eInit_2eByte_2exaa
| VX34455 = cCoq_2eInit_2eByte_2exab
| VX34455 = cCoq_2eInit_2eByte_2exac
| VX34455 = cCoq_2eInit_2eByte_2exad
| VX34455 = cCoq_2eInit_2eByte_2exae
| VX34455 = cCoq_2eInit_2eByte_2exaf
| VX34455 = cCoq_2eInit_2eByte_2exb0
| VX34455 = cCoq_2eInit_2eByte_2exb1
| VX34455 = cCoq_2eInit_2eByte_2exb2
| VX34455 = cCoq_2eInit_2eByte_2exb3
| VX34455 = cCoq_2eInit_2eByte_2exb4
| VX34455 = cCoq_2eInit_2eByte_2exb5
| VX34455 = cCoq_2eInit_2eByte_2exb6
| VX34455 = cCoq_2eInit_2eByte_2exb7
| VX34455 = cCoq_2eInit_2eByte_2exb8
| VX34455 = cCoq_2eInit_2eByte_2exb9
| VX34455 = cCoq_2eInit_2eByte_2exba
| VX34455 = cCoq_2eInit_2eByte_2exbb
| VX34455 = cCoq_2eInit_2eByte_2exbc
| VX34455 = cCoq_2eInit_2eByte_2exbd
| VX34455 = cCoq_2eInit_2eByte_2exbe
| VX34455 = cCoq_2eInit_2eByte_2exbf
| VX34455 = cCoq_2eInit_2eByte_2exc0
| VX34455 = cCoq_2eInit_2eByte_2exc1
| VX34455 = cCoq_2eInit_2eByte_2exc2
| VX34455 = cCoq_2eInit_2eByte_2exc3
| VX34455 = cCoq_2eInit_2eByte_2exc4
| VX34455 = cCoq_2eInit_2eByte_2exc5
| VX34455 = cCoq_2eInit_2eByte_2exc6
| VX34455 = cCoq_2eInit_2eByte_2exc7
| VX34455 = cCoq_2eInit_2eByte_2exc8
| VX34455 = cCoq_2eInit_2eByte_2exc9
| VX34455 = cCoq_2eInit_2eByte_2exca
| VX34455 = cCoq_2eInit_2eByte_2excb
| VX34455 = cCoq_2eInit_2eByte_2excc
| VX34455 = cCoq_2eInit_2eByte_2excd
| VX34455 = cCoq_2eInit_2eByte_2exce
| VX34455 = cCoq_2eInit_2eByte_2excf
| VX34455 = cCoq_2eInit_2eByte_2exd0
| VX34455 = cCoq_2eInit_2eByte_2exd1
| VX34455 = cCoq_2eInit_2eByte_2exd2
| VX34455 = cCoq_2eInit_2eByte_2exd3
| VX34455 = cCoq_2eInit_2eByte_2exd4
| VX34455 = cCoq_2eInit_2eByte_2exd5
| VX34455 = cCoq_2eInit_2eByte_2exd6
| VX34455 = cCoq_2eInit_2eByte_2exd7
| VX34455 = cCoq_2eInit_2eByte_2exd8
| VX34455 = cCoq_2eInit_2eByte_2exd9
| VX34455 = cCoq_2eInit_2eByte_2exda
| VX34455 = cCoq_2eInit_2eByte_2exdb
| VX34455 = cCoq_2eInit_2eByte_2exdc
| VX34455 = cCoq_2eInit_2eByte_2exdd
| VX34455 = cCoq_2eInit_2eByte_2exde
| VX34455 = cCoq_2eInit_2eByte_2exdf
| VX34455 = cCoq_2eInit_2eByte_2exe0
| VX34455 = cCoq_2eInit_2eByte_2exe1
| VX34455 = cCoq_2eInit_2eByte_2exe2
| VX34455 = cCoq_2eInit_2eByte_2exe3
| VX34455 = cCoq_2eInit_2eByte_2exe4
| VX34455 = cCoq_2eInit_2eByte_2exe5
| VX34455 = cCoq_2eInit_2eByte_2exe6
| VX34455 = cCoq_2eInit_2eByte_2exe7
| VX34455 = cCoq_2eInit_2eByte_2exe8
| VX34455 = cCoq_2eInit_2eByte_2exe9
| VX34455 = cCoq_2eInit_2eByte_2exea
| VX34455 = cCoq_2eInit_2eByte_2exeb
| VX34455 = cCoq_2eInit_2eByte_2exec
| VX34455 = cCoq_2eInit_2eByte_2exed
| VX34455 = cCoq_2eInit_2eByte_2exee
| VX34455 = cCoq_2eInit_2eByte_2exef
| VX34455 = cCoq_2eInit_2eByte_2exf0
| VX34455 = cCoq_2eInit_2eByte_2exf1
| VX34455 = cCoq_2eInit_2eByte_2exf2
| VX34455 = cCoq_2eInit_2eByte_2exf3
| VX34455 = cCoq_2eInit_2eByte_2exf4
| VX34455 = cCoq_2eInit_2eByte_2exf5
| VX34455 = cCoq_2eInit_2eByte_2exf6
| VX34455 = cCoq_2eInit_2eByte_2exf7
| VX34455 = cCoq_2eInit_2eByte_2exf8
| VX34455 = cCoq_2eInit_2eByte_2exf9
| VX34455 = cCoq_2eInit_2eByte_2exfa
| VX34455 = cCoq_2eInit_2eByte_2exfb
| VX34455 = cCoq_2eInit_2eByte_2exfc
| VX34455 = cCoq_2eInit_2eByte_2exfd
| VX34455 = cCoq_2eInit_2eByte_2exfe
| VX34455 = cCoq_2eInit_2eByte_2exff ) ) ).
fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
! [Vvar__0__P__3067,Vvar__1__Q__3068,Vvar__2___24Anonymous__3069] :
( cProp___24t(Vvar__0__P__3067)
=> ( cProp___24t(Vvar__1__Q__3068)
=> ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__3069)
=> ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__3067,Vvar__1__Q__3068,Vvar__2___24Anonymous__3069)
=> ( ( p(Vvar__0__P__3067)
& Vvar__2___24Anonymous__3069 = cCoq_2eInit_2eDatatypes_2etrue )
| ( p(Vvar__1__Q__3068)
& Vvar__2___24Anonymous__3069 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
! [Vvar__0__Peq__31512,Vvar__1__Plt__31513,Vvar__2__Pgt__31514,Vvar__3___24Anonymous__31515] :
( cProp___24t(Vvar__0__Peq__31512)
=> ( cProp___24t(Vvar__1__Plt__31513)
=> ( cProp___24t(Vvar__2__Pgt__31514)
=> ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__31515)
=> ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__31512,Vvar__1__Plt__31513,Vvar__2__Pgt__31514,Vvar__3___24Anonymous__31515)
=> ( ( p(Vvar__0__Peq__31512)
& Vvar__3___24Anonymous__31515 = cCoq_2eInit_2eDatatypes_2eEq )
| ( p(Vvar__1__Plt__31513)
& Vvar__3___24Anonymous__31515 = cCoq_2eInit_2eDatatypes_2eLt )
| ( p(Vvar__2__Pgt__31514)
& Vvar__3___24Anonymous__31515 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
! [VX2529] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(VX2529)
=> ( VX2529 = cCoq_2eInit_2eDatatypes_2etrue
| VX2529 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).
fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
! [VX303] :
( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX303)
=> ( VX303 = cCoq_2eInit_2eDatatypes_2eEq
| VX303 = cCoq_2eInit_2eDatatypes_2eLt
| VX303 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).
fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
! [Vvar__0__A__34496,Vvar__1__a__34497,Vvar__2___24Anonymous__34498] :
( cType___24t(Vvar__0__A__34496)
=> ( t(Vvar__1__a__34497,Vvar__0__A__34496)
=> ( t(Vvar__2___24Anonymous__34498,Vvar__0__A__34496)
=> ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__34496,Vvar__1__a__34497,Vvar__2___24Anonymous__34498)
=> Vvar__2___24Anonymous__34498 = Vvar__1__a__34497 ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.list',axiom,
! [Vvar__0__A__3120,VX3121] :
( cType___24t(Vvar__0__A__3120)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3120,VX3121)
=> ( VX3121 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__3120)
| ? [Vvar__1___24Anonymous__3124] :
( t(Vvar__1___24Anonymous__3124,Vvar__0__A__3120)
& ? [Vvar__2___24Anonymous__3125] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__3120,Vvar__2___24Anonymous__3125)
& VX3121 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__3120,Vvar__1___24Anonymous__3124,Vvar__2___24Anonymous__3125) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.nat',axiom,
! [VX266] :
( cCoq_2eInit_2eDatatypes_2enat___24t(VX266)
=> ( VX266 = cCoq_2eInit_2eDatatypes_2eO
| ? [Vvar__0___24Anonymous__267] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__267)
& VX266 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__267) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.option',axiom,
! [Vvar__0__A__3077,VX3078] :
( cType___24t(Vvar__0__A__3077)
=> ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__3077,VX3078)
=> ( ? [Vvar__1___24Anonymous__3080] :
( t(Vvar__1___24Anonymous__3080,Vvar__0__A__3077)
& VX3078 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__3077,Vvar__1___24Anonymous__3080) )
| VX3078 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__3077) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
! [Vvar__0__A__34468,Vvar__1__B__34469,VX34470] :
( cType___24t(Vvar__0__A__34468)
=> ( cType___24t(Vvar__1__B__34469)
=> ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__34468,Vvar__1__B__34469,VX34470)
=> ( ? [Vvar__2___24Anonymous__34473] :
( t(Vvar__2___24Anonymous__34473,Vvar__0__A__34468)
& VX34470 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__34468,Vvar__1__B__34469,Vvar__2___24Anonymous__34473) )
| ? [Vvar__2___24Anonymous__34476] :
( t(Vvar__2___24Anonymous__34476,Vvar__1__B__34469)
& VX34470 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__34468,Vvar__1__B__34469,Vvar__2___24Anonymous__34476) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
! [VX5] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(VX5)
=> VX5 = cCoq_2eInit_2eDatatypes_2ett ) ).
fof('$_inversion_Coq.Init.Decimal.int',axiom,
! [VX34633] :
( cCoq_2eInit_2eDecimal_2eint___24t(VX34633)
=> ( ? [Vvar__0__d__34634] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__34634)
& VX34633 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__34634) )
| ? [Vvar__0__d__34635] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__34635)
& VX34633 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__34635) ) ) ) ).
fof('$_inversion_Coq.Init.Decimal.uint',axiom,
! [VX34502] :
( cCoq_2eInit_2eDecimal_2euint___24t(VX34502)
=> ( VX34502 = cCoq_2eInit_2eDecimal_2eNil
| ? [Vvar__0___24Anonymous__34503] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34503)
& VX34502 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__34503) )
| ? [Vvar__0___24Anonymous__34504] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34504)
& VX34502 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__34504) )
| ? [Vvar__0___24Anonymous__34505] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34505)
& VX34502 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__34505) )
| ? [Vvar__0___24Anonymous__34506] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34506)
& VX34502 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__34506) )
| ? [Vvar__0___24Anonymous__34507] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34507)
& VX34502 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__34507) )
| ? [Vvar__0___24Anonymous__34508] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34508)
& VX34502 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__34508) )
| ? [Vvar__0___24Anonymous__34509] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34509)
& VX34502 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__34509) )
| ? [Vvar__0___24Anonymous__34510] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34510)
& VX34502 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__34510) )
| ? [Vvar__0___24Anonymous__34511] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34511)
& VX34502 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__34511) )
| ? [Vvar__0___24Anonymous__34512] :
( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__34512)
& VX34502 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__34512) ) ) ) ).
fof('$_inversion_Coq.Init.Peano.le',axiom,
! [Vvar__0__n__338,Vvar__1___24Anonymous__339] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__338)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__339)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__338,Vvar__1___24Anonymous__339))
=> ( Vvar__1___24Anonymous__339 = Vvar__0__n__338
| ? [Vvar__1__m__343] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__343)
& p(cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__338,Vvar__1__m__343))
& Vvar__1___24Anonymous__339 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__343) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig',axiom,
! [Vvar__0__A__29573,Vvar__1__P__29574,VX29577] :
( cType___24t(Vvar__0__A__29573)
=> ( c_24__type__29587___24t(Vvar__0__A__29573,Vvar__1__P__29574,Vvar__1__P__29574)
=> ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__29573,Vvar__1__P__29574,VX29577)
=> ? [Vvar__2__x__29582] :
( t(Vvar__2__x__29582,Vvar__0__A__29573)
& p(happ(Vvar__1__P__29574,Vvar__2__x__29582))
& VX29577 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__29573,Vvar__1__P__29574,Vvar__2__x__29582) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sig2',axiom,
! [Vvar__0__A__36737,Vvar__1__P__36738,Vvar__2__Q__36741,VX36744] :
( cType___24t(Vvar__0__A__36737)
=> ( c_24__type__36761___24t(Vvar__0__A__36737,Vvar__1__P__36738,Vvar__2__Q__36741,Vvar__1__P__36738)
=> ( c_24__type__36769___24t(Vvar__0__A__36737,Vvar__1__P__36738,Vvar__2__Q__36741,Vvar__2__Q__36741)
=> ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__36737,Vvar__1__P__36738,Vvar__2__Q__36741,VX36744)
=> ? [Vvar__3__x__36752] :
( t(Vvar__3__x__36752,Vvar__0__A__36737)
& p(happ(Vvar__1__P__36738,Vvar__3__x__36752))
& p(happ(Vvar__2__Q__36741,Vvar__3__x__36752))
& VX36744 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__36737,Vvar__1__P__36738,Vvar__2__Q__36741,Vvar__3__x__36752) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT',axiom,
! [Vvar__0__A__29612,Vvar__1__P__29613,VX29616] :
( cType___24t(Vvar__0__A__29612)
=> ( c_24__type__29626___24t(Vvar__0__A__29612,Vvar__1__P__29613,Vvar__1__P__29613)
=> ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__29612,Vvar__1__P__29613,VX29616)
=> ? [Vvar__2__x__29621] :
( t(Vvar__2__x__29621,Vvar__0__A__29612)
& ? [Vvar__3___24Anonymous__29622] :
( t(Vvar__3___24Anonymous__29622,happ(Vvar__1__P__29613,Vvar__2__x__29621))
& VX29616 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__29612,Vvar__1__P__29613,Vvar__2__x__29621,Vvar__3___24Anonymous__29622) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
! [Vvar__0__A__36793,Vvar__1__P__36794,Vvar__2__Q__36797,VX36800] :
( cType___24t(Vvar__0__A__36793)
=> ( c_24__type__36817___24t(Vvar__0__A__36793,Vvar__1__P__36794,Vvar__2__Q__36797,Vvar__1__P__36794)
=> ( c_24__type__36825___24t(Vvar__0__A__36793,Vvar__1__P__36794,Vvar__2__Q__36797,Vvar__2__Q__36797)
=> ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__36793,Vvar__1__P__36794,Vvar__2__Q__36797,VX36800)
=> ? [Vvar__3__x__36808] :
( t(Vvar__3__x__36808,Vvar__0__A__36793)
& ? [Vvar__4___24Anonymous__36809] :
( t(Vvar__4___24Anonymous__36809,happ(Vvar__1__P__36794,Vvar__3__x__36808))
& ? [Vvar__5___24Anonymous__36810] :
( t(Vvar__5___24Anonymous__36810,happ(Vvar__2__Q__36797,Vvar__3__x__36808))
& VX36800 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__36793,Vvar__1__P__36794,Vvar__2__Q__36797,Vvar__3__x__36808,Vvar__4___24Anonymous__36809,Vvar__5___24Anonymous__36810) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
! [Vvar__0__A__2936,Vvar__1__B__2937,VX2938] :
( cProp___24t(Vvar__0__A__2936)
=> ( cProp___24t(Vvar__1__B__2937)
=> ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__2936,Vvar__1__B__2937,VX2938)
=> ( ( p(Vvar__0__A__2936)
& VX2938 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__2936,Vvar__1__B__2937) )
| ( p(Vvar__1__B__2937)
& VX2938 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__2936,Vvar__1__B__2937) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Specif.sumor',axiom,
! [Vvar__0__A__29661,Vvar__1__B__29662,VX29663] :
( cType___24t(Vvar__0__A__29661)
=> ( cProp___24t(Vvar__1__B__29662)
=> ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__29661,Vvar__1__B__29662,VX29663)
=> ( ? [Vvar__2___24Anonymous__29666] :
( t(Vvar__2___24Anonymous__29666,Vvar__0__A__29661)
& VX29663 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__29661,Vvar__1__B__29662,Vvar__2___24Anonymous__29666) )
| ( p(Vvar__1__B__29662)
& VX29663 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__29661,Vvar__1__B__29662) ) ) ) ) ) ).
fof('$_inversion_Coq.Init.Wf.Acc',axiom,
! [Vvar__0__A__369,Vvar__1__R__370,Vvar__2__x__375] :
( cType___24t(Vvar__0__A__369)
=> ( c_24__type__404___24t(Vvar__0__A__369,Vvar__1__R__370,Vvar__2__x__375,Vvar__1__R__370)
=> ( t(Vvar__2__x__375,Vvar__0__A__369)
=> ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__369,Vvar__1__R__370,Vvar__2__x__375)
=> ( ! [Vvar__var__var__var__var__3__y__385__387__389__391__393] :
( t(Vvar__var__var__var__var__3__y__385__387__389__391__393,Vvar__0__A__369)
=> ( p(happ(happ(Vvar__1__R__370,Vvar__var__var__var__var__3__y__385__387__389__391__393),Vvar__2__x__375))
=> cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__369,Vvar__1__R__370,Vvar__var__var__var__var__3__y__385__387__389__391__393) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.Lists.List.NoDup',axiom,
! [Vvar__0__A__8355,Vvar__1___24Anonymous__8356] :
( cType___24t(Vvar__0__A__8355)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8355,Vvar__1___24Anonymous__8356)
=> ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8355,Vvar__1___24Anonymous__8356)
=> ( Vvar__1___24Anonymous__8356 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__8355)
| ? [Vvar__1__x__8360] :
( t(Vvar__1__x__8360,Vvar__0__A__8355)
& ? [Vvar__2__l__8361] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__8355,Vvar__2__l__8361)
& ~ p(cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__8355,Vvar__1__x__8360,Vvar__2__l__8361))
& cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__8355,Vvar__2__l__8361)
& Vvar__1___24Anonymous__8356 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__8355,Vvar__1__x__8360,Vvar__2__l__8361) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
! [Vvar__0__U__34835,Vvar__1__P__34836,Vvar__2__p__34839,Vvar__3__x__34840,Vvar__4__q__34841,Vvar__5___24Anonymous__34842] :
( cType___24t(Vvar__0__U__34835)
=> ( c_24__type__34857___24t(Vvar__0__U__34835,Vvar__1__P__34836,Vvar__2__p__34839,Vvar__3__x__34840,Vvar__4__q__34841,Vvar__5___24Anonymous__34842,Vvar__1__P__34836)
=> ( t(Vvar__2__p__34839,Vvar__0__U__34835)
=> ( t(Vvar__3__x__34840,happ(Vvar__1__P__34836,Vvar__2__p__34839))
=> ( t(Vvar__4__q__34841,Vvar__0__U__34835)
=> ( t(Vvar__5___24Anonymous__34842,happ(Vvar__1__P__34836,Vvar__4__q__34841))
=> ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__34835,Vvar__1__P__34836,Vvar__2__p__34839,Vvar__3__x__34840,Vvar__4__q__34841,Vvar__5___24Anonymous__34842)
=> ( Vvar__5___24Anonymous__34842 = Vvar__3__x__34840
& Vvar__4__q__34841 = Vvar__2__p__34839 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
! [VX3053] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(VX3053)
=> ( VX3053 = cCoq_2eNumbers_2eBinNums_2eN0
| ? [Vvar__0___24Anonymous__3054] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__3054)
& VX3053 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__3054) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
! [VX253] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX253)
=> ( VX253 = cCoq_2eNumbers_2eBinNums_2eZ0
| ? [Vvar__0___24Anonymous__254] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__254)
& VX253 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__254) )
| ? [Vvar__0___24Anonymous__255] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__255)
& VX253 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__255) ) ) ) ).
fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
! [VX242] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX242)
=> ( ? [Vvar__0___24Anonymous__243] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__243)
& VX242 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__243) )
| ? [Vvar__0___24Anonymous__244] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__244)
& VX242 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__244) )
| VX242 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).
fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [VX36990] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX36990)
=> ( VX36990 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
| ? [Vvar__0___24Anonymous__36991] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__36991)
& VX36990 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__36991) )
| VX36990 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).
fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
! [VX32053] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX32053)
=> ? [Vvar__0__Qnum__32054] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__32054)
& ? [Vvar__1__Qden__32055] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__32055)
& VX32053 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__32054,Vvar__1__Qden__32055) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
! [Vvar__0__A__32087,Vvar__1__R__32088] :
( cType___24t(Vvar__0__A__32087)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32087,Vvar__1__R__32088)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__32087,Vvar__1__R__32088)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__32087,Vvar__1__R__32088)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__32087,Vvar__1__R__32088)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
! [Vvar__0__A__32079,Vvar__1__R__32080] :
( cType___24t(Vvar__0__A__32079)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32079,Vvar__1__R__32080)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__32079,Vvar__1__R__32080)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__32079,Vvar__1__R__32080)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__32079,Vvar__1__R__32080)
& cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__32079,Vvar__1__R__32080)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
! [Vvar__0__A__32071,Vvar__1__R__32072] :
( cType___24t(Vvar__0__A__32071)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32071,Vvar__1__R__32072)
=> ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__32071,Vvar__1__R__32072)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__32071,Vvar__1__R__32072)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__32071,Vvar__1__R__32072)
& cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__32071,Vvar__1__R__32072)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
! [Vvar__0__A__32064,Vvar__1__R__32065] :
( cType___24t(Vvar__0__A__32064)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32064,Vvar__1__R__32065)
=> ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__32064,Vvar__1__R__32065)
=> ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__32064,Vvar__1__R__32065)
& cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__32064,Vvar__1__R__32065)
& p(c_24True) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
! [Vvar__0__A__10048,Vvar__1__R__10049,Vvar__2__x__10050,Vvar__3___24Anonymous__10051] :
( cType___24t(Vvar__0__A__10048)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__10048,Vvar__1__R__10049)
=> ( t(Vvar__2__x__10050,Vvar__0__A__10048)
=> ( t(Vvar__3___24Anonymous__10051,Vvar__0__A__10048)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__10048,Vvar__1__R__10049,Vvar__2__x__10050,Vvar__3___24Anonymous__10051)
=> ( ? [Vvar__3__y__10056] :
( t(Vvar__3__y__10056,Vvar__0__A__10048)
& p(happ(happ(Vvar__1__R__10049,Vvar__2__x__10050),Vvar__3__y__10056))
& Vvar__3___24Anonymous__10051 = Vvar__3__y__10056 )
| Vvar__3___24Anonymous__10051 = Vvar__2__x__10050 ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans',axiom,
! [Vvar__0__A__32263,Vvar__1__R__32264,Vvar__1___24Anonymous__32265,Vvar__2___24Anonymous__32266] :
( cType___24t(Vvar__0__A__32263)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32263,Vvar__1__R__32264)
=> ( t(Vvar__1___24Anonymous__32265,Vvar__0__A__32263)
=> ( t(Vvar__2___24Anonymous__32266,Vvar__0__A__32263)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__32263,Vvar__1__R__32264,Vvar__1___24Anonymous__32265,Vvar__2___24Anonymous__32266)
=> ( ? [Vvar__2__x__32270] :
( t(Vvar__2__x__32270,Vvar__0__A__32263)
& ? [Vvar__3__y__32271] :
( t(Vvar__3__y__32271,Vvar__0__A__32263)
& p(happ(happ(Vvar__1__R__32264,Vvar__2__x__32270),Vvar__3__y__32271))
& Vvar__2___24Anonymous__32266 = Vvar__3__y__32271
& Vvar__1___24Anonymous__32265 = Vvar__2__x__32270 ) )
| ? [Vvar__2__x__32275] :
( t(Vvar__2__x__32275,Vvar__0__A__32263)
& Vvar__2___24Anonymous__32266 = Vvar__2__x__32275
& Vvar__1___24Anonymous__32265 = Vvar__2__x__32275 )
| ? [Vvar__2__x__32278] :
( t(Vvar__2__x__32278,Vvar__0__A__32263)
& ? [Vvar__3__y__32279] :
( t(Vvar__3__y__32279,Vvar__0__A__32263)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__32263,Vvar__1__R__32264,Vvar__2__x__32278,Vvar__3__y__32279)
& Vvar__2___24Anonymous__32266 = Vvar__2__x__32278
& Vvar__1___24Anonymous__32265 = Vvar__3__y__32279 ) )
| ? [Vvar__2__x__32283] :
( t(Vvar__2__x__32283,Vvar__0__A__32263)
& ? [Vvar__3__y__32284] :
( t(Vvar__3__y__32284,Vvar__0__A__32263)
& ? [Vvar__4__z__32285] :
( t(Vvar__4__z__32285,Vvar__0__A__32263)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__32263,Vvar__1__R__32264,Vvar__2__x__32283,Vvar__3__y__32284)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(Vvar__0__A__32263,Vvar__1__R__32264,Vvar__3__y__32284,Vvar__4__z__32285)
& Vvar__2___24Anonymous__32266 = Vvar__4__z__32285
& Vvar__1___24Anonymous__32265 = Vvar__2__x__32283 ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
! [Vvar__0__A__32324,Vvar__1__R__32325,Vvar__2__x__32326,Vvar__3___24Anonymous__32327] :
( cType___24t(Vvar__0__A__32324)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32324,Vvar__1__R__32325)
=> ( t(Vvar__2__x__32326,Vvar__0__A__32324)
=> ( t(Vvar__3___24Anonymous__32327,Vvar__0__A__32324)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__32324,Vvar__1__R__32325,Vvar__2__x__32326,Vvar__3___24Anonymous__32327)
=> ( Vvar__3___24Anonymous__32327 = Vvar__2__x__32326
| ? [Vvar__3__y__32335] :
( t(Vvar__3__y__32335,Vvar__0__A__32324)
& ? [Vvar__4__z__32336] :
( t(Vvar__4__z__32336,Vvar__0__A__32324)
& ( p(happ(happ(Vvar__1__R__32325,Vvar__2__x__32326),Vvar__3__y__32335))
| p(happ(happ(Vvar__1__R__32325,Vvar__3__y__32335),Vvar__2__x__32326)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__32324,Vvar__1__R__32325,Vvar__3__y__32335,Vvar__4__z__32336)
& Vvar__3___24Anonymous__32327 = Vvar__4__z__32336 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
! [Vvar__0__A__32359,Vvar__1__R__32360,Vvar__2__x__32361,Vvar__3___24Anonymous__32362] :
( cType___24t(Vvar__0__A__32359)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32359,Vvar__1__R__32360)
=> ( t(Vvar__2__x__32361,Vvar__0__A__32359)
=> ( t(Vvar__3___24Anonymous__32362,Vvar__0__A__32359)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__32359,Vvar__1__R__32360,Vvar__2__x__32361,Vvar__3___24Anonymous__32362)
=> ( Vvar__3___24Anonymous__32362 = Vvar__2__x__32361
| ? [Vvar__3__y__32370] :
( t(Vvar__3__y__32370,Vvar__0__A__32359)
& ? [Vvar__4__z__32371] :
( t(Vvar__4__z__32371,Vvar__0__A__32359)
& ( p(happ(happ(Vvar__1__R__32360,Vvar__3__y__32370),Vvar__4__z__32371))
| p(happ(happ(Vvar__1__R__32360,Vvar__4__z__32371),Vvar__3__y__32370)) )
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__32359,Vvar__1__R__32360,Vvar__2__x__32361,Vvar__3__y__32370)
& Vvar__3___24Anonymous__32362 = Vvar__4__z__32371 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
! [Vvar__0__A__207,Vvar__1__R__208,Vvar__2__x__209,Vvar__3___24Anonymous__210] :
( cType___24t(Vvar__0__A__207)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__207,Vvar__1__R__208)
=> ( t(Vvar__2__x__209,Vvar__0__A__207)
=> ( t(Vvar__3___24Anonymous__210,Vvar__0__A__207)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__207,Vvar__1__R__208,Vvar__2__x__209,Vvar__3___24Anonymous__210)
=> ( ? [Vvar__3__y__215] :
( t(Vvar__3__y__215,Vvar__0__A__207)
& p(happ(happ(Vvar__1__R__208,Vvar__2__x__209),Vvar__3__y__215))
& Vvar__3___24Anonymous__210 = Vvar__3__y__215 )
| Vvar__3___24Anonymous__210 = Vvar__2__x__209
| ? [Vvar__3__y__223] :
( t(Vvar__3__y__223,Vvar__0__A__207)
& ? [Vvar__4__z__224] :
( t(Vvar__4__z__224,Vvar__0__A__207)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__207,Vvar__1__R__208,Vvar__2__x__209,Vvar__3__y__223)
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__207,Vvar__1__R__208,Vvar__3__y__223,Vvar__4__z__224)
& Vvar__3___24Anonymous__210 = Vvar__4__z__224 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
! [Vvar__0__A__32201,Vvar__1__R__32202,Vvar__2__x__32203,Vvar__3___24Anonymous__32204] :
( cType___24t(Vvar__0__A__32201)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32201,Vvar__1__R__32202)
=> ( t(Vvar__2__x__32203,Vvar__0__A__32201)
=> ( t(Vvar__3___24Anonymous__32204,Vvar__0__A__32201)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__32201,Vvar__1__R__32202,Vvar__2__x__32203,Vvar__3___24Anonymous__32204)
=> ( Vvar__3___24Anonymous__32204 = Vvar__2__x__32203
| ? [Vvar__3__y__32212] :
( t(Vvar__3__y__32212,Vvar__0__A__32201)
& ? [Vvar__4__z__32213] :
( t(Vvar__4__z__32213,Vvar__0__A__32201)
& p(happ(happ(Vvar__1__R__32202,Vvar__2__x__32203),Vvar__3__y__32212))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__32201,Vvar__1__R__32202,Vvar__3__y__32212,Vvar__4__z__32213)
& Vvar__3___24Anonymous__32204 = Vvar__4__z__32213 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
! [Vvar__0__A__32236,Vvar__1__R__32237,Vvar__2__x__32238,Vvar__3___24Anonymous__32239] :
( cType___24t(Vvar__0__A__32236)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32236,Vvar__1__R__32237)
=> ( t(Vvar__2__x__32238,Vvar__0__A__32236)
=> ( t(Vvar__3___24Anonymous__32239,Vvar__0__A__32236)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__32236,Vvar__1__R__32237,Vvar__2__x__32238,Vvar__3___24Anonymous__32239)
=> ( Vvar__3___24Anonymous__32239 = Vvar__2__x__32238
| ? [Vvar__3__y__32247] :
( t(Vvar__3__y__32247,Vvar__0__A__32236)
& ? [Vvar__4__z__32248] :
( t(Vvar__4__z__32248,Vvar__0__A__32236)
& p(happ(happ(Vvar__1__R__32237,Vvar__3__y__32247),Vvar__4__z__32248))
& cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__32236,Vvar__1__R__32237,Vvar__2__x__32238,Vvar__3__y__32247)
& Vvar__3___24Anonymous__32239 = Vvar__4__z__32248 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
! [Vvar__0__A__100,Vvar__1__R__101,Vvar__2__x__102,Vvar__3___24Anonymous__103] :
( cType___24t(Vvar__0__A__100)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__100,Vvar__1__R__101)
=> ( t(Vvar__2__x__102,Vvar__0__A__100)
=> ( t(Vvar__3___24Anonymous__103,Vvar__0__A__100)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__100,Vvar__1__R__101,Vvar__2__x__102,Vvar__3___24Anonymous__103)
=> ( ? [Vvar__3__y__108] :
( t(Vvar__3__y__108,Vvar__0__A__100)
& p(happ(happ(Vvar__1__R__101,Vvar__2__x__102),Vvar__3__y__108))
& Vvar__3___24Anonymous__103 = Vvar__3__y__108 )
| ? [Vvar__3__y__113] :
( t(Vvar__3__y__113,Vvar__0__A__100)
& ? [Vvar__4__z__114] :
( t(Vvar__4__z__114,Vvar__0__A__100)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__100,Vvar__1__R__101,Vvar__2__x__102,Vvar__3__y__113)
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__100,Vvar__1__R__101,Vvar__3__y__113,Vvar__4__z__114)
& Vvar__3___24Anonymous__103 = Vvar__4__z__114 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
! [Vvar__0__A__32118,Vvar__1__R__32119,Vvar__2__x__32120,Vvar__3___24Anonymous__32121] :
( cType___24t(Vvar__0__A__32118)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__32118,Vvar__1__R__32119)
=> ( t(Vvar__2__x__32120,Vvar__0__A__32118)
=> ( t(Vvar__3___24Anonymous__32121,Vvar__0__A__32118)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__32118,Vvar__1__R__32119,Vvar__2__x__32120,Vvar__3___24Anonymous__32121)
=> ( ? [Vvar__3__y__32126] :
( t(Vvar__3__y__32126,Vvar__0__A__32118)
& p(happ(happ(Vvar__1__R__32119,Vvar__2__x__32120),Vvar__3__y__32126))
& Vvar__3___24Anonymous__32121 = Vvar__3__y__32126 )
| ? [Vvar__3__y__32131] :
( t(Vvar__3__y__32131,Vvar__0__A__32118)
& ? [Vvar__4__z__32132] :
( t(Vvar__4__z__32132,Vvar__0__A__32118)
& p(happ(happ(Vvar__1__R__32119,Vvar__2__x__32120),Vvar__3__y__32131))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__32118,Vvar__1__R__32119,Vvar__3__y__32131,Vvar__4__z__32132)
& Vvar__3___24Anonymous__32121 = Vvar__4__z__32132 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
! [Vvar__0__A__2911,Vvar__1__R__2912,Vvar__2__x__2913,Vvar__3___24Anonymous__2914] :
( cType___24t(Vvar__0__A__2911)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__2911,Vvar__1__R__2912)
=> ( t(Vvar__2__x__2913,Vvar__0__A__2911)
=> ( t(Vvar__3___24Anonymous__2914,Vvar__0__A__2911)
=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__2911,Vvar__1__R__2912,Vvar__2__x__2913,Vvar__3___24Anonymous__2914)
=> ( ? [Vvar__3__y__2919] :
( t(Vvar__3__y__2919,Vvar__0__A__2911)
& p(happ(happ(Vvar__1__R__2912,Vvar__2__x__2913),Vvar__3__y__2919))
& Vvar__3___24Anonymous__2914 = Vvar__3__y__2919 )
| ? [Vvar__3__y__2924] :
( t(Vvar__3__y__2924,Vvar__0__A__2911)
& ? [Vvar__4__z__2925] :
( t(Vvar__4__z__2925,Vvar__0__A__2911)
& p(happ(happ(Vvar__1__R__2912,Vvar__3__y__2924),Vvar__4__z__2925))
& cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__2911,Vvar__1__R__2912,Vvar__2__x__2913,Vvar__3__y__2924)
& Vvar__3___24Anonymous__2914 = Vvar__4__z__2925 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Sorting.Permutation.Permutation',axiom,
! [Vvar__0__A__9911,Vvar__1___24Anonymous__9912,Vvar__2___24Anonymous__9913] :
( cType___24t(Vvar__0__A__9911)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__1___24Anonymous__9912)
=> ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__2___24Anonymous__9913)
=> ( cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__9911,Vvar__1___24Anonymous__9912,Vvar__2___24Anonymous__9913)
=> ( ( Vvar__2___24Anonymous__9913 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9911)
& Vvar__1___24Anonymous__9912 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__9911) )
| ? [Vvar__1__x__9917] :
( t(Vvar__1__x__9917,Vvar__0__A__9911)
& ? [Vvar__2__l__9918] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__2__l__9918)
& ? [Vvar__3__l_27__9919] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__3__l_27__9919)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__9911,Vvar__2__l__9918,Vvar__3__l_27__9919)
& Vvar__2___24Anonymous__9913 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9911,Vvar__1__x__9917,Vvar__3__l_27__9919)
& Vvar__1___24Anonymous__9912 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9911,Vvar__1__x__9917,Vvar__2__l__9918) ) ) )
| ? [Vvar__1__x__9922] :
( t(Vvar__1__x__9922,Vvar__0__A__9911)
& ? [Vvar__2__y__9923] :
( t(Vvar__2__y__9923,Vvar__0__A__9911)
& ? [Vvar__3__l__9924] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__3__l__9924)
& Vvar__2___24Anonymous__9913 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9911,Vvar__1__x__9922,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9911,Vvar__2__y__9923,Vvar__3__l__9924))
& Vvar__1___24Anonymous__9912 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9911,Vvar__2__y__9923,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__9911,Vvar__1__x__9922,Vvar__3__l__9924)) ) ) )
| ? [Vvar__1__l__9926] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__1__l__9926)
& ? [Vvar__2__l_27__9927] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__2__l_27__9927)
& ? [Vvar__3__l_27_27__9928] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__9911,Vvar__3__l_27_27__9928)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__9911,Vvar__1__l__9926,Vvar__2__l_27__9927)
& cCoq_2eSorting_2ePermutation_2ePermutation___24a3(Vvar__0__A__9911,Vvar__2__l_27__9927,Vvar__3__l_27_27__9928)
& Vvar__2___24Anonymous__9913 = Vvar__3__l_27_27__9928
& Vvar__1___24Anonymous__9912 = Vvar__1__l__9926 ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
! [VX34430] :
( cCoq_2eStrings_2eAscii_2eascii___24t(VX34430)
=> ? [Vvar__0___24Anonymous__34431] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__34431)
& ? [Vvar__1___24Anonymous__34432] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__34432)
& ? [Vvar__2___24Anonymous__34433] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__34433)
& ? [Vvar__3___24Anonymous__34434] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__34434)
& ? [Vvar__4___24Anonymous__34435] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__34435)
& ? [Vvar__5___24Anonymous__34436] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__34436)
& ? [Vvar__6___24Anonymous__34437] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__34437)
& ? [Vvar__7___24Anonymous__34438] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__34438)
& VX34430 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__34431,Vvar__1___24Anonymous__34432,Vvar__2___24Anonymous__34433,Vvar__3___24Anonymous__34434,Vvar__4___24Anonymous__34435,Vvar__5___24Anonymous__34436,Vvar__6___24Anonymous__34437,Vvar__7___24Anonymous__34438) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Strings.String.string',axiom,
! [VX36849] :
( cCoq_2eStrings_2eString_2estring___24t(VX36849)
=> ( VX36849 = cCoq_2eStrings_2eString_2eEmptyString
| ? [Vvar__0___24Anonymous__36850] :
( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__36850)
& ? [Vvar__1___24Anonymous__36851] :
( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__36851)
& VX36849 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__36850,Vvar__1___24Anonymous__36851) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
! [Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653,VX35654] :
( cType___24t(Vvar__0__X__35641)
=> ( c_24__type__35714___24t(Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653,Vvar__1__lt__35642)
=> ( c_24__type__35733___24t(Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653,Vvar__2__eq__35647)
=> ( t(Vvar__3__x__35652,Vvar__0__X__35641)
=> ( t(Vvar__4__y__35653,Vvar__0__X__35641)
=> ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653,VX35654)
=> ( ( p(happ(happ(Vvar__1__lt__35642,Vvar__3__x__35652),Vvar__4__y__35653))
& VX35654 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653) )
| ( p(happ(happ(Vvar__2__eq__35647,Vvar__3__x__35652),Vvar__4__y__35653))
& VX35654 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653) )
| ( p(happ(happ(Vvar__1__lt__35642,Vvar__4__y__35653),Vvar__3__x__35652))
& VX35654 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__35641,Vvar__1__lt__35642,Vvar__2__eq__35647,Vvar__3__x__35652,Vvar__4__y__35653) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
! [VX35833] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX35833)
=> ( VX35833 = cCoq_2eStructures_2eOrdersTac_2eOEQ
| VX35833 = cCoq_2eStructures_2eOrdersTac_2eOLT
| VX35833 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).
fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
! [Vvar__0__A__30763,Vvar__1___24Anonymous__30764,VX30765] :
( cType___24t(Vvar__0__A__30763)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__30764)
=> ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30763,Vvar__1___24Anonymous__30764,VX30765)
=> ( ( Vvar__1___24Anonymous__30764 = cCoq_2eInit_2eDatatypes_2eO
& VX30765 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__30763) )
| ? [Vvar__1__h__30768] :
( t(Vvar__1__h__30768,Vvar__0__A__30763)
& ? [Vvar__2__n__30769] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__30769)
& ? [Vvar__3___24Anonymous__30770] :
( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__30763,Vvar__2__n__30769,Vvar__3___24Anonymous__30770)
& Vvar__1___24Anonymous__30764 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__30769)
& VX30765 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__30763,Vvar__1__h__30768,Vvar__2__n__30769,Vvar__3___24Anonymous__30770) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
! [Vvar__0__a__36923,Vvar__1__b__36924,Vvar__2__d__36925] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__36923)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__36924)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__36925)
=> ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__36923,Vvar__1__b__36924,Vvar__2__d__36925)
=> ? [Vvar__3__u__36930] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__36930)
& ? [Vvar__4__v__36931] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__36931)
& cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__36930,Vvar__0__a__36923),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__36931,Vvar__1__b__36924)) = Vvar__2__d__36925
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
! [Vvar__0__a__36895,Vvar__1__b__36896,Vvar__2__g__36897] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__36895)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__36896)
=> ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__36897)
=> ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__36895,Vvar__1__b__36896,Vvar__2__g__36897)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__36897,Vvar__0__a__36895)
& cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__36897,Vvar__1__b__36896)
& ! [Vvar__var__var__var__var__5__x__36905__36908__36911__36914__36917] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__36905__36908__36911__36914__36917)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__36905__36908__36911__36914__36917,Vvar__0__a__36895)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__36905__36908__36911__36914__36917,Vvar__1__b__36896)
=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__36905__36908__36911__36914__36917,Vvar__2__g__36897) ) ) )
& p(c_24True) ) ) ) ) ) ).
fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
! [Vvar__0__p__36933] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__36933)
=> ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__36933)
=> ( cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__36933)
& ! [Vvar__var__var__2__n__36938__36940__36942] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__36938__36940__36942)
=> ( ( cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__36938__36940__36942)
& cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__36938__36940__36942,Vvar__0__p__36933) )
=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__36938__36940__36942,Vvar__0__p__36933) ) )
& p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
! [Vvar__0__T__34642,Vvar__1__F__34643] :
( cType___24t(Vvar__0__T__34642)
=> ( t(Vvar__1__F__34643,Vvar__0__T__34642)
=> ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__34642,Vvar__1__F__34643)
=> p(c_24True) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
! [VX34814] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX34814)
=> ( VX34814 = cCoq_2emicromega_2eEnvRing_2emon0
| ? [Vvar__0___24Anonymous__34815] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34815)
& ? [Vvar__1___24Anonymous__34816] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__34816)
& VX34814 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__34815,Vvar__1___24Anonymous__34816) ) )
| ? [Vvar__0___24Anonymous__34817] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34817)
& ? [Vvar__1___24Anonymous__34818] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__34818)
& VX34814 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__34817,Vvar__1___24Anonymous__34818) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
! [Vvar__0__C__34650,VX34651] :
( cType___24t(Vvar__0__C__34650)
=> ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,VX34651)
=> ( ? [Vvar__1___24Anonymous__34653] :
( t(Vvar__1___24Anonymous__34653,Vvar__0__C__34650)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__34650,Vvar__1___24Anonymous__34653) )
| ? [Vvar__1___24Anonymous__34655] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__34655)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__34650,Vvar__1___24Anonymous__34655) )
| ? [Vvar__1___24Anonymous__34657] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__1___24Anonymous__34657)
& ? [Vvar__2___24Anonymous__34658] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__2___24Anonymous__34658)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__34650,Vvar__1___24Anonymous__34657,Vvar__2___24Anonymous__34658) ) )
| ? [Vvar__1___24Anonymous__34660] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__1___24Anonymous__34660)
& ? [Vvar__2___24Anonymous__34661] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__2___24Anonymous__34661)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__34650,Vvar__1___24Anonymous__34660,Vvar__2___24Anonymous__34661) ) )
| ? [Vvar__1___24Anonymous__34663] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__1___24Anonymous__34663)
& ? [Vvar__2___24Anonymous__34664] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__2___24Anonymous__34664)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__34650,Vvar__1___24Anonymous__34663,Vvar__2___24Anonymous__34664) ) )
| ? [Vvar__1___24Anonymous__34666] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__1___24Anonymous__34666)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__34650,Vvar__1___24Anonymous__34666) )
| ? [Vvar__1___24Anonymous__34668] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__34650,Vvar__1___24Anonymous__34668)
& ? [Vvar__2___24Anonymous__34669] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__34669)
& VX34651 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__34650,Vvar__1___24Anonymous__34668,Vvar__2___24Anonymous__34669) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
! [Vvar__0__C__3251,VX3252] :
( cType___24t(Vvar__0__C__3251)
=> ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__3251,VX3252)
=> ( ? [Vvar__1___24Anonymous__3254] :
( t(Vvar__1___24Anonymous__3254,Vvar__0__C__3251)
& VX3252 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__3251,Vvar__1___24Anonymous__3254) )
| ? [Vvar__1___24Anonymous__3256] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__3256)
& ? [Vvar__2___24Anonymous__3257] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__3251,Vvar__2___24Anonymous__3257)
& VX3252 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__3251,Vvar__1___24Anonymous__3256,Vvar__2___24Anonymous__3257) ) )
| ? [Vvar__1___24Anonymous__3259] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__3251,Vvar__1___24Anonymous__3259)
& ? [Vvar__2___24Anonymous__3260] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__3260)
& ? [Vvar__3___24Anonymous__3261] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__3251,Vvar__3___24Anonymous__3261)
& VX3252 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__3251,Vvar__1___24Anonymous__3259,Vvar__2___24Anonymous__3260,Vvar__3___24Anonymous__3261) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
! [Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806] :
( cType___24t(Vvar__0__R__8775)
=> ( t(Vvar__1__rO__8776,Vvar__0__R__8775)
=> ( t(Vvar__2__rI__8777,Vvar__0__R__8775)
=> ( c_24__type__9207___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__3__rplus__8778)
=> ( c_24__type__9308___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__4__rtimes__8783)
=> ( c_24__type__9409___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__5__rminus__8788)
=> ( c_24__type__9499___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__6__ropp__8793)
=> ( c_24__type__9600___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__7__req__8796)
=> ( c_24__type__9701___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__8__rle__8801)
=> ( c_24__type__9802___24t(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806,Vvar__9__rlt__8806)
=> ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796,Vvar__8__rle__8801,Vvar__9__rlt__8806)
=> ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__8775,Vvar__7__req__8796)
& ! [Vvar__var__var__var__var__11__x1__8850__8856__8961__8967__8973] :
( t(Vvar__var__var__var__var__11__x1__8850__8856__8961__8967__8973,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__12__x2__8851__8857__8962__8968__8974] :
( t(Vvar__var__var__var__var__12__x2__8851__8857__8962__8968__8974,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__11__x1__8850__8856__8961__8967__8973),Vvar__var__var__var__var__12__x2__8851__8857__8962__8968__8974))
=> ! [Vvar__var__var__var__var__14__y1__8852__8858__8963__8969__8975] :
( t(Vvar__var__var__var__var__14__y1__8852__8858__8963__8969__8975,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__15__y2__8853__8859__8964__8970__8976] :
( t(Vvar__var__var__var__var__15__y2__8853__8859__8964__8970__8976,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__14__y1__8852__8858__8963__8969__8975),Vvar__var__var__var__var__15__y2__8853__8859__8964__8970__8976))
=> p(happ(happ(Vvar__7__req__8796,happ(happ(Vvar__3__rplus__8778,Vvar__var__var__var__var__11__x1__8850__8856__8961__8967__8973),Vvar__var__var__var__var__14__y1__8852__8858__8963__8969__8975)),happ(happ(Vvar__3__rplus__8778,Vvar__var__var__var__var__12__x2__8851__8857__8962__8968__8974),Vvar__var__var__var__var__15__y2__8853__8859__8964__8970__8976))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__12__x1__8863__8869__8979__8985__8991] :
( t(Vvar__var__var__var__var__12__x1__8863__8869__8979__8985__8991,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__13__x2__8864__8870__8980__8986__8992] :
( t(Vvar__var__var__var__var__13__x2__8864__8870__8980__8986__8992,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__12__x1__8863__8869__8979__8985__8991),Vvar__var__var__var__var__13__x2__8864__8870__8980__8986__8992))
=> ! [Vvar__var__var__var__var__15__y1__8865__8871__8981__8987__8993] :
( t(Vvar__var__var__var__var__15__y1__8865__8871__8981__8987__8993,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__16__y2__8866__8872__8982__8988__8994] :
( t(Vvar__var__var__var__var__16__y2__8866__8872__8982__8988__8994,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__15__y1__8865__8871__8981__8987__8993),Vvar__var__var__var__var__16__y2__8866__8872__8982__8988__8994))
=> p(happ(happ(Vvar__7__req__8796,happ(happ(Vvar__4__rtimes__8783,Vvar__var__var__var__var__12__x1__8863__8869__8979__8985__8991),Vvar__var__var__var__var__15__y1__8865__8871__8981__8987__8993)),happ(happ(Vvar__4__rtimes__8783,Vvar__var__var__var__var__13__x2__8864__8870__8980__8986__8992),Vvar__var__var__var__var__16__y2__8866__8872__8982__8988__8994))) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__13__x1__8876__8879__8997__9000__9003] :
( t(Vvar__var__var__var__var__13__x1__8876__8879__8997__9000__9003,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__14__x2__8877__8880__8998__9001__9004] :
( t(Vvar__var__var__var__var__14__x2__8877__8880__8998__9001__9004,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__13__x1__8876__8879__8997__9000__9003),Vvar__var__var__var__var__14__x2__8877__8880__8998__9001__9004))
=> p(happ(happ(Vvar__7__req__8796,happ(Vvar__6__ropp__8793,Vvar__var__var__var__var__13__x1__8876__8879__8997__9000__9003)),happ(Vvar__6__ropp__8793,Vvar__var__var__var__var__14__x2__8877__8880__8998__9001__9004))) ) ) )
& ! [Vvar__var__var__var__var__14__x1__8883__8889__9006__9012__9018] :
( t(Vvar__var__var__var__var__14__x1__8883__8889__9006__9012__9018,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__15__x2__8884__8890__9007__9013__9019] :
( t(Vvar__var__var__var__var__15__x2__8884__8890__9007__9013__9019,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__14__x1__8883__8889__9006__9012__9018),Vvar__var__var__var__var__15__x2__8884__8890__9007__9013__9019))
=> ! [Vvar__var__var__var__var__17__y1__8885__8891__9008__9014__9020] :
( t(Vvar__var__var__var__var__17__y1__8885__8891__9008__9014__9020,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__18__y2__8886__8892__9009__9015__9021] :
( t(Vvar__var__var__var__var__18__y2__8886__8892__9009__9015__9021,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__17__y1__8885__8891__9008__9014__9020),Vvar__var__var__var__var__18__y2__8886__8892__9009__9015__9021))
=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__var__14__x1__8883__8889__9006__9012__9018),Vvar__var__var__var__var__17__y1__8885__8891__9008__9014__9020))
<=> p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__var__15__x2__8884__8890__9007__9013__9019),Vvar__var__var__var__var__18__y2__8886__8892__9009__9015__9021)) ) ) ) ) ) ) )
& ! [Vvar__var__var__var__var__15__x1__8896__8902__9024__9030__9036] :
( t(Vvar__var__var__var__var__15__x1__8896__8902__9024__9030__9036,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__16__x2__8897__8903__9025__9031__9037] :
( t(Vvar__var__var__var__var__16__x2__8897__8903__9025__9031__9037,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__15__x1__8896__8902__9024__9030__9036),Vvar__var__var__var__var__16__x2__8897__8903__9025__9031__9037))
=> ! [Vvar__var__var__var__var__18__y1__8898__8904__9026__9032__9038] :
( t(Vvar__var__var__var__var__18__y1__8898__8904__9026__9032__9038,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__19__y2__8899__8905__9027__9033__9039] :
( t(Vvar__var__var__var__var__19__y2__8899__8905__9027__9033__9039,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__18__y1__8898__8904__9026__9032__9038),Vvar__var__var__var__var__19__y2__8899__8905__9027__9033__9039))
=> ( p(happ(happ(Vvar__9__rlt__8806,Vvar__var__var__var__var__15__x1__8896__8902__9024__9030__9036),Vvar__var__var__var__var__18__y1__8898__8904__9026__9032__9038))
<=> p(happ(happ(Vvar__9__rlt__8806,Vvar__var__var__var__var__16__x2__8897__8903__9025__9031__9037),Vvar__var__var__var__var__19__y2__8899__8905__9027__9033__9039)) ) ) ) ) ) ) )
& cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__8775,Vvar__1__rO__8776,Vvar__2__rI__8777,Vvar__3__rplus__8778,Vvar__4__rtimes__8783,Vvar__5__rminus__8788,Vvar__6__ropp__8793,Vvar__7__req__8796)
& ! [Vvar__var__var__var__17__n__8910__8911__9042__9043] :
( t(Vvar__var__var__var__17__n__8910__8911__9042__9043,Vvar__0__R__8775)
=> p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__17__n__8910__8911__9042__9043),Vvar__var__var__var__17__n__8910__8911__9042__9043)) )
& ! [Vvar__var__var__var__var__18__n__8913__8917__9044__9048__9052] :
( t(Vvar__var__var__var__var__18__n__8913__8917__9044__9048__9052,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__19__m__8914__8918__9045__9049__9053] :
( t(Vvar__var__var__var__var__19__m__8914__8918__9045__9049__9053,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__var__18__n__8913__8917__9044__9048__9052),Vvar__var__var__var__var__19__m__8914__8918__9045__9049__9053))
=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__var__19__m__8914__8918__9045__9049__9053),Vvar__var__var__var__var__18__n__8913__8917__9044__9048__9052))
=> p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__18__n__8913__8917__9044__9048__9052),Vvar__var__var__var__var__19__m__8914__8918__9045__9049__9053)) ) ) ) )
& ! [Vvar__var__var__var__19__n__8922__8927__9056__9061] :
( t(Vvar__var__var__var__19__n__8922__8927__9056__9061,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__20__m__8923__8928__9057__9062] :
( t(Vvar__var__var__var__20__m__8923__8928__9057__9062,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__21__p__8924__8929__9058__9063] :
( t(Vvar__var__var__var__21__p__8924__8929__9058__9063,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__19__n__8922__8927__9056__9061),Vvar__var__var__var__20__m__8923__8928__9057__9062))
=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__20__m__8923__8928__9057__9062),Vvar__var__var__var__21__p__8924__8929__9058__9063))
=> p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__19__n__8922__8927__9056__9061),Vvar__var__var__var__21__p__8924__8929__9058__9063)) ) ) ) ) )
& ! [Vvar__var__var__var__var__var__20__n__8933__8935__9066__9068__9070__9072] :
( t(Vvar__var__var__var__var__var__20__n__8933__8935__9066__9068__9070__9072,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__var__21__m__8934__8936__9067__9069__9071__9073] :
( t(Vvar__var__var__var__var__var__21__m__8934__8936__9067__9069__9071__9073,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__9__rlt__8806,Vvar__var__var__var__var__var__20__n__8933__8935__9066__9068__9070__9072),Vvar__var__var__var__var__var__21__m__8934__8936__9067__9069__9071__9073))
<=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__var__var__20__n__8933__8935__9066__9068__9070__9072),Vvar__var__var__var__var__var__21__m__8934__8936__9067__9069__9071__9073))
& ~ p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__var__20__n__8933__8935__9066__9068__9070__9072),Vvar__var__var__var__var__var__21__m__8934__8936__9067__9069__9071__9073)) ) ) ) )
& ! [Vvar__var__var__var__var__21__n__8938__8940__9074__9076__9078] :
( t(Vvar__var__var__var__var__21__n__8938__8940__9074__9076__9078,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__22__m__8939__8941__9075__9077__9079] :
( t(Vvar__var__var__var__var__22__m__8939__8941__9075__9077__9079,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__9__rlt__8806,Vvar__var__var__var__var__21__n__8938__8940__9074__9076__9078),Vvar__var__var__var__var__22__m__8939__8941__9075__9077__9079))
| p(happ(happ(Vvar__7__req__8796,Vvar__var__var__var__var__21__n__8938__8940__9074__9076__9078),Vvar__var__var__var__var__22__m__8939__8941__9075__9077__9079))
| p(happ(happ(Vvar__9__rlt__8806,Vvar__var__var__var__var__22__m__8939__8941__9075__9077__9079),Vvar__var__var__var__var__21__n__8938__8940__9074__9076__9078)) ) ) )
& ! [Vvar__var__var__var__var__22__n__8943__8947__9080__9084__9088] :
( t(Vvar__var__var__var__var__22__n__8943__8947__9080__9084__9088,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__23__m__8944__8948__9081__9085__9089] :
( t(Vvar__var__var__var__var__23__m__8944__8948__9081__9085__9089,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__24__p__8945__8949__9082__9086__9090] :
( t(Vvar__var__var__var__var__24__p__8945__8949__9082__9086__9090,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__8__rle__8801,Vvar__var__var__var__var__22__n__8943__8947__9080__9084__9088),Vvar__var__var__var__var__23__m__8944__8948__9081__9085__9089))
=> p(happ(happ(Vvar__8__rle__8801,happ(happ(Vvar__3__rplus__8778,Vvar__var__var__var__var__24__p__8945__8949__9082__9086__9090),Vvar__var__var__var__var__22__n__8943__8947__9080__9084__9088)),happ(happ(Vvar__3__rplus__8778,Vvar__var__var__var__var__24__p__8945__8949__9082__9086__9090),Vvar__var__var__var__var__23__m__8944__8948__9081__9085__9089))) ) ) ) )
& ! [Vvar__var__var__var__var__var__23__n__8952__8956__9092__9096__9100__9104] :
( t(Vvar__var__var__var__var__var__23__n__8952__8956__9092__9096__9100__9104,Vvar__0__R__8775)
=> ! [Vvar__var__var__var__var__var__24__m__8953__8957__9093__9097__9101__9105] :
( t(Vvar__var__var__var__var__var__24__m__8953__8957__9093__9097__9101__9105,Vvar__0__R__8775)
=> ( p(happ(happ(Vvar__9__rlt__8806,Vvar__1__rO__8776),Vvar__var__var__var__var__var__23__n__8952__8956__9092__9096__9100__9104))
=> ( p(happ(happ(Vvar__9__rlt__8806,Vvar__1__rO__8776),Vvar__var__var__var__var__var__24__m__8953__8957__9093__9097__9101__9105))
=> p(happ(happ(Vvar__9__rlt__8806,Vvar__1__rO__8776),happ(happ(Vvar__4__rtimes__8783,Vvar__var__var__var__var__var__23__n__8952__8956__9092__9096__9100__9104),Vvar__var__var__var__var__var__24__m__8953__8957__9093__9097__9101__9105))) ) ) ) )
& ~ p(happ(happ(Vvar__7__req__8796,Vvar__1__rO__8776),Vvar__2__rI__8777))
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
! [VX35834] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX35834)
=> ( VX35834 = cCoq_2emicromega_2eRMicromega_2eC0
| VX35834 = cCoq_2emicromega_2eRMicromega_2eC1
| ? [Vvar__0__r__35835] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__35835)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__35835) )
| ? [Vvar__0__r__35836] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__35836)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__35836) )
| ? [Vvar__0__r1__35837] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35837)
& ? [Vvar__1__r2__35838] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__35838)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__35837,Vvar__1__r2__35838) ) )
| ? [Vvar__0__r1__35839] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35839)
& ? [Vvar__1__r2__35840] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__35840)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__35839,Vvar__1__r2__35840) ) )
| ? [Vvar__0__r1__35841] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35841)
& ? [Vvar__1__r2__35842] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__35842)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__35841,Vvar__1__r2__35842) ) )
| ? [Vvar__0__r1__35843] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__35843)
& ? [Vvar__1__z__35844] :
( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__35844)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__35843,Vvar__1__z__35844) ) )
| ? [Vvar__0__r__35845] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__35845)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__35845) )
| ? [Vvar__0__r__35846] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__35846)
& VX35834 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__35846) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
! [Vvar__0__T__32403,VX32404] :
( cType___24t(Vvar__0__T__32403)
=> ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__32403,VX32404)
=> ? [Vvar__1__Flhs__32406] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__32403,Vvar__1__Flhs__32406)
& ? [Vvar__2__Fop__32407] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__32407)
& ? [Vvar__3__Frhs__32408] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__32403,Vvar__3__Frhs__32408)
& VX32404 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__32403,Vvar__1__Flhs__32406,Vvar__2__Fop__32407,Vvar__3__Frhs__32408) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
! [VX16219] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX16219)
=> ( VX16219 = cCoq_2emicromega_2eRingMicromega_2eEqual
| VX16219 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
| VX16219 = cCoq_2emicromega_2eRingMicromega_2eStrict
| VX16219 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
! [VX35985] :
( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX35985)
=> ( VX35985 = cCoq_2emicromega_2eRingMicromega_2eOpEq
| VX35985 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
| VX35985 = cCoq_2emicromega_2eRingMicromega_2eOpLe
| VX35985 = cCoq_2emicromega_2eRingMicromega_2eOpGe
| VX35985 = cCoq_2emicromega_2eRingMicromega_2eOpLt
| VX35985 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).
fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
! [Vvar__0__C__16439,VX16440] :
( cType___24t(Vvar__0__C__16439)
=> ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__16439,VX16440)
=> ( ? [Vvar__1___24Anonymous__16442] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__16442)
& VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__16439,Vvar__1___24Anonymous__16442) )
| ? [Vvar__1___24Anonymous__16444] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__16439,Vvar__1___24Anonymous__16444)
& VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__16439,Vvar__1___24Anonymous__16444) )
| ? [Vvar__1___24Anonymous__16446] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__16439,Vvar__1___24Anonymous__16446)
& ? [Vvar__2___24Anonymous__16447] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__16439,Vvar__2___24Anonymous__16447)
& VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__16439,Vvar__1___24Anonymous__16446,Vvar__2___24Anonymous__16447) ) )
| ? [Vvar__1___24Anonymous__16449] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__16439,Vvar__1___24Anonymous__16449)
& ? [Vvar__2___24Anonymous__16450] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__16439,Vvar__2___24Anonymous__16450)
& VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__16439,Vvar__1___24Anonymous__16449,Vvar__2___24Anonymous__16450) ) )
| ? [Vvar__1___24Anonymous__16452] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__16439,Vvar__1___24Anonymous__16452)
& ? [Vvar__2___24Anonymous__16453] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__16439,Vvar__2___24Anonymous__16453)
& VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__16439,Vvar__1___24Anonymous__16452,Vvar__2___24Anonymous__16453) ) )
| ? [Vvar__1___24Anonymous__16455] :
( t(Vvar__1___24Anonymous__16455,Vvar__0__C__16439)
& VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__16439,Vvar__1___24Anonymous__16455) )
| VX16440 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__16439) ) ) ) ).
fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
! [Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,VX29705] :
( cType___24t(Vvar__0__TA__29701)
=> ( cType___24t(Vvar__1__TX__29702)
=> ( cType___24t(Vvar__2__AA__29703)
=> ( cType___24t(Vvar__3__AF__29704)
=> ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,VX29705)
=> ( VX29705 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704)
| VX29705 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704)
| ? [Vvar__4___24Anonymous__29718] :
( t(Vvar__4___24Anonymous__29718,Vvar__1__TX__29702)
& VX29705 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29718) )
| ? [Vvar__4___24Anonymous__29723] :
( t(Vvar__4___24Anonymous__29723,Vvar__0__TA__29701)
& ? [Vvar__5___24Anonymous__29724] :
( t(Vvar__5___24Anonymous__29724,Vvar__2__AA__29703)
& VX29705 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29723,Vvar__5___24Anonymous__29724) ) )
| ? [Vvar__4___24Anonymous__29729] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29729)
& ? [Vvar__5___24Anonymous__29730] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__5___24Anonymous__29730)
& VX29705 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29729,Vvar__5___24Anonymous__29730) ) )
| ? [Vvar__4___24Anonymous__29735] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29735)
& ? [Vvar__5___24Anonymous__29736] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__5___24Anonymous__29736)
& VX29705 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29735,Vvar__5___24Anonymous__29736) ) )
| ? [Vvar__4___24Anonymous__29741] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29741)
& VX29705 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29741) )
| ? [Vvar__4___24Anonymous__29746] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29746)
& ? [Vvar__5___24Anonymous__29747] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__29704,Vvar__5___24Anonymous__29747)
& ? [Vvar__6___24Anonymous__29748] :
( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__6___24Anonymous__29748)
& VX29705 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__29701,Vvar__1__TX__29702,Vvar__2__AA__29703,Vvar__3__AF__29704,Vvar__4___24Anonymous__29746,Vvar__5___24Anonymous__29747,Vvar__6___24Anonymous__29748) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.VarMap.t',axiom,
! [Vvar__0__A__36858,VX36859] :
( cType___24t(Vvar__0__A__36858)
=> ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__36858,VX36859)
=> ( VX36859 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__36858)
| ? [Vvar__1___24Anonymous__36862] :
( t(Vvar__1___24Anonymous__36862,Vvar__0__A__36858)
& VX36859 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__36858,Vvar__1___24Anonymous__36862) )
| ? [Vvar__1___24Anonymous__36864] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__36858,Vvar__1___24Anonymous__36864)
& ? [Vvar__2___24Anonymous__36865] :
( t(Vvar__2___24Anonymous__36865,Vvar__0__A__36858)
& ? [Vvar__3___24Anonymous__36866] :
( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__36858,Vvar__3___24Anonymous__36866)
& VX36859 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__36858,Vvar__1___24Anonymous__36864,Vvar__2___24Anonymous__36865,Vvar__3___24Anonymous__36866) ) ) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
! [Vvar__0___24Anonymous__36957] :
( cProp___24t(Vvar__0___24Anonymous__36957)
=> ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__36957)
=> ( ? [Vvar__0__S__36959] :
( cType___24t(Vvar__0__S__36959)
& ? [Vvar__1__x__36960] :
( t(Vvar__1__x__36960,Vvar__0__S__36959)
& ? [Vvar__2__y__36961] :
( t(Vvar__2__y__36961,Vvar__0__S__36959)
& Vvar__0___24Anonymous__36957 = c_24__prop__36981___24a4(Vvar__0___24Anonymous__36957,Vvar__0__S__36959,Vvar__1__x__36960,Vvar__2__y__36961) ) ) )
| ? [Vvar__0__x__36962] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__36962)
& ? [Vvar__1__y__36963] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__36963)
& Vvar__0___24Anonymous__36957 = c_24__prop__36982___24a3(Vvar__0___24Anonymous__36957,Vvar__0__x__36962,Vvar__1__y__36963) ) )
| ? [Vvar__0__x__36964] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__36964)
& ? [Vvar__1__s__36965] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__36965)
& Vvar__0___24Anonymous__36957 = c_24__prop__36983___24a3(Vvar__0___24Anonymous__36957,Vvar__0__x__36964,Vvar__1__s__36965) ) )
| Vvar__0___24Anonymous__36957 = c_24True
| Vvar__0___24Anonymous__36957 = c_24False
| ? [Vvar__0__P__36966] :
( cProp___24t(Vvar__0__P__36966)
& ? [Vvar__1__Q__36967] :
( cProp___24t(Vvar__1__Q__36967)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__36966)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__36967)
& Vvar__0___24Anonymous__36957 = c_24__prop__36984___24a3(Vvar__0___24Anonymous__36957,Vvar__0__P__36966,Vvar__1__Q__36967) ) )
| ? [Vvar__0__P__36970] :
( cProp___24t(Vvar__0__P__36970)
& ? [Vvar__1__Q__36971] :
( cProp___24t(Vvar__1__Q__36971)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__36970)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__36971)
& Vvar__0___24Anonymous__36957 = c_24__prop__36985___24a3(Vvar__0___24Anonymous__36957,Vvar__0__P__36970,Vvar__1__Q__36971) ) )
| ? [Vvar__0__P__36974] :
( cProp___24t(Vvar__0__P__36974)
& ? [Vvar__1__Q__36975] :
( cProp___24t(Vvar__1__Q__36975)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__36974)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__36975)
& Vvar__0___24Anonymous__36957 = c_24__prop__36986___24a3(Vvar__0___24Anonymous__36957,Vvar__0__P__36974,Vvar__1__Q__36975) ) )
| ? [Vvar__0__P__36979] :
( cProp___24t(Vvar__0__P__36979)
& cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__36979)
& Vvar__0___24Anonymous__36957 = c_24__prop__36987___24a2(Vvar__0___24Anonymous__36957,Vvar__0__P__36979) ) ) ) ) ).
fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [VX31139] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX31139)
=> ( VX31139 = cCoq_2emicromega_2eZMicromega_2eDoneProof
| ? [Vvar__0___24Anonymous__31140] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__31140)
& ? [Vvar__1___24Anonymous__31141] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__31141)
& VX31139 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__31140,Vvar__1___24Anonymous__31141) ) )
| ? [Vvar__0___24Anonymous__31142] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__31142)
& ? [Vvar__1___24Anonymous__31143] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__31143)
& VX31139 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__31142,Vvar__1___24Anonymous__31143) ) )
| ? [Vvar__0___24Anonymous__31144] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__31144)
& ? [Vvar__1___24Anonymous__31145] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__31145)
& ? [Vvar__2___24Anonymous__31146] :
( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__31146)
& VX31139 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__31144,Vvar__1___24Anonymous__31145,Vvar__2___24Anonymous__31146) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
! [Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531] :
( cType___24t(Vvar__0__R__3502)
=> ( t(Vvar__1__rO__3503,Vvar__0__R__3502)
=> ( t(Vvar__2__rI__3504,Vvar__0__R__3502)
=> ( c_24__type__3696___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__3__radd__3505)
=> ( c_24__type__3789___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__4__rmul__3510)
=> ( c_24__type__3882___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__5__rsub__3515)
=> ( c_24__type__3964___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__6__ropp__3520)
=> ( c_24__type__4057___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__7__rdiv__3523)
=> ( c_24__type__4139___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__8__rinv__3528)
=> ( c_24__type__4232___24t(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531,Vvar__9__req__3531)
=> ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__7__rdiv__3523,Vvar__8__rinv__3528,Vvar__9__req__3531)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__3502,Vvar__1__rO__3503,Vvar__2__rI__3504,Vvar__3__radd__3505,Vvar__4__rmul__3510,Vvar__5__rsub__3515,Vvar__6__ropp__3520,Vvar__9__req__3531)
& ~ p(happ(happ(Vvar__9__req__3531,Vvar__2__rI__3504),Vvar__1__rO__3503))
& ! [Vvar__var__var__var__var__var__var__12__p__3574__3576__3583__3585__3587__3589__3591] :
( t(Vvar__var__var__var__var__var__var__12__p__3574__3576__3583__3585__3587__3589__3591,Vvar__0__R__3502)
=> ! [Vvar__var__var__var__var__var__var__13__q__3575__3577__3584__3586__3588__3590__3592] :
( t(Vvar__var__var__var__var__var__var__13__q__3575__3577__3584__3586__3588__3590__3592,Vvar__0__R__3502)
=> p(happ(happ(Vvar__9__req__3531,happ(happ(Vvar__7__rdiv__3523,Vvar__var__var__var__var__var__var__12__p__3574__3576__3583__3585__3587__3589__3591),Vvar__var__var__var__var__var__var__13__q__3575__3577__3584__3586__3588__3590__3592)),happ(happ(Vvar__4__rmul__3510,Vvar__var__var__var__var__var__var__12__p__3574__3576__3583__3585__3587__3589__3591),happ(Vvar__8__rinv__3528,Vvar__var__var__var__var__var__var__13__q__3575__3577__3584__3586__3588__3590__3592)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__3579__3581__3593__3595__3597__3599__3601__3603] :
( t(Vvar__var__var__var__var__var__var__var__13__p__3579__3581__3593__3595__3597__3599__3601__3603,Vvar__0__R__3502)
=> ( ~ p(happ(happ(Vvar__9__req__3531,Vvar__var__var__var__var__var__var__var__13__p__3579__3581__3593__3595__3597__3599__3601__3603),Vvar__1__rO__3503))
=> p(happ(happ(Vvar__9__req__3531,happ(happ(Vvar__4__rmul__3510,happ(Vvar__8__rinv__3528,Vvar__var__var__var__var__var__var__var__13__p__3579__3581__3593__3595__3597__3599__3601__3603)),Vvar__var__var__var__var__var__var__var__13__p__3579__3581__3593__3595__3597__3599__3601__3603)),Vvar__2__rI__3504)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
! [Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892] :
( cType___24t(Vvar__0__R__34863)
=> ( t(Vvar__1__rO__34864,Vvar__0__R__34863)
=> ( t(Vvar__2__rI__34865,Vvar__0__R__34863)
=> ( c_24__type__35057___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__3__radd__34866)
=> ( c_24__type__35150___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__4__rmul__34871)
=> ( c_24__type__35243___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__5__rsub__34876)
=> ( c_24__type__35325___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__6__ropp__34881)
=> ( c_24__type__35418___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__7__rdiv__34884)
=> ( c_24__type__35500___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__8__rinv__34889)
=> ( c_24__type__35593___24t(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892,Vvar__9__req__34892)
=> ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__7__rdiv__34884,Vvar__8__rinv__34889,Vvar__9__req__34892)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__34863,Vvar__1__rO__34864,Vvar__2__rI__34865,Vvar__3__radd__34866,Vvar__4__rmul__34871,Vvar__5__rsub__34876,Vvar__6__ropp__34881,Vvar__9__req__34892)
& ~ p(happ(happ(Vvar__9__req__34892,Vvar__2__rI__34865),Vvar__1__rO__34864))
& ! [Vvar__var__var__var__var__var__var__12__p__34935__34937__34944__34946__34948__34950__34952] :
( t(Vvar__var__var__var__var__var__var__12__p__34935__34937__34944__34946__34948__34950__34952,Vvar__0__R__34863)
=> ! [Vvar__var__var__var__var__var__var__13__q__34936__34938__34945__34947__34949__34951__34953] :
( t(Vvar__var__var__var__var__var__var__13__q__34936__34938__34945__34947__34949__34951__34953,Vvar__0__R__34863)
=> p(happ(happ(Vvar__9__req__34892,happ(happ(Vvar__7__rdiv__34884,Vvar__var__var__var__var__var__var__12__p__34935__34937__34944__34946__34948__34950__34952),Vvar__var__var__var__var__var__var__13__q__34936__34938__34945__34947__34949__34951__34953)),happ(happ(Vvar__4__rmul__34871,Vvar__var__var__var__var__var__var__12__p__34935__34937__34944__34946__34948__34950__34952),happ(Vvar__8__rinv__34889,Vvar__var__var__var__var__var__var__13__q__34936__34938__34945__34947__34949__34951__34953)))) ) )
& ! [Vvar__var__var__var__var__var__var__var__13__p__34940__34942__34954__34956__34958__34960__34962__34964] :
( t(Vvar__var__var__var__var__var__var__var__13__p__34940__34942__34954__34956__34958__34960__34962__34964,Vvar__0__R__34863)
=> ( ~ p(happ(happ(Vvar__9__req__34892,Vvar__var__var__var__var__var__var__var__13__p__34940__34942__34954__34956__34958__34960__34962__34964),Vvar__1__rO__34864))
=> p(happ(happ(Vvar__9__req__34892,happ(happ(Vvar__4__rmul__34871,happ(Vvar__8__rinv__34889,Vvar__var__var__var__var__var__var__var__13__p__34940__34942__34954__34956__34958__34960__34962__34964)),Vvar__var__var__var__var__var__var__var__13__p__34940__34942__34954__34956__34958__34960__34962__34964)),Vvar__2__rI__34865)) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
! [Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099] :
( cType___24t(Vvar__0__R__23078)
=> ( t(Vvar__1__rO__23079,Vvar__0__R__23078)
=> ( t(Vvar__2__rI__23080,Vvar__0__R__23078)
=> ( c_24__type__23327___24t(Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099,Vvar__3__radd__23081)
=> ( c_24__type__23390___24t(Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099,Vvar__4__rmul__23086)
=> ( c_24__type__23453___24t(Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099,Vvar__5__rsub__23091)
=> ( c_24__type__23507___24t(Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099,Vvar__6__ropp__23096)
=> ( c_24__type__23570___24t(Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099,Vvar__7__req__23099)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__23078,Vvar__1__rO__23079,Vvar__2__rI__23080,Vvar__3__radd__23081,Vvar__4__rmul__23086,Vvar__5__rsub__23091,Vvar__6__ropp__23096,Vvar__7__req__23099)
=> ( ! [Vvar__var__var__var__var__var__8__x__23132__23133__23186__23187__23188__23189] :
( t(Vvar__var__var__var__var__var__8__x__23132__23133__23186__23187__23188__23189,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__3__radd__23081,Vvar__1__rO__23079),Vvar__var__var__var__var__var__8__x__23132__23133__23186__23187__23188__23189)),Vvar__var__var__var__var__var__8__x__23132__23133__23186__23187__23188__23189)) )
& ! [Vvar__var__var__var__var__9__x__23135__23137__23190__23192__23194] :
( t(Vvar__var__var__var__var__9__x__23135__23137__23190__23192__23194,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__10__y__23136__23138__23191__23193__23195] :
( t(Vvar__var__var__var__var__10__y__23136__23138__23191__23193__23195,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__9__x__23135__23137__23190__23192__23194),Vvar__var__var__var__var__10__y__23136__23138__23191__23193__23195)),happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__10__y__23136__23138__23191__23193__23195),Vvar__var__var__var__var__9__x__23135__23137__23190__23192__23194))) ) )
& ! [Vvar__var__var__var__var__10__x__23140__23143__23196__23199__23202] :
( t(Vvar__var__var__var__var__10__x__23140__23143__23196__23199__23202,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__11__y__23141__23144__23197__23200__23203] :
( t(Vvar__var__var__var__var__11__y__23141__23144__23197__23200__23203,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__12__z__23142__23145__23198__23201__23204] :
( t(Vvar__var__var__var__var__12__z__23142__23145__23198__23201__23204,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__10__x__23140__23143__23196__23199__23202),happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__11__y__23141__23144__23197__23200__23203),Vvar__var__var__var__var__12__z__23142__23145__23198__23201__23204))),happ(happ(Vvar__3__radd__23081,happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__10__x__23140__23143__23196__23199__23202),Vvar__var__var__var__var__11__y__23141__23144__23197__23200__23203)),Vvar__var__var__var__var__12__z__23142__23145__23198__23201__23204))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__23147__23148__23205__23206__23207__23208] :
( t(Vvar__var__var__var__var__var__11__x__23147__23148__23205__23206__23207__23208,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__4__rmul__23086,Vvar__2__rI__23080),Vvar__var__var__var__var__var__11__x__23147__23148__23205__23206__23207__23208)),Vvar__var__var__var__var__var__11__x__23147__23148__23205__23206__23207__23208)) )
& ! [Vvar__var__var__var__var__var__12__x__23150__23151__23209__23210__23211__23212] :
( t(Vvar__var__var__var__var__var__12__x__23150__23151__23209__23210__23211__23212,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__4__rmul__23086,Vvar__1__rO__23079),Vvar__var__var__var__var__var__12__x__23150__23151__23209__23210__23211__23212)),Vvar__1__rO__23079)) )
& ! [Vvar__var__var__var__var__13__x__23153__23155__23213__23215__23217] :
( t(Vvar__var__var__var__var__13__x__23153__23155__23213__23215__23217,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__14__y__23154__23156__23214__23216__23218] :
( t(Vvar__var__var__var__var__14__y__23154__23156__23214__23216__23218,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__13__x__23153__23155__23213__23215__23217),Vvar__var__var__var__var__14__y__23154__23156__23214__23216__23218)),happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__14__y__23154__23156__23214__23216__23218),Vvar__var__var__var__var__13__x__23153__23155__23213__23215__23217))) ) )
& ! [Vvar__var__var__var__var__14__x__23158__23161__23219__23222__23225] :
( t(Vvar__var__var__var__var__14__x__23158__23161__23219__23222__23225,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__15__y__23159__23162__23220__23223__23226] :
( t(Vvar__var__var__var__var__15__y__23159__23162__23220__23223__23226,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__16__z__23160__23163__23221__23224__23227] :
( t(Vvar__var__var__var__var__16__z__23160__23163__23221__23224__23227,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__14__x__23158__23161__23219__23222__23225),happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__15__y__23159__23162__23220__23223__23226),Vvar__var__var__var__var__16__z__23160__23163__23221__23224__23227))),happ(happ(Vvar__4__rmul__23086,happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__14__x__23158__23161__23219__23222__23225),Vvar__var__var__var__var__15__y__23159__23162__23220__23223__23226)),Vvar__var__var__var__var__16__z__23160__23163__23221__23224__23227))) ) ) )
& ! [Vvar__var__var__var__var__var__15__x__23165__23168__23228__23231__23234__23237] :
( t(Vvar__var__var__var__var__var__15__x__23165__23168__23228__23231__23234__23237,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__var__16__y__23166__23169__23229__23232__23235__23238] :
( t(Vvar__var__var__var__var__var__16__y__23166__23169__23229__23232__23235__23238,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__var__17__z__23167__23170__23230__23233__23236__23239] :
( t(Vvar__var__var__var__var__var__17__z__23167__23170__23230__23233__23236__23239,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__4__rmul__23086,happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__var__15__x__23165__23168__23228__23231__23234__23237),Vvar__var__var__var__var__var__16__y__23166__23169__23229__23232__23235__23238)),Vvar__var__var__var__var__var__17__z__23167__23170__23230__23233__23236__23239)),happ(happ(Vvar__3__radd__23081,happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__var__15__x__23165__23168__23228__23231__23234__23237),Vvar__var__var__var__var__var__17__z__23167__23170__23230__23233__23236__23239)),happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__var__16__y__23166__23169__23229__23232__23235__23238),Vvar__var__var__var__var__var__17__z__23167__23170__23230__23233__23236__23239)))) ) ) )
& ! [Vvar__var__var__var__var__var__16__x__23172__23174__23240__23242__23244__23246] :
( t(Vvar__var__var__var__var__var__16__x__23172__23174__23240__23242__23244__23246,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__var__17__y__23173__23175__23241__23243__23245__23247] :
( t(Vvar__var__var__var__var__var__17__y__23173__23175__23241__23243__23245__23247,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(Vvar__6__ropp__23096,happ(happ(Vvar__4__rmul__23086,Vvar__var__var__var__var__var__16__x__23172__23174__23240__23242__23244__23246),Vvar__var__var__var__var__var__17__y__23173__23175__23241__23243__23245__23247))),happ(happ(Vvar__4__rmul__23086,happ(Vvar__6__ropp__23096,Vvar__var__var__var__var__var__16__x__23172__23174__23240__23242__23244__23246)),Vvar__var__var__var__var__var__17__y__23173__23175__23241__23243__23245__23247))) ) )
& ! [Vvar__var__var__var__var__var__17__x__23177__23179__23248__23250__23252__23254] :
( t(Vvar__var__var__var__var__var__17__x__23177__23179__23248__23250__23252__23254,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__var__18__y__23178__23180__23249__23251__23253__23255] :
( t(Vvar__var__var__var__var__var__18__y__23178__23180__23249__23251__23253__23255,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(Vvar__6__ropp__23096,happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__var__17__x__23177__23179__23248__23250__23252__23254),Vvar__var__var__var__var__var__18__y__23178__23180__23249__23251__23253__23255))),happ(happ(Vvar__3__radd__23081,happ(Vvar__6__ropp__23096,Vvar__var__var__var__var__var__17__x__23177__23179__23248__23250__23252__23254)),happ(Vvar__6__ropp__23096,Vvar__var__var__var__var__var__18__y__23178__23180__23249__23251__23253__23255)))) ) )
& ! [Vvar__var__var__var__var__var__var__18__x__23182__23184__23256__23258__23260__23262__23264] :
( t(Vvar__var__var__var__var__var__var__18__x__23182__23184__23256__23258__23260__23262__23264,Vvar__0__R__23078)
=> ! [Vvar__var__var__var__var__var__var__19__y__23183__23185__23257__23259__23261__23263__23265] :
( t(Vvar__var__var__var__var__var__var__19__y__23183__23185__23257__23259__23261__23263__23265,Vvar__0__R__23078)
=> p(happ(happ(Vvar__7__req__23099,happ(happ(Vvar__5__rsub__23091,Vvar__var__var__var__var__var__var__18__x__23182__23184__23256__23258__23260__23262__23264),Vvar__var__var__var__var__var__var__19__y__23183__23185__23257__23259__23261__23263__23265)),happ(happ(Vvar__3__radd__23081,Vvar__var__var__var__var__var__var__18__x__23182__23184__23256__23258__23260__23262__23264),happ(Vvar__6__ropp__23096,Vvar__var__var__var__var__var__var__19__y__23183__23185__23257__23259__23261__23263__23265)))) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
! [Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738] :
( cType___24t(Vvar__0__R__23724)
=> ( c_24__type__23829___24t(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738,Vvar__1__radd__23725)
=> ( c_24__type__23859___24t(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738,Vvar__2__rmul__23730)
=> ( c_24__type__23883___24t(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738,Vvar__3__ropp__23735)
=> ( c_24__type__23913___24t(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738,Vvar__4__req__23738)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__23943___24a5(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23724,c_24__type__23967___24a5(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738),Vvar__4__req__23738,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23724,Vvar__0__R__23724,Vvar__4__req__23738,Vvar__4__req__23738)),Vvar__1__radd__23725)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__24000___24a5(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23724,c_24__type__24024___24a5(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738),Vvar__4__req__23738,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23724,Vvar__0__R__23724,Vvar__4__req__23738,Vvar__4__req__23738)),Vvar__2__rmul__23730)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__24051___24a5(Vvar__0__R__23724,Vvar__1__radd__23725,Vvar__2__rmul__23730,Vvar__3__ropp__23735,Vvar__4__req__23738),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__23724,Vvar__0__R__23724,Vvar__4__req__23738,Vvar__4__req__23738),Vvar__3__ropp__23735)
& p(c_24True) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
! [Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271] :
( cType___24t(Vvar__0__R__36250)
=> ( t(Vvar__1__rO__36251,Vvar__0__R__36250)
=> ( t(Vvar__2__rI__36252,Vvar__0__R__36250)
=> ( c_24__type__36474___24t(Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271,Vvar__3__radd__36253)
=> ( c_24__type__36537___24t(Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271,Vvar__4__rmul__36258)
=> ( c_24__type__36600___24t(Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271,Vvar__5__rsub__36263)
=> ( c_24__type__36654___24t(Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271,Vvar__6__ropp__36268)
=> ( c_24__type__36717___24t(Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271,Vvar__7__req__36271)
=> ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__36250,Vvar__1__rO__36251,Vvar__2__rI__36252,Vvar__3__radd__36253,Vvar__4__rmul__36258,Vvar__5__rsub__36263,Vvar__6__ropp__36268,Vvar__7__req__36271)
=> ( ! [Vvar__var__var__var__var__var__8__x__36304__36305__36348__36349__36350__36351] :
( t(Vvar__var__var__var__var__var__8__x__36304__36305__36348__36349__36350__36351,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__3__radd__36253,Vvar__1__rO__36251),Vvar__var__var__var__var__var__8__x__36304__36305__36348__36349__36350__36351)),Vvar__var__var__var__var__var__8__x__36304__36305__36348__36349__36350__36351)) )
& ! [Vvar__var__var__var__var__9__x__36307__36309__36352__36354__36356] :
( t(Vvar__var__var__var__var__9__x__36307__36309__36352__36354__36356,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__10__y__36308__36310__36353__36355__36357] :
( t(Vvar__var__var__var__var__10__y__36308__36310__36353__36355__36357,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__9__x__36307__36309__36352__36354__36356),Vvar__var__var__var__var__10__y__36308__36310__36353__36355__36357)),happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__10__y__36308__36310__36353__36355__36357),Vvar__var__var__var__var__9__x__36307__36309__36352__36354__36356))) ) )
& ! [Vvar__var__var__var__var__10__x__36312__36315__36358__36361__36364] :
( t(Vvar__var__var__var__var__10__x__36312__36315__36358__36361__36364,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__11__y__36313__36316__36359__36362__36365] :
( t(Vvar__var__var__var__var__11__y__36313__36316__36359__36362__36365,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__12__z__36314__36317__36360__36363__36366] :
( t(Vvar__var__var__var__var__12__z__36314__36317__36360__36363__36366,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__10__x__36312__36315__36358__36361__36364),happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__11__y__36313__36316__36359__36362__36365),Vvar__var__var__var__var__12__z__36314__36317__36360__36363__36366))),happ(happ(Vvar__3__radd__36253,happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__10__x__36312__36315__36358__36361__36364),Vvar__var__var__var__var__11__y__36313__36316__36359__36362__36365)),Vvar__var__var__var__var__12__z__36314__36317__36360__36363__36366))) ) ) )
& ! [Vvar__var__var__var__var__var__11__x__36319__36320__36367__36368__36369__36370] :
( t(Vvar__var__var__var__var__var__11__x__36319__36320__36367__36368__36369__36370,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__4__rmul__36258,Vvar__2__rI__36252),Vvar__var__var__var__var__var__11__x__36319__36320__36367__36368__36369__36370)),Vvar__var__var__var__var__var__11__x__36319__36320__36367__36368__36369__36370)) )
& ! [Vvar__var__var__var__var__12__x__36322__36324__36371__36373__36375] :
( t(Vvar__var__var__var__var__12__x__36322__36324__36371__36373__36375,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__13__y__36323__36325__36372__36374__36376] :
( t(Vvar__var__var__var__var__13__y__36323__36325__36372__36374__36376,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__12__x__36322__36324__36371__36373__36375),Vvar__var__var__var__var__13__y__36323__36325__36372__36374__36376)),happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__13__y__36323__36325__36372__36374__36376),Vvar__var__var__var__var__12__x__36322__36324__36371__36373__36375))) ) )
& ! [Vvar__var__var__var__var__13__x__36327__36330__36377__36380__36383] :
( t(Vvar__var__var__var__var__13__x__36327__36330__36377__36380__36383,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__14__y__36328__36331__36378__36381__36384] :
( t(Vvar__var__var__var__var__14__y__36328__36331__36378__36381__36384,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__15__z__36329__36332__36379__36382__36385] :
( t(Vvar__var__var__var__var__15__z__36329__36332__36379__36382__36385,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__13__x__36327__36330__36377__36380__36383),happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__14__y__36328__36331__36378__36381__36384),Vvar__var__var__var__var__15__z__36329__36332__36379__36382__36385))),happ(happ(Vvar__4__rmul__36258,happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__13__x__36327__36330__36377__36380__36383),Vvar__var__var__var__var__14__y__36328__36331__36378__36381__36384)),Vvar__var__var__var__var__15__z__36329__36332__36379__36382__36385))) ) ) )
& ! [Vvar__var__var__var__var__var__14__x__36334__36337__36386__36389__36392__36395] :
( t(Vvar__var__var__var__var__var__14__x__36334__36337__36386__36389__36392__36395,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__var__15__y__36335__36338__36387__36390__36393__36396] :
( t(Vvar__var__var__var__var__var__15__y__36335__36338__36387__36390__36393__36396,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__var__16__z__36336__36339__36388__36391__36394__36397] :
( t(Vvar__var__var__var__var__var__16__z__36336__36339__36388__36391__36394__36397,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__4__rmul__36258,happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__var__14__x__36334__36337__36386__36389__36392__36395),Vvar__var__var__var__var__var__15__y__36335__36338__36387__36390__36393__36396)),Vvar__var__var__var__var__var__16__z__36336__36339__36388__36391__36394__36397)),happ(happ(Vvar__3__radd__36253,happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__var__14__x__36334__36337__36386__36389__36392__36395),Vvar__var__var__var__var__var__16__z__36336__36339__36388__36391__36394__36397)),happ(happ(Vvar__4__rmul__36258,Vvar__var__var__var__var__var__15__y__36335__36338__36387__36390__36393__36396),Vvar__var__var__var__var__var__16__z__36336__36339__36388__36391__36394__36397)))) ) ) )
& ! [Vvar__var__var__var__var__var__var__15__x__36341__36343__36398__36400__36402__36404__36406] :
( t(Vvar__var__var__var__var__var__var__15__x__36341__36343__36398__36400__36402__36404__36406,Vvar__0__R__36250)
=> ! [Vvar__var__var__var__var__var__var__16__y__36342__36344__36399__36401__36403__36405__36407] :
( t(Vvar__var__var__var__var__var__var__16__y__36342__36344__36399__36401__36403__36405__36407,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__5__rsub__36263,Vvar__var__var__var__var__var__var__15__x__36341__36343__36398__36400__36402__36404__36406),Vvar__var__var__var__var__var__var__16__y__36342__36344__36399__36401__36403__36405__36407)),happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__var__var__15__x__36341__36343__36398__36400__36402__36404__36406),happ(Vvar__6__ropp__36268,Vvar__var__var__var__var__var__var__16__y__36342__36344__36399__36401__36403__36405__36407)))) ) )
& ! [Vvar__var__var__var__var__var__var__16__x__36346__36347__36408__36409__36410__36411__36412] :
( t(Vvar__var__var__var__var__var__var__16__x__36346__36347__36408__36409__36410__36411__36412,Vvar__0__R__36250)
=> p(happ(happ(Vvar__7__req__36271,happ(happ(Vvar__3__radd__36253,Vvar__var__var__var__var__var__var__16__x__36346__36347__36408__36409__36410__36411__36412),happ(Vvar__6__ropp__36268,Vvar__var__var__var__var__var__var__16__x__36346__36347__36408__36409__36410__36411__36412))),Vvar__1__rO__36251)) )
& p(c_24True) ) ) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
! [Vvar__0__R__35986,Vvar__1__rO__35987,Vvar__2__rI__35988,Vvar__3__radd__35989,Vvar__4__rmul__35994,Vvar__5__req__35999] :
( cType___24t(Vvar__0__R__35986)
=> ( t(Vvar__1__rO__35987,Vvar__0__R__35986)
=> ( t(Vvar__2__rI__35988,Vvar__0__R__35986)
=> ( c_24__type__36154___24t(Vvar__0__R__35986,Vvar__1__rO__35987,Vvar__2__rI__35988,Vvar__3__radd__35989,Vvar__4__rmul__35994,Vvar__5__req__35999,Vvar__3__radd__35989)
=> ( c_24__type__36193___24t(Vvar__0__R__35986,Vvar__1__rO__35987,Vvar__2__rI__35988,Vvar__3__radd__35989,Vvar__4__rmul__35994,Vvar__5__req__35999,Vvar__4__rmul__35994)
=> ( c_24__type__36232___24t(Vvar__0__R__35986,Vvar__1__rO__35987,Vvar__2__rI__35988,Vvar__3__radd__35989,Vvar__4__rmul__35994,Vvar__5__req__35999,Vvar__5__req__35999)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__35986,Vvar__1__rO__35987,Vvar__2__rI__35988,Vvar__3__radd__35989,Vvar__4__rmul__35994,Vvar__5__req__35999)
=> ( ! [Vvar__var__var__var__var__var__6__n__36024__36025__36063__36064__36065__36066] :
( t(Vvar__var__var__var__var__var__6__n__36024__36025__36063__36064__36065__36066,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__3__radd__35989,Vvar__1__rO__35987),Vvar__var__var__var__var__var__6__n__36024__36025__36063__36064__36065__36066)),Vvar__var__var__var__var__var__6__n__36024__36025__36063__36064__36065__36066)) )
& ! [Vvar__var__var__var__var__7__n__36027__36029__36067__36069__36071] :
( t(Vvar__var__var__var__var__7__n__36027__36029__36067__36069__36071,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__8__m__36028__36030__36068__36070__36072] :
( t(Vvar__var__var__var__var__8__m__36028__36030__36068__36070__36072,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__3__radd__35989,Vvar__var__var__var__var__7__n__36027__36029__36067__36069__36071),Vvar__var__var__var__var__8__m__36028__36030__36068__36070__36072)),happ(happ(Vvar__3__radd__35989,Vvar__var__var__var__var__8__m__36028__36030__36068__36070__36072),Vvar__var__var__var__var__7__n__36027__36029__36067__36069__36071))) ) )
& ! [Vvar__var__var__var__var__8__n__36032__36035__36073__36076__36079] :
( t(Vvar__var__var__var__var__8__n__36032__36035__36073__36076__36079,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__9__m__36033__36036__36074__36077__36080] :
( t(Vvar__var__var__var__var__9__m__36033__36036__36074__36077__36080,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__10__p__36034__36037__36075__36078__36081] :
( t(Vvar__var__var__var__var__10__p__36034__36037__36075__36078__36081,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__3__radd__35989,Vvar__var__var__var__var__8__n__36032__36035__36073__36076__36079),happ(happ(Vvar__3__radd__35989,Vvar__var__var__var__var__9__m__36033__36036__36074__36077__36080),Vvar__var__var__var__var__10__p__36034__36037__36075__36078__36081))),happ(happ(Vvar__3__radd__35989,happ(happ(Vvar__3__radd__35989,Vvar__var__var__var__var__8__n__36032__36035__36073__36076__36079),Vvar__var__var__var__var__9__m__36033__36036__36074__36077__36080)),Vvar__var__var__var__var__10__p__36034__36037__36075__36078__36081))) ) ) )
& ! [Vvar__var__var__var__var__var__9__n__36039__36040__36082__36083__36084__36085] :
( t(Vvar__var__var__var__var__var__9__n__36039__36040__36082__36083__36084__36085,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__4__rmul__35994,Vvar__2__rI__35988),Vvar__var__var__var__var__var__9__n__36039__36040__36082__36083__36084__36085)),Vvar__var__var__var__var__var__9__n__36039__36040__36082__36083__36084__36085)) )
& ! [Vvar__var__var__var__var__var__10__n__36042__36043__36086__36087__36088__36089] :
( t(Vvar__var__var__var__var__var__10__n__36042__36043__36086__36087__36088__36089,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__4__rmul__35994,Vvar__1__rO__35987),Vvar__var__var__var__var__var__10__n__36042__36043__36086__36087__36088__36089)),Vvar__1__rO__35987)) )
& ! [Vvar__var__var__var__var__11__n__36045__36047__36090__36092__36094] :
( t(Vvar__var__var__var__var__11__n__36045__36047__36090__36092__36094,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__12__m__36046__36048__36091__36093__36095] :
( t(Vvar__var__var__var__var__12__m__36046__36048__36091__36093__36095,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__11__n__36045__36047__36090__36092__36094),Vvar__var__var__var__var__12__m__36046__36048__36091__36093__36095)),happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__12__m__36046__36048__36091__36093__36095),Vvar__var__var__var__var__11__n__36045__36047__36090__36092__36094))) ) )
& ! [Vvar__var__var__var__var__12__n__36050__36053__36096__36099__36102] :
( t(Vvar__var__var__var__var__12__n__36050__36053__36096__36099__36102,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__13__m__36051__36054__36097__36100__36103] :
( t(Vvar__var__var__var__var__13__m__36051__36054__36097__36100__36103,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__14__p__36052__36055__36098__36101__36104] :
( t(Vvar__var__var__var__var__14__p__36052__36055__36098__36101__36104,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__12__n__36050__36053__36096__36099__36102),happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__13__m__36051__36054__36097__36100__36103),Vvar__var__var__var__var__14__p__36052__36055__36098__36101__36104))),happ(happ(Vvar__4__rmul__35994,happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__12__n__36050__36053__36096__36099__36102),Vvar__var__var__var__var__13__m__36051__36054__36097__36100__36103)),Vvar__var__var__var__var__14__p__36052__36055__36098__36101__36104))) ) ) )
& ! [Vvar__var__var__var__var__var__13__n__36057__36060__36105__36108__36111__36114] :
( t(Vvar__var__var__var__var__var__13__n__36057__36060__36105__36108__36111__36114,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__var__14__m__36058__36061__36106__36109__36112__36115] :
( t(Vvar__var__var__var__var__var__14__m__36058__36061__36106__36109__36112__36115,Vvar__0__R__35986)
=> ! [Vvar__var__var__var__var__var__15__p__36059__36062__36107__36110__36113__36116] :
( t(Vvar__var__var__var__var__var__15__p__36059__36062__36107__36110__36113__36116,Vvar__0__R__35986)
=> p(happ(happ(Vvar__5__req__35999,happ(happ(Vvar__4__rmul__35994,happ(happ(Vvar__3__radd__35989,Vvar__var__var__var__var__var__13__n__36057__36060__36105__36108__36111__36114),Vvar__var__var__var__var__var__14__m__36058__36061__36106__36109__36112__36115)),Vvar__var__var__var__var__var__15__p__36059__36062__36107__36110__36113__36116)),happ(happ(Vvar__3__radd__35989,happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__var__13__n__36057__36060__36105__36108__36111__36114),Vvar__var__var__var__var__var__15__p__36059__36062__36107__36110__36113__36116)),happ(happ(Vvar__4__rmul__35994,Vvar__var__var__var__var__var__14__m__36058__36061__36106__36109__36112__36115),Vvar__var__var__var__var__var__15__p__36059__36062__36107__36110__36113__36116)))) ) ) )
& p(c_24True) ) ) ) ) ) ) ) ) ).
fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
! [Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671] :
( cType___24t(Vvar__0__R__32660)
=> ( c_24__type__32746___24t(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671,Vvar__1__radd__32661)
=> ( c_24__type__32769___24t(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671,Vvar__2__rmul__32666)
=> ( c_24__type__32792___24t(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671,Vvar__3__req__32671)
=> ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671)
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32815___24a4(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__32660,c_24__type__32833___24a4(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671),Vvar__3__req__32671,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__32660,Vvar__0__R__32660,Vvar__3__req__32671,Vvar__3__req__32671)),Vvar__1__radd__32661)
& cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__32859___24a4(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__32660,c_24__type__32877___24a4(Vvar__0__R__32660,Vvar__1__radd__32661,Vvar__2__rmul__32666,Vvar__3__req__32671),Vvar__3__req__32671,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__32660,Vvar__0__R__32660,Vvar__3__req__32671,Vvar__3__req__32671)),Vvar__2__rmul__32666)
& p(c_24True) ) ) ) ) ) ) ).
fof('$_inversion_hahn.HahnBase.Equality.type',axiom,
! [VX36947] :
( chahn_2eHahnBase_2eEquality_2etype___24t(VX36947)
=> ? [Vvar__0__sort__36948] :
( cType___24t(Vvar__0__sort__36948)
& ? [Vvar__1___24Anonymous__36949] :
( chahn_2eHahnBase_2eEquality_2emixin__of___24t(Vvar__0__sort__36948,Vvar__1___24Anonymous__36949)
& ? [Vvar__2___24Anonymous__36950] :
( cType___24t(Vvar__2___24Anonymous__36950)
& VX36947 = chahn_2eHahnBase_2eEquality_2ePack___24a3(Vvar__0__sort__36948,Vvar__1___24Anonymous__36949,Vvar__2___24Anonymous__36950) ) ) ) ) ).
fof('$_inversion_hahn.HahnMinPath.min_cycle_mod',axiom,
! [Vvar__0__X__2638,Vvar__1__r__2639,Vvar__2__f__2640,Vvar__3__n__2643] :
( cType___24t(Vvar__0__X__2638)
=> ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__X__2638,Vvar__1__r__2639)
=> ( c_24__type__2684___24t(Vvar__0__X__2638,Vvar__1__r__2639,Vvar__2__f__2640,Vvar__3__n__2643,Vvar__2__f__2640)
=> ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__2643)
=> ( chahn_2eHahnMinPath_2emin__cycle__mod___24a4(Vvar__0__X__2638,Vvar__1__r__2639,Vvar__2__f__2640,Vvar__3__n__2643)
=> ( Vvar__3__n__2643 != cCoq_2eInit_2eDatatypes_2eO
& ! [Vvar__var__var__var__5__x__2653__2654__2665__2666] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__5__x__2653__2654__2665__2666)
=> happ(Vvar__2__f__2640,Vvar__var__var__var__5__x__2653__2654__2665__2666) = happ(Vvar__2__f__2640,cCoq_2eInit_2eNat_2emodulo___24a2(Vvar__var__var__var__5__x__2653__2654__2665__2666,Vvar__3__n__2643)) )
& ! [Vvar__var__var__var__6__i__2656__2657__2667__2668] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__6__i__2656__2657__2667__2668)
=> p(happ(happ(Vvar__1__r__2639,happ(Vvar__2__f__2640,Vvar__var__var__var__6__i__2656__2657__2667__2668)),happ(Vvar__2__f__2640,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__var__var__var__6__i__2656__2657__2667__2668)))) )
& ! [Vvar__var__var__var__var__7__i__2659__2662__2669__2672__2675] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__var__7__i__2659__2662__2669__2672__2675)
=> ! [Vvar__var__var__var__var__8__j__2660__2663__2670__2673__2676] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__var__var__var__var__8__j__2660__2663__2670__2673__2676)
=> ( p(happ(happ(Vvar__1__r__2639,happ(Vvar__2__f__2640,Vvar__var__var__var__var__7__i__2659__2662__2669__2672__2675)),happ(Vvar__2__f__2640,Vvar__var__var__var__var__8__j__2660__2663__2670__2673__2676)))
=> cCoq_2eInit_2eNat_2emodulo___24a2(Vvar__var__var__var__var__8__j__2660__2663__2670__2673__2676,Vvar__3__n__2643) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__var__var__var__var__7__i__2659__2662__2669__2672__2675),Vvar__3__n__2643) ) ) )
& p(c_24True) ) ) ) ) ) ) ).
fof('$_lam_13',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__13___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24False) ) ).
fof('$_lam_2570',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__2570___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO) = Vv__CANONICAL__1 ) ).
fof('$_lam_2577',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2577___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('$_lam_2595',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2595___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ! [Vv__CANONICAL__5] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__5,Vv__CANONICAL__3))
=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__5)),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__5)))) ) ) ) ).
fof('$_lam_2637',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__2637___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('$_lam_2869',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2869___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_2873',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2873___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_2880',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__2880___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ~ p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ).
fof('$_lam_3',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__3___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('$_lam_31589',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__31589___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_31625',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__31625___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__1 ).
fof('$_lam_31628',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__31628___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 ).
fof('$_lam_31634',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__31634___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('$_lam_31640',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__31640___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,happ(Vv__CANONICAL__1,Vv__CANONICAL__3)) ).
fof('$_lam_31649',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__31649___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('$_lam_31658',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__31658___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ).
fof('$_lam_31669',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__31669___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('$_lam_31808',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__31808___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4)
| p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ).
fof('$_lam_31816',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__31816___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('$_lam_32097',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__32097___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(happ(Vv__CANONICAL__1,Vv__CANONICAL__3),Vv__CANONICAL__2)) ) ).
fof('$_lam_32101',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__32101___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('$_lam_32402',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__32402___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5)
<=> p(happ(happ(Vv__CANONICAL__3,happ(Vv__CANONICAL__2,Vv__CANONICAL__4)),happ(Vv__CANONICAL__2,Vv__CANONICAL__5))) ) ).
fof('$_lam_33029',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__33029___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_33049',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__33049___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).
fof('$_lam_33091',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
( c_24__lam__33091___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
<=> p(c_24True) ) ).
fof('$_lam_33094',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__33094___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_33148',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33148___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_33165',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__33165___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___24a1(Vv__CANONICAL__0),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(Vv__CANONICAL__0),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__1) ) ).
fof('$_lam_33192',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__33192___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> ! [Vv__CANONICAL__3] :
( c_24__type__33194___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> p(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__33091___24a1(Vv__CANONICAL__0),c_24__lam__33200___24a2(Vv__CANONICAL__0,Vv__CANONICAL__3))),chahn_2eHahnRelationsBasic_2ebunion___24a4(cCoq_2eInit_2eDatatypes_2enat,Vv__CANONICAL__0,c_24__lam__33091___24a1(Vv__CANONICAL__0),c_24__lam__33208___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)))) ) ) ).
fof('$_lam_33200',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__33200___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = happ(Vv__CANONICAL__1,Vv__CANONICAL__2) ).
fof('$_lam_33208',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__33208___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('$_lam_33274',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__33274___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
<=> p(happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ).
fof('$_lam_33348',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
( c_24__lam__33348___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
<=> p(c_24True) ) ).
fof('$_lam_33730',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33730___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eseq___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__3) ).
fof('$_lam_33742',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33742___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('$_lam_33759',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__33759___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(c_24False) ) ).
fof('$_lam_33772',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33772___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_33783',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33783___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2einter__rel___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2) ).
fof('$_lam_33794',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33794___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2eminus__rel___24a3(Vv__CANONICAL__1,happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__2) ).
fof('$_lam_33800',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__33800___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = chahn_2eHahnRelationsBasic_2epow__rel___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2)) ).
fof('$_lam_33849',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__33849___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_33859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33859___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_33874',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33874___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = chahn_2eHahnRelationsBasic_2erestr__rel___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,happ(Vv__CANONICAL__3,Vv__CANONICAL__4)) ).
fof('$_lam_33880',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__33880___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).
fof('$_lam_33898',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__33898___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__2,Vv__CANONICAL__4) ).
fof('$_lam_33910',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__33910___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4,happ(Vv__CANONICAL__2,Vv__CANONICAL__5)) ).
fof('$_lam_34030',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] : c_24__lam__34030___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = happ(Vv__CANONICAL__3,Vv__CANONICAL__4) ).
fof('$_lam_34043',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] : c_24__lam__34043___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,happ(Vv__CANONICAL__4,Vv__CANONICAL__5)) ).
fof('$_lam_34187',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__34187___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('$_lam_34194',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__34194___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> p(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2eO))) ) ).
fof('$_lam_54',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
( c_24__lam__54___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('$_lam_7212',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
( c_24__lam__7212___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
<=> ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
& p(happ(Vv__CANONICAL__2,Vv__CANONICAL__3)) ) ) ).
fof('$_lam_7223',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
( c_24__lam__7223___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('$_prop_2531',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__2531___24a2(V0__A,V1__B))
<=> ( p(V0__A)
| p(V1__B) ) ) ).
fof('$_prop_2532',axiom,
! [V0__A,V1__B] :
( p(c_24__prop__2532___24a2(V0__A,V1__B))
<=> ( p(V0__A)
& p(V1__B) ) ) ).
fof('$_prop_2533',axiom,
! [V0__A] :
( p(c_24__prop__2533___24a1(V0__A))
<=> ~ p(V0__A) ) ).
fof('$_prop_36981',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__S__36959,Vvar__1__x__36960,Vvar__2__y__36961] :
( p(c_24__prop__36981___24a4(Vvar__0___24Anonymous__36957,Vvar__0__S__36959,Vvar__1__x__36960,Vvar__2__y__36961))
<=> Vvar__1__x__36960 = Vvar__2__y__36961 ) ).
fof('$_prop_36982',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__x__36962,Vvar__1__y__36963] :
( p(c_24__prop__36982___24a3(Vvar__0___24Anonymous__36957,Vvar__0__x__36962,Vvar__1__y__36963))
<=> Vvar__0__x__36962 = Vvar__1__y__36963 ) ).
fof('$_prop_36983',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__x__36964,Vvar__1__s__36965] :
( p(c_24__prop__36983___24a3(Vvar__0___24Anonymous__36957,Vvar__0__x__36964,Vvar__1__s__36965))
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__36964,Vvar__1__s__36965) = cCoq_2eInit_2eDatatypes_2etrue ) ).
fof('$_prop_36984',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__P__36966,Vvar__1__Q__36967] :
( p(c_24__prop__36984___24a3(Vvar__0___24Anonymous__36957,Vvar__0__P__36966,Vvar__1__Q__36967))
<=> ( p(Vvar__0__P__36966)
& p(Vvar__1__Q__36967) ) ) ).
fof('$_prop_36985',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__P__36970,Vvar__1__Q__36971] :
( p(c_24__prop__36985___24a3(Vvar__0___24Anonymous__36957,Vvar__0__P__36970,Vvar__1__Q__36971))
<=> ( p(Vvar__0__P__36970)
| p(Vvar__1__Q__36971) ) ) ).
fof('$_prop_36986',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__P__36974,Vvar__1__Q__36975] :
( p(c_24__prop__36986___24a3(Vvar__0___24Anonymous__36957,Vvar__0__P__36974,Vvar__1__Q__36975))
<=> ( p(Vvar__0__P__36974)
=> p(Vvar__1__Q__36975) ) ) ).
fof('$_prop_36987',axiom,
! [Vvar__0___24Anonymous__36957,Vvar__0__P__36979] :
( p(c_24__prop__36987___24a2(Vvar__0___24Anonymous__36957,Vvar__0__P__36979))
<=> ~ p(Vvar__0__P__36979) ) ).
fof('$_prop_7330',axiom,
! [V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314] :
( p(c_24__prop__7330___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314)) ) ).
fof('$_prop_7342',axiom,
! [V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314] :
( p(c_24__prop__7342___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314))
<=> ~ p(cCoq_2eLists_2eList_2eIn___24a3(V1__A,Vvar__1___24Anonymous__7313,Vvar__2___24Anonymous__7314)) ) ).
fof('$_type_125',axiom,
! [Vvar__126] :
( c_24__type__125___24t(Vvar__126)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__126,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_17',axiom,
! [Vv__CANONICAL__0,Vvar__18] :
( c_24__type__17___24t(Vv__CANONICAL__0,Vvar__18)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__18,Vv__CANONICAL__1)) ) ) ).
fof('$_type_174',axiom,
! [Vvar__175] :
( c_24__type__174___24t(Vvar__175)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__175,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_187',axiom,
! [Vvar__188] :
( c_24__type__187___24t(Vvar__188)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___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__188,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_200',axiom,
! [Vvar__201] :
( c_24__type__200___24t(Vvar__201)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__201,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_22',axiom,
! [Vv__CANONICAL__0,Vvar__23] :
( c_24__type__22___24t(Vv__CANONICAL__0,Vvar__23)
<=> ! [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__23,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_22732',axiom,
! [Vvar__22733] :
( c_24__type__22732___24t(Vvar__22733)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__3387___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__22733,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_23327',axiom,
! [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__23328] :
( c_24__type__23327___24t(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__23328)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23328,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23390',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23391] :
( c_24__type__23390___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23391)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23391,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23453',axiom,
! [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__23454] :
( c_24__type__23453___24t(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__23454)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23454,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23507',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23508] :
( c_24__type__23507___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__23508)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__23508,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_23570',axiom,
! [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__23571] :
( c_24__type__23570___24t(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__23571)
<=> ! [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__23571,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_237',axiom,
! [Vvar__238] :
( c_24__type__237___24t(Vvar__238)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__238,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_23829',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23830] :
( c_24__type__23829___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23830)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23830,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23860] :
( c_24__type__23859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23860)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23860,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23883',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23884] :
( c_24__type__23883___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23884)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__23884,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_23913',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23914] :
( c_24__type__23913___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23914)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__23914,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_23943',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23944] :
( c_24__type__23943___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23944)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__23944,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_23967',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23968] :
( c_24__type__23967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__23968)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__23968,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_24000',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24001] :
( c_24__type__24000___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24001)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__24001,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_24024',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24025] :
( c_24__type__24024___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24025)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__24025,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_24051',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24052] :
( c_24__type__24051___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__24052)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(Vvar__24052,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).
fof('$_type_2436',axiom,
! [Vvar__2437] :
( c_24__type__2436___24t(Vvar__2437)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__2437,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2443',axiom,
! [Vvar__2444] :
( c_24__type__2443___24t(Vvar__2444)
<=> ! [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__2444,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2450',axiom,
! [Vvar__2451] :
( c_24__type__2450___24t(Vvar__2451)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__2451,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2460',axiom,
! [Vvar__2461] :
( c_24__type__2460___24t(Vvar__2461)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2461,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2523',axiom,
! [Vvar__2524] :
( c_24__type__2523___24t(Vvar__2524)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cCoq_2eInit_2ePeano_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__2524,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2538',axiom,
! [Vvar__2539] :
( c_24__type__2538___24t(Vvar__2539)
<=> ! [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__2539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2540',axiom,
! [Vvar__2541] :
( c_24__type__2540___24t(Vvar__2541)
<=> ! [Vv__CANONICAL__0] :
( chahn_2eHahnBase_2eEquality_2etype___24t(Vv__CANONICAL__0)
=> chahn_2eHahnBase_2eEquality_2eaxiom___24t(chahn_2eHahnBase_2eEquality_2esort___24a1(Vv__CANONICAL__0),chahn_2eHahnBase_2eeq__op___24a1(Vv__CANONICAL__0),happ(Vvar__2541,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2548',axiom,
! [Vvar__2549] :
( c_24__type__2548___24t(Vvar__2549)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__2550___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2549,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2550',axiom,
! [Vvar__2551] :
( c_24__type__2550___24t(Vvar__2551)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2eunit___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2551,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2563',axiom,
! [Vv__CANONICAL__0,Vvar__2564] :
( c_24__type__2563___24t(Vv__CANONICAL__0,Vvar__2564)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__2564,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_264',axiom,
! [Vvar__265] :
( c_24__type__264___24t(Vvar__265)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__265,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2684',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2685] :
( c_24__type__2684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__2685)
<=> ! [Vv__CANONICAL__4] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
=> t(happ(Vvar__2685,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_271',axiom,
! [Vvar__272] :
( c_24__type__271___24t(Vvar__272)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__272,Vv__CANONICAL__0)) ) ) ).
fof('$_type_273',axiom,
! [Vvar__274] :
( c_24__type__273___24t(Vvar__274)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__274,Vv__CANONICAL__0)) ) ) ).
fof('$_type_27995',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27996] :
( c_24__type__27995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27996)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(happ(Vvar__27996,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).
fof('$_type_28',axiom,
! [Vv__CANONICAL__0,Vvar__29] :
( c_24__type__28___24t(Vv__CANONICAL__0,Vvar__29)
<=> ! [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__29,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_28038',axiom,
! [Vvar__28039] :
( c_24__type__28038___24t(Vvar__28039)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__90___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__27995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cProp___24t(happ(happ(happ(happ(Vvar__28039,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_285',axiom,
! [Vvar__286] :
( c_24__type__285___24t(Vvar__286)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__286,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2886',axiom,
! [Vvar__2887] :
( c_24__type__2886___24t(Vvar__2887)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__2887,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_2895',axiom,
! [Vvar__2896] :
( c_24__type__2895___24t(Vvar__2896)
<=> ! [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__2896,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2905',axiom,
! [Vvar__2906] :
( c_24__type__2905___24t(Vvar__2906)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__2906,Vv__CANONICAL__0)) ) ) ).
fof('$_type_2946',axiom,
! [Vvar__2947] :
( c_24__type__2946___24t(Vvar__2947)
<=> ! [Vv__CANONICAL__0] :
( cProp___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__2947,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29587',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29588] :
( c_24__type__29587___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29588)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__29588,Vv__CANONICAL__2)) ) ) ).
fof('$_type_29591',axiom,
! [Vvar__29592] :
( c_24__type__29591___24t(Vvar__29592)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29592,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29626',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29627] :
( c_24__type__29626___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__29627)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__29627,Vv__CANONICAL__2)) ) ) ).
fof('$_type_29630',axiom,
! [Vvar__29631] :
( c_24__type__29630___24t(Vvar__29631)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__473___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29631,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_29671',axiom,
! [Vvar__29672] :
( c_24__type__29671___24t(Vvar__29672)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cProp___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__29672,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_2968',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2969] :
( c_24__type__2968___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__2969)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__2969,Vv__CANONICAL__2)) ) ) ).
fof('$_type_29755',axiom,
! [Vvar__29756] :
( c_24__type__29755___24t(Vvar__29756)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cType___24t(Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cType___24t(Vv__CANONICAL__3)
=> cType___24t(happ(happ(happ(happ(Vvar__29756,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_2985',axiom,
! [Vvar__2986] :
( c_24__type__2985___24t(Vvar__2986)
<=> ! [Vv__CANONICAL__0] :
( chahn_2eHahnBase_2eEquality_2etype___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__2986,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3000',axiom,
! [Vvar__3001] :
( c_24__type__3000___24t(Vvar__3001)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__3001,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3004',axiom,
! [Vvar__3005] :
( c_24__type__3004___24t(Vvar__3005)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3005,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3021',axiom,
! [Vvar__3022] :
( c_24__type__3021___24t(Vvar__3022)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__3022,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3058',axiom,
! [Vvar__3059] :
( c_24__type__3058___24t(Vvar__3059)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__3059,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3064',axiom,
! [Vvar__3065] :
( c_24__type__3064___24t(Vvar__3065)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__3065,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_30772',axiom,
! [Vvar__30773] :
( c_24__type__30772___24t(Vvar__30773)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cType___24t(happ(happ(Vvar__30773,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__309] :
( c_24__type__308___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__309)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__309,Vv__CANONICAL__2)) ) ) ).
fof('$_type_3092',axiom,
! [Vvar__3093] :
( c_24__type__3092___24t(Vvar__3093)
<=> ! [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__3093,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3094',axiom,
! [Vvar__3095] :
( c_24__type__3094___24t(Vvar__3095)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__3095,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31',axiom,
! [Vv__CANONICAL__0,Vvar__32] :
( c_24__type__31___24t(Vv__CANONICAL__0,Vvar__32)
<=> ! [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__32,Vv__CANONICAL__1)) ) ) ).
fof('$_type_31250',axiom,
! [Vvar__31251] :
( c_24__type__31250___24t(Vvar__31251)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__31251,Vv__CANONICAL__0)) ) ) ).
fof('$_type_31260',axiom,
! [Vvar__31261] :
( c_24__type__31260___24t(Vvar__31261)
<=> ! [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__31261,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31266',axiom,
! [Vvar__31267] :
( c_24__type__31266___24t(Vvar__31267)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__31267,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3138',axiom,
! [Vvar__3139] :
( c_24__type__3138___24t(Vvar__3139)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__3139,Vv__CANONICAL__0)) ) ) ).
fof('$_type_3143',axiom,
! [Vvar__3144] :
( c_24__type__3143___24t(Vvar__3144)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3144,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31689',axiom,
! [Vvar__31690] :
( c_24__type__31689___24t(Vvar__31690)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___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__31690,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_31713',axiom,
! [Vvar__31714] :
( c_24__type__31713___24t(Vvar__31714)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__31714,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31727',axiom,
! [Vvar__31728] :
( c_24__type__31727___24t(Vvar__31728)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___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__31728,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_31747',axiom,
! [Vvar__31748] :
( c_24__type__31747___24t(Vvar__31748)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__31748,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31769',axiom,
! [Vvar__31770] :
( c_24__type__31769___24t(Vvar__31770)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__31774___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__31770,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).
fof('$_type_31774',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31775] :
( c_24__type__31774___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31775)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__31775,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31783',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31784] :
( c_24__type__31783___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31784)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__31784,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31787',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31788] :
( c_24__type__31787___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__31788)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__31788,Vv__CANONICAL__2)) ) ) ).
fof('$_type_31818',axiom,
! [Vvar__31819] :
( c_24__type__31818___24t(Vvar__31819)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__31819,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_31825',axiom,
! [Vvar__31826] :
( c_24__type__31825___24t(Vvar__31826)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__31826,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_31843',axiom,
! [Vvar__31844] :
( c_24__type__31843___24t(Vvar__31844)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__308___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__31844,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_31864',axiom,
! [Vvar__31865] :
( c_24__type__31864___24t(Vvar__31865)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__31783___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(happ(Vvar__31865,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_3198',axiom,
! [Vv__CANONICAL__0,Vvar__3199] :
( c_24__type__3198___24t(Vv__CANONICAL__0,Vvar__3199)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__3199,Vv__CANONICAL__1)) ) ) ).
fof('$_type_320',axiom,
! [Vvar__321] :
( c_24__type__320___24t(Vvar__321)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__321,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3234',axiom,
! [Vvar__3235] :
( c_24__type__3234___24t(Vvar__3235)
<=> ! [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__3235,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_3246',axiom,
! [Vvar__3247] :
( c_24__type__3246___24t(Vvar__3247)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__3247,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_32746',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32747] :
( c_24__type__32746___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32747)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32747,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32770] :
( c_24__type__32769___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32770)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32770,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32792',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32793] :
( c_24__type__32792___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32793)
<=> ! [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__32793,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).
fof('$_type_32815',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32816] :
( c_24__type__32815___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32816)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32816,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32833',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32834] :
( c_24__type__32833___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32834)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__32834,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_32859',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32860] :
( c_24__type__32859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32860)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__32860,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_32877',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32878] :
( c_24__type__32877___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__32878)
<=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> t(happ(Vvar__32878,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).
fof('$_type_33041',axiom,
! [Vvar__33042] :
( c_24__type__33041___24t(Vvar__33042)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33046___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__33042,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_33046',axiom,
! [Vv__CANONICAL__0,Vvar__33047] :
( c_24__type__33046___24t(Vv__CANONICAL__0,Vvar__33047)
<=> ! [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__33047,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_33061',axiom,
! [Vvar__33062] :
( c_24__type__33061___24t(Vvar__33062)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33066___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__33062,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).
fof('$_type_33066',axiom,
! [Vv__CANONICAL__0,Vvar__33067] :
( c_24__type__33066___24t(Vv__CANONICAL__0,Vvar__33067)
<=> ! [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__33067,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_331',axiom,
! [Vvar__332] :
( c_24__type__331___24t(Vvar__332)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__332,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33116',axiom,
! [Vvar__33117] :
( c_24__type__33116___24t(Vvar__33117)
<=> ! [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__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(happ(Vvar__33117,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_33125',axiom,
! [Vv__CANONICAL__0,Vvar__33126] :
( c_24__type__33125___24t(Vv__CANONICAL__0,Vvar__33126)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__33126,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33194',axiom,
! [Vv__CANONICAL__0,Vvar__33195] :
( c_24__type__33194___24t(Vv__CANONICAL__0,Vvar__33195)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__33195,Vv__CANONICAL__1)) ) ) ).
fof('$_type_33211',axiom,
! [Vvar__33212] :
( c_24__type__33211___24t(Vvar__33212)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__31___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__33212,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33394',axiom,
! [Vv__CANONICAL__0,Vvar__33395] :
( c_24__type__33394___24t(Vv__CANONICAL__0,Vvar__33395)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__33395,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ).
fof('$_type_33401',axiom,
! [Vv__CANONICAL__0,Vvar__33402] :
( c_24__type__33401___24t(Vv__CANONICAL__0,Vvar__33402)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__33402,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33455',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33456] :
( c_24__type__33455___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33456)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__57___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(Vvar__33456,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_33475',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33476] :
( c_24__type__33475___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33476)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__33476,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_33483',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33484] :
( c_24__type__33483___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33484)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__33484,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33495',axiom,
! [Vv__CANONICAL__0,Vvar__33496] :
( c_24__type__33495___24t(Vv__CANONICAL__0,Vvar__33496)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__33496,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33513',axiom,
! [Vv__CANONICAL__0,Vvar__33514] :
( c_24__type__33513___24t(Vv__CANONICAL__0,Vvar__33514)
<=> ! [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(Vvar__33514,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33526',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33527] :
( c_24__type__33526___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33527)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__31774___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(Vvar__33527,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_33536',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33537] :
( c_24__type__33536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33537)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__31774___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__33537,Vv__CANONICAL__2)) ) ) ).
fof('$_type_33557',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33558] :
( c_24__type__33557___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33558)
<=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(Vvar__33558,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_33565',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33566] :
( c_24__type__33565___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__33566)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(Vvar__33566,Vv__CANONICAL__2)) ) ) ).
fof('$_type_336',axiom,
! [Vvar__337] :
( c_24__type__336___24t(Vvar__337)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__337,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_33633',axiom,
! [Vv__CANONICAL__0,Vvar__33634] :
( c_24__type__33633___24t(Vv__CANONICAL__0,Vvar__33634)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__33634,Vv__CANONICAL__1)) ) ) ).
fof('$_type_33649',axiom,
! [Vv__CANONICAL__0,Vvar__33650] :
( c_24__type__33649___24t(Vv__CANONICAL__0,Vvar__33650)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__33650,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_33706',axiom,
! [Vv__CANONICAL__0,Vvar__33707] :
( c_24__type__33706___24t(Vv__CANONICAL__0,Vvar__33707)
<=> ! [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__33707,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_3387',axiom,
! [Vv__CANONICAL__0,Vvar__3388] :
( c_24__type__3387___24t(Vv__CANONICAL__0,Vvar__3388)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3388,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34016',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34017] :
( c_24__type__34016___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34017)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__34017,Vv__CANONICAL__3)) ) ) ).
fof('$_type_34021',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34022] :
( c_24__type__34021___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34022)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(Vvar__34022,Vv__CANONICAL__3)) ) ) ).
fof('$_type_34095',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34096] :
( c_24__type__34095___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34096)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> t(happ(Vvar__34096,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_34107',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34108] :
( c_24__type__34107___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34108)
<=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(Vvar__34108,Vv__CANONICAL__2)) ) ) ).
fof('$_type_34212',axiom,
! [Vv__CANONICAL__0,Vvar__34213] :
( c_24__type__34212___24t(Vv__CANONICAL__0,Vvar__34213)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__34213,Vv__CANONICAL__1)) ) ) ).
fof('$_type_34256',axiom,
! [Vv__CANONICAL__0,Vvar__34257] :
( c_24__type__34256___24t(Vv__CANONICAL__0,Vvar__34257)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> cType___24t(happ(Vvar__34257,Vv__CANONICAL__1)) ) ) ).
fof('$_type_34269',axiom,
! [Vvar__34270] :
( c_24__type__34269___24t(Vvar__34270)
<=> ! [Vv__CANONICAL__0] :
( c_24__type__34271___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [Vv__CANONICAL__2] :
( c_24__type__34276___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(happ(Vvar__34270,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_34271',axiom,
! [Vvar__34272] :
( c_24__type__34271___24t(Vvar__34272)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__34272,Vv__CANONICAL__0)) ) ) ).
fof('$_type_34276',axiom,
! [Vv__CANONICAL__0,Vvar__34277] :
( c_24__type__34276___24t(Vv__CANONICAL__0,Vvar__34277)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__34277,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_34281',axiom,
! [Vv__CANONICAL__0,Vvar__34282] :
( c_24__type__34281___24t(Vv__CANONICAL__0,Vvar__34282)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
=> t(happ(happ(Vvar__34282,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(Vv__CANONICAL__1))) ) ) ) ).
fof('$_type_34296',axiom,
! [Vv__CANONICAL__0,Vvar__34297] :
( c_24__type__34296___24t(Vv__CANONICAL__0,Vvar__34297)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33046___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__34297,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_34307',axiom,
! [Vv__CANONICAL__0,Vvar__34308] :
( c_24__type__34307___24t(Vv__CANONICAL__0,Vvar__34308)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__33046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__34308,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34316',axiom,
! [Vv__CANONICAL__0,Vvar__34317] :
( c_24__type__34316___24t(Vv__CANONICAL__0,Vvar__34317)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__34317,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_34370',axiom,
! [Vv__CANONICAL__0,Vvar__34371] :
( c_24__type__34370___24t(Vv__CANONICAL__0,Vvar__34371)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( c_24__type__33066___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
=> t(happ(happ(happ(Vvar__34371,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ).
fof('$_type_34381',axiom,
! [Vv__CANONICAL__0,Vvar__34382] :
( c_24__type__34381___24t(Vv__CANONICAL__0,Vvar__34382)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__33066___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
=> t(happ(happ(Vvar__34382,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_34466',axiom,
! [Vvar__34467] :
( c_24__type__34466___24t(Vvar__34467)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__34467,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_346',axiom,
! [Vvar__347] :
( c_24__type__346___24t(Vvar__347)
<=> ! [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__347,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_34648',axiom,
! [Vv__CANONICAL__0,Vvar__34649] :
( c_24__type__34648___24t(Vv__CANONICAL__0,Vvar__34649)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
=> t(happ(Vvar__34649,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_3467',axiom,
! [Vv__CANONICAL__0,Vvar__3468] :
( c_24__type__3467___24t(Vv__CANONICAL__0,Vvar__3468)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> t(happ(Vvar__3468,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).
fof('$_type_34857',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34858] :
( c_24__type__34857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__34858)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__34858,Vv__CANONICAL__6)) ) ) ).
fof('$_type_35057',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__35058] :
( c_24__type__35057___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__35058)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35058,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35150',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35151] :
( c_24__type__35150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35151)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35151,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35243',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__35244] :
( c_24__type__35243___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__35244)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35244,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35325',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35326] :
( c_24__type__35325___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35326)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__35326,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_35418',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__35419] :
( c_24__type__35418___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__35419)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__35419,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_35500',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35501] :
( c_24__type__35500___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__35501)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__35501,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_35593',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__35594] :
( c_24__type__35593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__35594)
<=> ! [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__35594,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_35604',axiom,
! [Vvar__35605] :
( c_24__type__35604___24t(Vvar__35605)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35605,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_35627',axiom,
! [Vvar__35628] :
( c_24__type__35627___24t(Vvar__35628)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( c_24__type__8654___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__35628,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_35714',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__35715] :
( c_24__type__35714___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__35715)
<=> ! [Vv__CANONICAL__5] :
( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__35715,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_35733',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__35734] :
( c_24__type__35733___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__35734)
<=> ! [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__35734,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).
fof('$_type_35753',axiom,
! [Vvar__35754] :
( c_24__type__35753___24t(Vvar__35754)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__4] :
( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
=> cType___24t(happ(happ(happ(happ(happ(Vvar__35754,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_35980',axiom,
! [Vvar__35981] :
( c_24__type__35980___24t(Vvar__35981)
<=> ! [Vv__CANONICAL__0] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__35981,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_36154',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36155] :
( c_24__type__36154___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36155)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36155,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36193',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36194] :
( c_24__type__36193___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36194)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36194,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36232',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36233] :
( c_24__type__36232___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36233)
<=> ! [Vv__CANONICAL__6] :
( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__7] :
( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__36233,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).
fof('$_type_36474',axiom,
! [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__36475] :
( c_24__type__36474___24t(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__36475)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36475,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36537',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__36538] :
( c_24__type__36537___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__36538)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36538,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36600',axiom,
! [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__36601] :
( c_24__type__36600___24t(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__36601)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__36601,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_36654',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__36655] :
( c_24__type__36654___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__36655)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> t(happ(Vvar__36655,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).
fof('$_type_367',axiom,
! [Vvar__368] :
( c_24__type__367___24t(Vvar__368)
<=> ! [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__368,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_36717',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__36718] :
( c_24__type__36717___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vvar__36718)
<=> ! [Vv__CANONICAL__8] :
( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__9] :
( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__36718,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).
fof('$_type_36761',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36762] :
( c_24__type__36761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36762)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__36762,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36769',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36770] :
( c_24__type__36769___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36770)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__36770,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36777',axiom,
! [Vvar__36778] :
( c_24__type__36777___24t(Vvar__36778)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__36778,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_36817',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36818] :
( c_24__type__36817___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36818)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__36818,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36825',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36826] :
( c_24__type__36825___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__36826)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__36826,Vv__CANONICAL__3)) ) ) ).
fof('$_type_36833',axiom,
! [Vvar__36834] :
( c_24__type__36833___24t(Vvar__36834)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__473___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__473___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cType___24t(happ(happ(happ(Vvar__36834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_3696',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__3697] :
( c_24__type__3696___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__3697)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3697,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3789',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__3790] :
( c_24__type__3789___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__3790)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3790,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3882',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__3883] :
( c_24__type__3882___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__3883)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__3883,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_3964',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__3965] :
( c_24__type__3964___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__3965)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__3965,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_404',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__405] :
( c_24__type__404___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__405)
<=> ! [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__405,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).
fof('$_type_4057',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4058] :
( c_24__type__4057___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4058)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__4058,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_4139',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__4140] :
( c_24__type__4139___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__4140)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__4140,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_4232',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4233] :
( c_24__type__4232___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__4233)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__4233,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_473',axiom,
! [Vv__CANONICAL__0,Vvar__474] :
( c_24__type__473___24t(Vv__CANONICAL__0,Vvar__474)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__474,Vv__CANONICAL__1)) ) ) ).
fof('$_type_549',axiom,
! [Vvar__550] :
( c_24__type__549___24t(Vvar__550)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__550,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_57',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__58)
<=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> t(happ(Vvar__58,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).
fof('$_type_65',axiom,
! [Vvar__66] :
( c_24__type__65___24t(Vvar__66)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__66,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7',axiom,
! [Vv__CANONICAL__0,Vvar__8] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vvar__8)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> cProp___24t(happ(Vvar__8,Vv__CANONICAL__1)) ) ) ).
fof('$_type_7179',axiom,
! [Vv__CANONICAL__0,Vvar__7180] :
( c_24__type__7179___24t(Vv__CANONICAL__0,Vvar__7180)
<=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(Vvar__7180,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_7184',axiom,
! [Vv__CANONICAL__0,Vvar__7185] :
( c_24__type__7184___24t(Vv__CANONICAL__0,Vvar__7185)
<=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(Vvar__7185,Vv__CANONICAL__1)) ) ) ).
fof('$_type_7344',axiom,
! [Vvar__7345] :
( c_24__type__7344___24t(Vvar__7345)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(Vvar__7345,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7447',axiom,
! [Vvar__7448] :
( c_24__type__7447___24t(Vvar__7448)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,happ(happ(Vvar__7448,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_7452',axiom,
! [Vvar__7453] :
( c_24__type__7452___24t(Vvar__7453)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(happ(Vvar__7453,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7471',axiom,
! [Vvar__7472] :
( c_24__type__7471___24t(Vvar__7472)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___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__7472,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).
fof('$_type_7491',axiom,
! [Vvar__7492] :
( c_24__type__7491___24t(Vvar__7492)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__7___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__7492,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_7536',axiom,
! [Vvar__7537] :
( c_24__type__7536___24t(Vvar__7537)
<=> ! [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__7537,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_76',axiom,
! [Vvar__77] :
( c_24__type__76___24t(Vvar__77)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cType___24t(Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( c_24__type__57___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
=> ! [Vv__CANONICAL__3] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
=> cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__77,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).
fof('$_type_8009',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8010] :
( c_24__type__8009___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__8010)
<=> ! [Vv__CANONICAL__3] :
( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
=> t(happ(Vvar__8010,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).
fof('$_type_81',axiom,
! [Vvar__82] :
( c_24__type__81___24t(Vvar__82)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> cProp___24t(happ(happ(Vvar__82,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).
fof('$_type_8654',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8655] :
( c_24__type__8654___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8655)
<=> ! [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__8655,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).
fof('$_type_90',axiom,
! [Vv__CANONICAL__0,Vvar__91] :
( c_24__type__90___24t(Vv__CANONICAL__0,Vvar__91)
<=> ! [Vv__CANONICAL__1] :
( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__2] :
( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__91,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).
fof('$_type_92',axiom,
! [Vvar__93] :
( c_24__type__92___24t(Vvar__93)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> cType___24t(happ(Vvar__93,Vv__CANONICAL__0)) ) ) ).
fof('$_type_9207',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9208] :
( c_24__type__9207___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9208)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9208,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9308',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9309] :
( c_24__type__9308___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9309)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9309,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9409',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9410] :
( c_24__type__9409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9410)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> t(happ(happ(Vvar__9410,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).
fof('$_type_9499',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9500] :
( c_24__type__9499___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9500)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> t(happ(Vvar__9500,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).
fof('$_type_9600',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9601] :
( c_24__type__9600___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vvar__9601)
<=> ! [Vv__CANONICAL__10] :
( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__11] :
( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
=> cProp___24t(happ(happ(Vvar__9601,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_9701',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9702] :
( c_24__type__9701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9702)
<=> ! [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__9702,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_type_98',axiom,
! [Vvar__99] :
( c_24__type__98___24t(Vvar__99)
<=> ! [Vv__CANONICAL__0] :
( cType___24t(Vv__CANONICAL__0)
=> ! [Vv__CANONICAL__1] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
=> ! [Vv__CANONICAL__2] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
=> cProp___24t(happ(happ(happ(Vvar__99,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).
fof('$_type_9802',axiom,
! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__9803] :
( c_24__type__9802___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__9803)
<=> ! [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__9803,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).
fof('$_typeof_A',axiom,
cType___24t(cA) ).
fof('$_typeof_Coq.Arith.Compare_dec.le_gt_dec',axiom,
c_24__type__2523___24t(cCoq_2eArith_2eCompare__dec_2ele__gt__dec) ).
fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
c_24__type__33061___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).
fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
c_24__type__2460___24t(cCoq_2eBool_2eBool_2ereflect) ).
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('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).
fof('$_typeof_Coq.Init.Byte.byte',axiom,
cType___24t(cCoq_2eInit_2eByte_2ebyte) ).
fof('$_typeof_Coq.Init.Datatypes.Eq',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eEq) ).
fof('$_typeof_Coq.Init.Datatypes.Gt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eGt) ).
fof('$_typeof_Coq.Init.Datatypes.IDProp',axiom,
cProp___24t(cCoq_2eInit_2eDatatypes_2eIDProp) ).
fof('$_typeof_Coq.Init.Datatypes.Lt',axiom,
cCoq_2eInit_2eDatatypes_2ecomparison___24t(cCoq_2eInit_2eDatatypes_2eLt) ).
fof('$_typeof_Coq.Init.Datatypes.None',axiom,
c_24__type__3094___24t(cCoq_2eInit_2eDatatypes_2eNone) ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).
fof('$_typeof_Coq.Init.Datatypes.S',axiom,
c_24__type__271___24t(cCoq_2eInit_2eDatatypes_2eS) ).
fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
c_24__type__3092___24t(cCoq_2eInit_2eDatatypes_2eSome) ).
fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
c_24__type__3064___24t(cCoq_2eInit_2eDatatypes_2eandb) ).
fof('$_typeof_Coq.Init.Datatypes.app',axiom,
c_24__type__3246___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('$_typeof_Coq.Init.Datatypes.cons',axiom,
c_24__type__3143___24t(cCoq_2eInit_2eDatatypes_2econs) ).
fof('$_typeof_Coq.Init.Datatypes.false',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2efalse) ).
fof('$_typeof_Coq.Init.Datatypes.length',axiom,
c_24__type__3234___24t(cCoq_2eInit_2eDatatypes_2elength) ).
fof('$_typeof_Coq.Init.Datatypes.list',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2elist) ).
fof('$_typeof_Coq.Init.Datatypes.nat',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2enat) ).
fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
c_24__type__3138___24t(cCoq_2eInit_2eDatatypes_2enil) ).
fof('$_typeof_Coq.Init.Datatypes.option',axiom,
c_24__type__92___24t(cCoq_2eInit_2eDatatypes_2eoption) ).
fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
c_24__type__285___24t(cCoq_2eInit_2eDatatypes_2esum) ).
fof('$_typeof_Coq.Init.Datatypes.true',axiom,
cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2eInit_2eDatatypes_2etrue) ).
fof('$_typeof_Coq.Init.Datatypes.tt',axiom,
cCoq_2eInit_2eDatatypes_2eunit___24t(cCoq_2eInit_2eDatatypes_2ett) ).
fof('$_typeof_Coq.Init.Datatypes.unit',axiom,
cType___24t(cCoq_2eInit_2eDatatypes_2eunit) ).
fof('$_typeof_Coq.Init.Decimal.int',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2eint) ).
fof('$_typeof_Coq.Init.Decimal.uint',axiom,
cType___24t(cCoq_2eInit_2eDecimal_2euint) ).
fof('$_typeof_Coq.Init.Nat.add',axiom,
c_24__type__2895___24t(cCoq_2eInit_2eNat_2eadd) ).
fof('$_typeof_Coq.Init.Nat.modulo',axiom,
c_24__type__2895___24t(cCoq_2eInit_2eNat_2emodulo) ).
fof('$_typeof_Coq.Init.Nat.pred',axiom,
c_24__type__271___24t(cCoq_2eInit_2eNat_2epred) ).
fof('$_typeof_Coq.Init.Nat.sub',axiom,
c_24__type__2895___24t(cCoq_2eInit_2eNat_2esub) ).
fof('$_typeof_Coq.Init.Peano.ge',axiom,
c_24__type__346___24t(cCoq_2eInit_2ePeano_2ege) ).
fof('$_typeof_Coq.Init.Peano.gt',axiom,
c_24__type__346___24t(cCoq_2eInit_2ePeano_2egt) ).
fof('$_typeof_Coq.Init.Peano.lt',axiom,
c_24__type__346___24t(cCoq_2eInit_2ePeano_2elt) ).
fof('$_typeof_Coq.Init.Specif.sig',axiom,
c_24__type__29591___24t(cCoq_2eInit_2eSpecif_2esig) ).
fof('$_typeof_Coq.Init.Specif.sig2',axiom,
c_24__type__36777___24t(cCoq_2eInit_2eSpecif_2esig2) ).
fof('$_typeof_Coq.Init.Specif.sigT',axiom,
c_24__type__29630___24t(cCoq_2eInit_2eSpecif_2esigT) ).
fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
c_24__type__36833___24t(cCoq_2eInit_2eSpecif_2esigT2) ).
fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
c_24__type__2946___24t(cCoq_2eInit_2eSpecif_2esumbool) ).
fof('$_typeof_Coq.Init.Specif.sumor',axiom,
c_24__type__29671___24t(cCoq_2eInit_2eSpecif_2esumor) ).
fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
c_24__type__549___24t(cCoq_2eInit_2eWf_2ewell__founded) ).
fof('$_typeof_Coq.Lists.List.In',axiom,
c_24__type__7536___24t(cCoq_2eLists_2eList_2eIn) ).
fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
c_24__type__28038___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).
fof('$_typeof_Coq.Logic.ChoiceFacts.FunctionalChoice_on',axiom,
c_24__type__34466___24t(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on) ).
fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
c_24__type__31260___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).
fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
c_24__type__31260___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).
fof('$_typeof_Coq.NArith.BinNat.N.peano_rect',axiom,
c_24__type__34269___24t(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect) ).
fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
c_24__type__33041___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).
fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
c_24__type__31250___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).
fof('$_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__3058___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('$_typeof_Coq.Numbers.BinNums.Zneg',axiom,
c_24__type__264___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).
fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
c_24__type__264___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('$_typeof_Coq.Numbers.BinNums.xI',axiom,
c_24__type__2450___24t(cCoq_2eNumbers_2eBinNums_2exI) ).
fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
c_24__type__2450___24t(cCoq_2eNumbers_2eBinNums_2exO) ).
fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).
fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).
fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).
fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
c_24__type__35980___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.antisymmetric',axiom,
c_24__type__81___24t(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.commut',axiom,
c_24__type__98___24t(cCoq_2eRelations_2eRelation__Definitions_2ecommut) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.equiv',axiom,
c_24__type__81___24t(cCoq_2eRelations_2eRelation__Definitions_2eequiv) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.inclusion',axiom,
c_24__type__98___24t(cCoq_2eRelations_2eRelation__Definitions_2einclusion) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.reflexive',axiom,
c_24__type__81___24t(cCoq_2eRelations_2eRelation__Definitions_2ereflexive) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
c_24__type__92___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.same_relation',axiom,
c_24__type__98___24t(cCoq_2eRelations_2eRelation__Definitions_2esame__relation) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.symmetric',axiom,
c_24__type__81___24t(cCoq_2eRelations_2eRelation__Definitions_2esymmetric) ).
fof('$_typeof_Coq.Relations.Relation_Definitions.transitive',axiom,
c_24__type__81___24t(cCoq_2eRelations_2eRelation__Definitions_2etransitive) ).
fof('$_typeof_Coq.Relations.Relation_Operators.transp',axiom,
c_24__type__367___24t(cCoq_2eRelations_2eRelation__Operators_2etransp) ).
fof('$_typeof_Coq.Relations.Relation_Operators.union',axiom,
c_24__type__237___24t(cCoq_2eRelations_2eRelation__Operators_2eunion) ).
fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
c_24__type__81___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).
fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
c_24__type__92___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).
fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).
fof('$_typeof_Coq.Strings.String.string',axiom,
cType___24t(cCoq_2eStrings_2eString_2estring) ).
fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
c_24__type__35753___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).
fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).
fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
c_24__type__30772___24t(cCoq_2eVectors_2eVectorDef_2et) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
c_24__type__2443___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
c_24__type__2443___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
c_24__type__2443___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).
fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
c_24__type__2443___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).
fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
c_24__type__2443___24t(cCoq_2eZArith_2eBinInt_2eZne) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
c_24__type__3000___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
c_24__type__2436___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
c_24__type__3000___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
c_24__type__3021___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
c_24__type__3004___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
c_24__type__3000___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).
fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
c_24__type__3004___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).
fof('$_typeof_Coq.micromega.Env.Env',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eEnv_2eEnv) ).
fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).
fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).
fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).
fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).
fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).
fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).
fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).
fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
c_24__type__29755___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).
fof('$_typeof_Coq.micromega.VarMap.t',axiom,
c_24__type__92___24t(cCoq_2emicromega_2eVarMap_2et) ).
fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).
fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
c_24__type__22732___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).
fof('$_typeof_hahn.HahnBase.Equality.sort',axiom,
c_24__type__2985___24t(chahn_2eHahnBase_2eEquality_2esort) ).
fof('$_typeof_hahn.HahnBase.Equality.type',axiom,
cType___24t(chahn_2eHahnBase_2eEquality_2etype) ).
fof('$_typeof_hahn.HahnBase.NW',axiom,
c_24__type__2548___24t(chahn_2eHahnBase_2eNW) ).
fof('$_typeof_hahn.HahnBase.eqP',axiom,
c_24__type__2540___24t(chahn_2eHahnBase_2eeqP) ).
fof('$_typeof_hahn.HahnBase.eq_op',axiom,
c_24__type__2538___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.dom_cond',axiom,
c_24__type__33116___24t(chahn_2eHahnDom_2edom__cond) ).
fof('$_typeof_hahn.HahnDom.doma',axiom,
c_24__type__125___24t(chahn_2eHahnDom_2edoma) ).
fof('$_typeof_hahn.HahnDom.domb',axiom,
c_24__type__125___24t(chahn_2eHahnDom_2edomb) ).
fof('$_typeof_hahn.HahnEquational.good_ctx',axiom,
c_24__type__33211___24t(chahn_2eHahnEquational_2egood__ctx) ).
fof('$_typeof_hahn.HahnFuneq.funeq',axiom,
c_24__type__31689___24t(chahn_2eHahnFuneq_2efuneq) ).
fof('$_typeof_hahn.HahnList.undup',axiom,
c_24__type__7344___24t(chahn_2eHahnList_2eundup) ).
fof('$_typeof_hahn.HahnMaxElt.max_elt',axiom,
c_24__type__7452___24t(chahn_2eHahnMaxElt_2emax__elt) ).
fof('$_typeof_hahn.HahnMaxElt.wmax_elt',axiom,
c_24__type__7452___24t(chahn_2eHahnMaxElt_2ewmax__elt) ).
fof('$_typeof_hahn.HahnRelationsBasic.acyclic',axiom,
c_24__type__81___24t(chahn_2eHahnRelationsBasic_2eacyclic) ).
fof('$_typeof_hahn.HahnRelationsBasic.bunion',axiom,
c_24__type__31769___24t(chahn_2eHahnRelationsBasic_2ebunion) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl',axiom,
c_24__type__336___24t(chahn_2eHahnRelationsBasic_2eclos__refl) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_refl_sym',axiom,
c_24__type__336___24t(chahn_2eHahnRelationsBasic_2eclos__refl__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.clos_sym',axiom,
c_24__type__336___24t(chahn_2eHahnRelationsBasic_2eclos__sym) ).
fof('$_typeof_hahn.HahnRelationsBasic.codom_rel',axiom,
c_24__type__7452___24t(chahn_2eHahnRelationsBasic_2ecodom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.collect_rel',axiom,
c_24__type__76___24t(chahn_2eHahnRelationsBasic_2ecollect__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.cross_rel',axiom,
c_24__type__7471___24t(chahn_2eHahnRelationsBasic_2ecross__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.dom_rel',axiom,
c_24__type__7452___24t(chahn_2eHahnRelationsBasic_2edom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eq_rel',axiom,
c_24__type__35604___24t(chahn_2eHahnRelationsBasic_2eeq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_dom_rel',axiom,
c_24__type__7447___24t(chahn_2eHahnRelationsBasic_2eeqv__dom__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.eqv_rel',axiom,
c_24__type__65___24t(chahn_2eHahnRelationsBasic_2eeqv__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.functional',axiom,
c_24__type__81___24t(chahn_2eHahnRelationsBasic_2efunctional) ).
fof('$_typeof_hahn.HahnRelationsBasic.immediate',axiom,
c_24__type__336___24t(chahn_2eHahnRelationsBasic_2eimmediate) ).
fof('$_typeof_hahn.HahnRelationsBasic.inter_rel',axiom,
c_24__type__174___24t(chahn_2eHahnRelationsBasic_2einter__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.irreflexive',axiom,
c_24__type__81___24t(chahn_2eHahnRelationsBasic_2eirreflexive) ).
fof('$_typeof_hahn.HahnRelationsBasic.is_total',axiom,
c_24__type__2886___24t(chahn_2eHahnRelationsBasic_2eis__total) ).
fof('$_typeof_hahn.HahnRelationsBasic.map_rel',axiom,
c_24__type__187___24t(chahn_2eHahnRelationsBasic_2emap__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.minus_rel',axiom,
c_24__type__174___24t(chahn_2eHahnRelationsBasic_2eminus__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.pow_rel',axiom,
c_24__type__31747___24t(chahn_2eHahnRelationsBasic_2epow__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_eq_rel',axiom,
c_24__type__331___24t(chahn_2eHahnRelationsBasic_2erestr__eq__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_rel',axiom,
c_24__type__320___24t(chahn_2eHahnRelationsBasic_2erestr__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.restr_subset',axiom,
c_24__type__31727___24t(chahn_2eHahnRelationsBasic_2erestr__subset) ).
fof('$_typeof_hahn.HahnRelationsBasic.seq',axiom,
c_24__type__174___24t(chahn_2eHahnRelationsBasic_2eseq) ).
fof('$_typeof_hahn.HahnRelationsBasic.singl_rel',axiom,
c_24__type__31713___24t(chahn_2eHahnRelationsBasic_2esingl__rel) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_partial_order',axiom,
c_24__type__81___24t(chahn_2eHahnRelationsBasic_2estrict__partial__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.strict_total_order',axiom,
c_24__type__2886___24t(chahn_2eHahnRelationsBasic_2estrict__total__order) ).
fof('$_typeof_hahn.HahnRelationsBasic.upward_closed',axiom,
c_24__type__125___24t(chahn_2eHahnRelationsBasic_2eupward__closed) ).
fof('$_typeof_hahn.HahnSets.set_bunion',axiom,
c_24__type__35627___24t(chahn_2eHahnSets_2eset__bunion) ).
fof('$_typeof_hahn.HahnSets.set_collect',axiom,
c_24__type__31843___24t(chahn_2eHahnSets_2eset__collect) ).
fof('$_typeof_hahn.HahnSets.set_compl',axiom,
c_24__type__31825___24t(chahn_2eHahnSets_2eset__compl) ).
fof('$_typeof_hahn.HahnSets.set_disjoint',axiom,
c_24__type__7491___24t(chahn_2eHahnSets_2eset__disjoint) ).
fof('$_typeof_hahn.HahnSets.set_empty',axiom,
c_24__type__31818___24t(chahn_2eHahnSets_2eset__empty) ).
fof('$_typeof_hahn.HahnSets.set_equiv',axiom,
c_24__type__7491___24t(chahn_2eHahnSets_2eset__equiv) ).
fof('$_typeof_hahn.HahnSets.set_full',axiom,
c_24__type__31818___24t(chahn_2eHahnSets_2eset__full) ).
fof('$_typeof_hahn.HahnSets.set_inter',axiom,
c_24__type__200___24t(chahn_2eHahnSets_2eset__inter) ).
fof('$_typeof_hahn.HahnSets.set_map',axiom,
c_24__type__31864___24t(chahn_2eHahnSets_2eset__map) ).
fof('$_typeof_hahn.HahnSets.set_subset',axiom,
c_24__type__7491___24t(chahn_2eHahnSets_2eset__subset) ).
fof('$_typeof_hahn.HahnSets.set_union',axiom,
c_24__type__200___24t(chahn_2eHahnSets_2eset__union) ).
fof('$_typeof_r',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr) ).
fof('$_typeof_r\'',axiom,
cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,cr_27) ).
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.PeanoNat.Nat.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).
fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
=> ( V0__n = V1__m
=> p(cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.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_succ_l',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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m))
<=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__346,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__273,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_exists_pred',axiom,
! [V0__z] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__z)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__z,V1__n))
=> ? [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
& V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(V3__k)
& p(cCoq_2eInit_2ePeano_2ele___24a2(V0__z,V3__k)) ) ) ) ) ).
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_succ_l',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(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),V1__m))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.lt_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__346,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__273,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_1_r',axiom,
! [V0__a] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__a)
=> cCoq_2eInit_2eNat_2emodulo___24a2(V0__a,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) = cCoq_2eInit_2eDatatypes_2eO ) ).
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.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__33066___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33066___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3467___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.Arith.PeanoNat.Nat.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34370___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__34381___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__33066___24a1(V0__A),c_24__type__2563___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,c_24__type__3467___24a1(V0__A),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,V0__A,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),V1__Aeq))),cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A)) ) ) ).
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.Init.Datatypes.nat_ind',axiom,
! [V0__P] :
( c_24__type__273___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_O',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> V0__n = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eO) ) ).
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__2968___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.Wf.Acc_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( c_24__type__90___24t(V0__A,V1__R)
=> ! [V2__P] :
( c_24__type__7___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__90___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.NoDup_ind',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__3198___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.Logic.ClassicalDescription.unique_choice',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__R] :
( c_24__type__8654___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__33274___24a4(V0__A,V1__B,V2__R,V3__x))) )
=> ? [V4__f] :
( c_24__type__57___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('Coq.Logic.Classical_Prop.NNPP',axiom,
! [V0__p] :
( cProp___24t(V0__p)
=> ( ~ ~ p(V0__p)
=> p(V0__p) ) ) ).
fof('Coq.Logic.Classical_Prop.classic',axiom,
! [V0__P] :
( cProp___24t(V0__P)
=> ( p(V0__P)
| ~ p(V0__P) ) ) ).
fof('Coq.Logic.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__2532___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__2533___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__2531___24a2(V0__A,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_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_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.NArith.BinNat.N.eq_equiv',axiom,
cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).
fof('Coq.NArith.BinNat.N.eq_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( V0__n = V1__m
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.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_succ_l',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n),V1__m)
<=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.le_wd',axiom,
cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31260,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__31266,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_le_incl',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> ! [V1__m] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
=> ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).
fof('Coq.NArith.BinNat.N.lt_succ_diag_r',axiom,
! [V0__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n)) ) ).
fof('Coq.NArith.BinNat.N.peano_ind',axiom,
! [V0__P] :
( c_24__type__31266___24t(V0__P)
=> ( p(happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ( ! [V2__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
=> ( p(happ(V0__P,V2__n))
=> p(happ(V0__P,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V2__n))) ) )
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> p(happ(V0__P,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.peano_rect_succ',axiom,
! [V0__P] :
( c_24__type__34271___24t(V0__P)
=> ! [V1__a] :
( t(V1__a,happ(V0__P,cCoq_2eNumbers_2eBinNums_2eN0))
=> ! [V2__f] :
( c_24__type__34281___24t(V0__P,V2__f)
=> ! [V3__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V3__n)
=> cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V3__n)) = happ(happ(V2__f,V3__n),cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V0__P,V1__a,V2__f,V3__n)) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_succ',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> ! [V2__a] :
( t(V2__a,V0__A)
=> ! [V3__f] :
( c_24__type__33046___24t(V0__A,V3__f)
=> ( p(happ(happ(V1__Aeq,V2__a),V2__a))
=> ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33046___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__3467___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),V3__f)
=> ! [V6__n] :
( cCoq_2eNumbers_2eBinNums_2eN___24t(V6__n)
=> p(happ(happ(V1__Aeq,cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V6__n))),happ(happ(V3__f,V6__n),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V0__A,V2__a,V3__f,V6__n)))) ) ) ) ) ) ) ) ).
fof('Coq.NArith.BinNat.N.recursion_wd',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__Aeq] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__Aeq)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34296___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,c_24__type__34307___24a1(V0__A),V1__Aeq,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__33046___24a1(V0__A),c_24__type__34316___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,c_24__type__3467___24a1(V0__A),c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,V0__A,V1__Aeq,V1__Aeq)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eNumbers_2eBinNums_2eN,V0__A,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN),V1__Aeq))),cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A)) ) ) ).
fof('Coq.Relations.Operators_Properties.clos_r_clos_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V0__A,V1__R),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__R))) ) ) ).
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__7___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__7___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)
=> p(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_rst1n_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__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_rst_rstn1_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__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_clos_rst',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> p(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__sym__trans___24a2(V0__A,V1__R))) ) ) ).
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)
=> p(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__7___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__7___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__7___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__90___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__90___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__90___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__7___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__7___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__90___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__90___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__90___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__90___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__7___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__7___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__90___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__90___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__90___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__90___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__7___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__7___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__90___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__57___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__32402___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.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_sub',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(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___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_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_minus2',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(V1__m,V0__n))
=> cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2esub___24a2(V0__n,V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).
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.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.OMEGA5',axiom,
! [V0__x] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
=> ! [V1__y] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
=> ! [V2__z] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
=> ( V0__x = cCoq_2eNumbers_2eBinNums_2eZ0
=> ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
=> 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_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__2905___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__2905___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__2905___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__2905___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__2905___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__2905___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__2905___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__2905___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__2905___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__2905___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__2905___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_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__2905___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__2905___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('HahnPath.PathAbsorb.minus_seq_l',axiom,
! [V0__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__r)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__r_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,V0__r)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V0__r,V1__r_27),V0__r),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V0__r,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(cA,V1__r_27,V0__r)))) ) ) ) ).
fof('HahnPath.PathAbsorb.path_absorb',axiom,
! [V0__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__r)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__r_27)
=> ( ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V0__r))
| p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V1__r_27)) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,V0__r,V1__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27)))) ) ) ) ).
fof('HahnPath.PathAbsorb.path_absorb1',axiom,
! [V0__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__r)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__r_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V1__r_27))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,V0__r,V1__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27)))) ) ) ) ).
fof('HahnPath.PathAbsorb.path_absorb2',axiom,
! [V0__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__r)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__r_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V0__r))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,V0__r,V1__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27)))) ) ) ) ).
fof('HahnPath.PathAbsorb.path_absorb_lt',axiom,
! [V0__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__r)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__r_27)
=> ( ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V0__r))
| p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V1__r_27)) )
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,V0__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,V0__r,V1__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V1__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V0__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,V1__r_27)))) ) ) ) ) ).
fof('HahnPath.PathAbsorb.path_absorb_rt',axiom,
! [V0__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V0__r)
=> ! [V1__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(cA,V1__r_27)
=> ( ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V0__r))
| p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,V1__r_27,V0__r),V1__r_27)) )
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,V1__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,V0__r,V1__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(cA,V0__r),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(cA,V0__r),V1__r_27))) ) ) ) ) ).
fof('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('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('HahnPath.ct_union_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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b))
=> 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_2esingl__rel___24a3(V0__A,V2__a,V3__b)))) ) ) ) ) ) ).
fof('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__7___24t(V0__A,V2__dom)
=> ! [V3__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r_27)
=> ( p(chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V2__dom,V3__r_27))
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V3__r_27,V2__dom))
=> ( p(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('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('HahnPath.rt_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__refl__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__refl__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('HahnPath.rt_union_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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__b))
=> 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,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)))) ) ) ) ) ) ).
fof('T',axiom,
cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(cA,cr_27) ).
fof('hahn.HahnDom.acyc_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__7___24t(V0__A,V2__d)
=> ! [V3__e] :
( c_24__type__7___24t(V0__A,V3__e)
=> ( p(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__e)),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__e))))))
=> ( p(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__e)),c_24__lam__13___24a1(V0__A)))
=> ! [V6__dd] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__dd)
=> ( V6__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)))
=> ! [V8__de] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__de)
=> ( V8__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__e)))
=> ! [V10__ed] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V10__ed)
=> ( V10__ed = chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__e),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d)))
=> ! [V12__ee] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V12__ee)
=> ( V12__ee = chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__e),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__e)))
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V6__dd))
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V12__ee))
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V10__ed,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V8__de,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee))))))
=> p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.codom_cr',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,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnSets_2eset__full___24a1(V0__A)) ) ) ).
fof('hahn.HahnDom.codom_crt',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__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnSets_2eset__full___24a1(V0__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.codom_eqv1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d))),chahn_2eHahnSets_2eset__inter___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),V2__d)) ) ) ) ).
fof('hahn.HahnDom.codom_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_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnDom.codom_rel_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),V2__d)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d))) ) ) ) ) ).
fof('hahn.HahnDom.codom_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_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V2__r_27)) ) ) ) ).
fof('hahn.HahnDom.codom_transp',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_2etransp___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnDom.codom_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_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnSets_2eset__union___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V2__r_27))) ) ) ) ).
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__7___24t(V0__A,V2__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> p(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__7___24t(V0__A,V2__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),V2__d)) ) ) ) ) ).
fof('hahn.HahnDom.dom_codom_rel_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),V2__d)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r),V3__d_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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)))) ) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_cond_elim',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnDom_2edom__cond___24a3(V0__A,V1__r,V2__d))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r))) ) ) ) ).
fof('hahn.HahnDom.dom_cond_elim1',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__7___24t(V0__A,V3__d)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnDom_2edom__cond___24a3(V0__A,V2__r_27,V3__d))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),V1__r))) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_cond_elim2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V3__d_27,chahn_2eHahnDom_2edom__cond___24a3(V0__A,V1__r,V2__d)),chahn_2eHahnDom_2edom__cond___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27),V1__r),V2__d)) ) ) ) ) ).
fof('hahn.HahnDom.dom_cond_in',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__7___24t(V0__A,V3__d)
=> ! [V4__d_27] :
( c_24__type__7___24t(V0__A,V4__d_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),V2__r_27)))
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,V4__d_27,chahn_2eHahnDom_2edom__cond___24a3(V0__A,V1__r,V3__d)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_cond_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33394___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__33401___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A))),chahn_2eHahnDom_2edom__cond___24a1(V0__A)) ) ).
fof('hahn.HahnDom.dom_cond_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> ! [V4__x] :
( c_24__type__7___24t(V0__A,V4__x)
=> ! [V5__y] :
( c_24__type__7___24t(V0__A,V5__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V4__x,V5__y)
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnDom_2edom__cond___24a3(V0__A,V1__x,V4__x),chahn_2eHahnDom_2edom__cond___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_cond_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33394___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__33401___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_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A))),chahn_2eHahnDom_2edom__cond___24a1(V0__A)) ) ).
fof('hahn.HahnDom.dom_cond_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__d] :
( c_24__type__7___24t(V0__A,V3__d)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnDom_2edom__cond___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27),V3__d),chahn_2eHahnSets_2eset__inter___24a3(V0__A,chahn_2eHahnDom_2edom__cond___24a3(V0__A,V1__r,V3__d),chahn_2eHahnDom_2edom__cond___24a3(V0__A,V2__r_27,V3__d))) ) ) ) ) ).
fof('hahn.HahnDom.dom_cr',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,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnSets_2eset__full___24a1(V0__A)) ) ) ).
fof('hahn.HahnDom.dom_crt',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__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnSets_2eset__full___24a1(V0__A)) ) ) ).
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.dom_eqv1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r)),chahn_2eHahnSets_2eset__inter___24a3(V0__A,V2__d,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r))) ) ) ) ).
fof('hahn.HahnDom.dom_helper_1',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,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)))))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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)))) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_helper_2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,c_24__lam__33348___24a1(V0__A),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)))))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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)))) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_helper_3',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V2__d,V3__d_27)))
<=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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)))) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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))))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r)) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_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_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnDom.dom_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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))))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27))) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_rel_eqv_codom_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)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V2__r_27)))),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r_27)))) ) ) ) ).
fof('hahn.HahnDom.dom_rel_eqv_dom_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)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V2__r_27)))),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ).
fof('hahn.HahnDom.dom_rel_ext',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_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27))),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnDom.dom_rel_fun_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__w] :
( t(V2__w,V0__A)
=> chahn_2eHahnSets_2eset__equiv___24a3(V0__A,c_24__lam__32097___24a3(V0__A,V1__r,V2__w),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__w))))) ) ) ) ).
fof('hahn.HahnDom.dom_rel_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),V2__d)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r)) ) ) ) ) ).
fof('hahn.HahnDom.dom_rel_helper_in',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),V2__d)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r))) ) ) ) ) ).
fof('hahn.HahnDom.dom_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_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnDom.dom_to_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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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))))
=> p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d)) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_to_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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,V1__r,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))))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d_27)) ) ) ) ) ) ).
fof('hahn.HahnDom.dom_transp',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_2etransp___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__r)) ) ) ).
fof('hahn.HahnDom.dom_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_2eHahnSets_2eset__equiv___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnSets_2eset__union___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.HahnDom.doma_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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_fold',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(happ(V2__d,V5__a))
=> p(happ(V3__d_27,V5__a)) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27),V1__r),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnDom.doma_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r)))
<=> p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___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)) ) )
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d_27)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.doma_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V2__d,V3__d_27)))
<=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
& p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d_27)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.doma_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7184___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),cProp,chahn_2eHahnSets_2eset__equiv___24a1(V0__A),c_3c_3d_3e)),chahn_2eHahnDom_2edoma___24a1(V0__A)) ) ).
fof('hahn.HahnDom.doma_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> ! [V4__x] :
( c_24__type__7___24t(V0__A,V4__x)
=> ! [V5__y] :
( c_24__type__7___24t(V0__A,V5__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__x,V4__x),chahn_2eHahnDom_2edoma___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.doma_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7184___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_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),cProp,chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl)),chahn_2eHahnDom_2edoma___24a1(V0__A)) ) ).
fof('hahn.HahnDom.doma_rewrite',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V1__r))) ) ) ) ) ).
fof('hahn.HahnDom.domab_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,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)))))
<=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
& p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d_27)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domab_helper2',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__57___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__57___24t(V0__A,V1__B,V4__g)
=> ! [V5__d] :
( c_24__type__308___24t(V0__A,V1__B,V5__d)
=> ! [V6__d_27] :
( c_24__type__308___24t(V0__A,V1__B,V6__d_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V5__d,V6__d_27)))
<=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V2__r,V5__d))
& p(chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r,V6__d_27)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domb_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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_fold',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> ( ! [V5__a] :
( t(V5__a,V0__A)
=> ( p(happ(V2__d,V5__a))
=> p(happ(V3__d_27,V5__a)) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domb_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d))))
<=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___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)) ) )
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d_27)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domb_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V2__d,V3__d_27)))
<=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
& p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d_27)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domb_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7184___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),cProp,chahn_2eHahnSets_2eset__equiv___24a1(V0__A),c_3c_3d_3e)),chahn_2eHahnDom_2edomb___24a1(V0__A)) ) ).
fof('hahn.HahnDom.domb_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> ! [V4__x] :
( c_24__type__7___24t(V0__A,V4__x)
=> ! [V5__y] :
( c_24__type__7___24t(V0__A,V5__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V4__x,V5__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__x,V4__x),chahn_2eHahnDom_2edomb___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.domb_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__7179___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7184___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_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),cProp,chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl)),chahn_2eHahnDom_2edomb___24a1(V0__A)) ) ).
fof('hahn.HahnDom.domb_rewrite',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d)))) ) ) ) ) ).
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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(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))))))
=> ( p(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__13___24a1(V0__A)))
=> ( p(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)))))
=> ( p(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)))))
=> p(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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d))
=> p(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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V3__d)) ) ) ) ) ) ).
fof('hahn.HahnDom.path_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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(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))))))
=> ( p(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__13___24a1(V0__A)))
=> ! [V6__dd] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__dd)
=> ( V6__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)))
=> ! [V8__de] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__de)
=> ( V8__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)))
=> ! [V10__ed] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V10__ed)
=> ( V10__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)))
=> ! [V12__ee] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V12__ee)
=> ( V12__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)))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(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,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V6__dd),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,V6__dd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V8__de,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee),V10__ed)))),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V12__ee),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,V12__ee),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V10__ed,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd),V8__de)))),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V10__ed,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd),V8__de)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V10__ed,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd))))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V8__de,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee),V10__ed)))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V8__de,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnDom.path_dom_same',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(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))))))
=> ( p(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__13___24a1(V0__A)))
=> ! [V6__dd] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__dd)
=> ( V6__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)))
=> ! [V8__de] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V8__de)
=> ( V8__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)))
=> ! [V10__ed] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V10__ed)
=> ( V10__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)))
=> ! [V12__ee] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V12__ee)
=> ( V12__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)))
=> p(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_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d))),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V6__dd),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,V6__dd),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V8__de,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V12__ee),V10__ed)))),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V6__dd))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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__7___24t(V0__A,V2__d)
=> p(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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> p(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__7___24t(V0__A,V2__d)
=> p(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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> p(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__57___24t(V0__A,V1__B,V3__f)
=> ! [V4__d] :
( c_24__type__308___24t(V0__A,V1__B,V4__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V2__r,V4__d))
=> p(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__57___24t(V0__A,V1__B,V3__f)
=> ! [V4__d] :
( c_24__type__308___24t(V0__A,V1__B,V4__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r,V4__d))
=> p(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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d))
=> p(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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r_27,V3__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V3__d)) ) ) ) ) ) ).
fof('hahn.HahnDom.seq_eqv_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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27),V1__r),V2__d)) ) ) ) ) ) ).
fof('hahn.HahnDom.seq_eqv_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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d_27)),V2__d)) ) ) ) ) ) ).
fof('hahn.HahnDom.seq_r_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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d))
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V2__r_27,V3__d))
=> p(chahn_2eHahnDom_2edoma___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__r_27),V3__d)) ) ) ) ) ) ) ).
fof('hahn.HahnDom.seq_r_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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d))
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r_27,V3__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,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__7___24t(V0__A,V2__d)
=> ! [V3__d_27] :
( c_24__type__7___24t(V0__A,V3__d_27)
=> ( p(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)))
=> p(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.transp_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__7___24t(V0__A,V2__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edoma___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),V2__d)) ) ) ) ) ).
fof('hahn.HahnDom.transp_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__7___24t(V0__A,V2__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V2__d))
=> p(chahn_2eHahnDom_2edomb___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),V2__d)) ) ) ) ) ).
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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V1__r,V3__d))
=> ( p(chahn_2eHahnDom_2edoma___24a3(V0__A,V2__r_27,V3__d))
=> p(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__7___24t(V0__A,V3__d)
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V1__r,V3__d))
=> ( p(chahn_2eHahnDom_2edomb___24a3(V0__A,V2__r_27,V3__d))
=> p(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__7___24t(V0__A,V2__f)
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r))
<=> ( p(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)
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__r))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r))
=> p(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__17___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',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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.acyclic_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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)
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)))
<=> p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r))) ) ) ) ) ).
fof('hahn.HahnEquational.add_dom_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__s] :
( c_24__type__7___24t(V0__A,V2__s)
=> ! [V3__s_27] :
( c_24__type__7___24t(V0__A,V3__s_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),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,V2__s)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.add_dom_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ! [V2__s] :
( c_24__type__7___24t(V0__A,V2__s)
=> ! [V3__s_27] :
( c_24__type__7___24t(V0__A,V3__s_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s))))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),V1__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_empty',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__rr] :
( c_24__type__31774___24t(V0__B,V1__A,V2__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,chahn_2eHahnSets_2eset__empty___24a1(V0__B),V2__rr),c_24__lam__33759___24a2(V0__B,V1__A)) ) ) ) ).
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__31774___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.bunion_inter_compat_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__7___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__31774___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__33772___24a4(V0__B,V1__A,V3__r,V4__rr)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__A,V3__r,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr))) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_inter_compat_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__7___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__31774___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__33783___24a4(V0__B,V1__A,V3__r,V4__rr)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr),V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_minus_compat_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__7___24t(V0__B,V2__s)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__A,V3__r)
=> ! [V4__rr] :
( c_24__type__31774___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__33794___24a4(V0__B,V1__A,V3__r,V4__rr)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr),V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33526___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__33536___24a2(V0__A,V1__B),chahn_2eHahnSets_2eset__equiv___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__31774___24a2(V0__A,V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),c_3d___24a1(c_24__type__31774___24a2(V0__A,V1__B)),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ebunion___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.bunion_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__7___24t(V0__A,V2__x)
=> ! [V3__y] :
( c_24__type__7___24t(V0__A,V3__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V2__x,V3__y)
=> ! [V5__x] :
( c_24__type__31774___24t(V0__A,V1__B,V5__x)
=> ! [V6__y] :
( c_24__type__31774___24t(V0__A,V1__B,V6__y)
=> ( V5__x = V6__y
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__y,V6__y))) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33526___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__33536___24a2(V0__A,V1__B),chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__31774___24a2(V0__A,V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),c_3d___24a1(c_24__type__31774___24a2(V0__A,V1__B)),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ebunion___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.bunion_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__7___24t(V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__308___24t(V0__A,V1__B,V3__s)
=> ! [V4__rr] :
( c_24__type__31774___24t(V0__A,V1__B,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__33874___24a4(V0__A,V1__B,V2__f,V4__rr)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V1__B,V2__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__33880___24a3(V0__A,V1__B,V4__rr)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_union_l',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__7___24t(V0__B,V2__s)
=> ! [V3__s_27] :
( c_24__type__7___24t(V0__B,V3__s_27)
=> ! [V4__rr] :
( c_24__type__31774___24t(V0__B,V1__A,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,chahn_2eHahnSets_2eset__union___24a3(V0__B,V2__s,V3__s_27),V4__rr),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V3__s_27,V4__rr))) ) ) ) ) ) ).
fof('hahn.HahnEquational.bunion_union_r',axiom,
! [V0__B] :
( cType___24t(V0__B)
=> ! [V1__A] :
( cType___24t(V1__A)
=> ! [V2__s] :
( c_24__type__7___24t(V0__B,V2__s)
=> ! [V3__rr] :
( c_24__type__31774___24t(V0__B,V1__A,V3__rr)
=> ! [V4__rr_27] :
( c_24__type__31774___24t(V0__B,V1__A,V4__rr_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,c_24__lam__33148___24a4(V0__B,V1__A,V3__rr,V4__rr_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__A,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V3__rr),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__B,V1__A,V2__s,V4__rr_27))) ) ) ) ) ) ).
fof('hahn.HahnEquational.clos_refl_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__y))) ) ) ) ) ).
fof('hahn.HahnEquational.clos_refl_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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_sym_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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__sym___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_refl_sym_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V2__y))) ) ) ) ) ).
fof('hahn.HahnEquational.clos_refl_sym_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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__sym___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__31___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',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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__y))) ) ) ) ) ).
fof('hahn.HahnEquational.clos_refl_trans_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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__31___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_sym_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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__sym___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.clos_sym_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__y))) ) ) ) ) ).
fof('hahn.HahnEquational.clos_sym_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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__sym___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)
=> ( p(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)
=> ( p(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)
=> ( p(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_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> p(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__31___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__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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.codom_rel_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2ecodom__rel___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.codom_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),chahn_2eHahnSets_2eset__subset___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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r)))
=> p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__57___24t(V0__A,V1__B,V3__f)
=> ! [V4__s] :
( c_24__type__34016___24t(V0__A,V1__B,V2__C,V4__s)
=> ! [V5__rr] :
( c_24__type__34021___24t(V0__A,V1__B,V2__C,V5__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V2__C,V0__A,V4__s,c_24__lam__34030___24a4(V0__A,V1__B,V2__C,V5__rr))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V2__C,V1__B,V4__s,c_24__lam__34043___24a5(V0__A,V1__B,V2__C,V3__f,V5__rr))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__57___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__8009___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V2__C,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V2__C,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V1__B,V2__C,V4__g,V3__f),V5__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V1__B,V2__C,V4__g,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__f,V5__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V3__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r)))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_crt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> p(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_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r)))
=> p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V3__r)) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27)),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V3__r,V4__r_27)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33557___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__57___24a2(V0__A,V1__B),c_24__type__33565___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__57___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ecollect__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.collect_rel_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__57___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__57___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__y)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V5__x,V6__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V3__y,V6__y))) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33557___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__57___24a2(V0__A,V1__B),c_24__type__33565___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__57___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V1__B))),chahn_2eHahnRelationsBasic_2ecollect__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.collect_rel_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V3__r)),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.collect_rel_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___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_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V3__r,V4__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__B,chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V3__r),chahn_2eHahnRelationsBasic_2ecollect__rel___24a4(V0__A,V1__B,V2__f,V4__r_27))) ) ) ) ) ) ).
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__31589___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_helper',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__7___24t(V0__A,V3__d)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(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,V3__d),V2__r_27)))
=> p(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_2eeqv__rel___24a2(V0__A,V3__d)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)))) ) ) ) ) ) ).
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_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,chahn_2eHahnRelationsBasic_2eclos__refl___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.cr_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,chahn_2eHahnRelationsBasic_2eclos__refl___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.cr_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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___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,V1__r,V2__r_27))) ) ) ) ).
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.cr_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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),V2__r_27)) ) ) ) ).
fof('hahn.HahnEquational.cr_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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.cross_inter_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,V2__s_27)
=> ! [V3__s_27_27] :
( c_24__type__7___24t(V0__A,V3__s_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V1__s,V2__s_27),V3__s_27_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V2__s_27,V3__s_27_27))) ) ) ) ) ).
fof('hahn.HahnEquational.cross_inter_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,V2__s_27)
=> ! [V3__s_27_27] :
( c_24__type__7___24t(V0__A,V3__s_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V2__s_27,V3__s_27_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__s_27_27))) ) ) ) ) ).
fof('hahn.HahnEquational.cross_minus_compl_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,V2__s_27)
=> ! [V3__s_27_27] :
( c_24__type__7___24t(V0__A,V3__s_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,chahn_2eHahnSets_2eset__compl___24a2(V0__A,V1__s),V3__s_27_27)),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27)) ) ) ) ) ).
fof('hahn.HahnEquational.cross_minus_compl_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,V2__s_27)
=> ! [V3__s_27_27] :
( c_24__type__7___24t(V0__A,V3__s_27_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V3__s_27_27,chahn_2eHahnSets_2eset__compl___24a2(V0__A,V2__s_27))),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__s,V2__s_27)) ) ) ) ) ).
fof('hahn.HahnEquational.cross_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__7___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__7___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V1__x,V2__y)
=> ! [V4__x] :
( c_24__type__7___24t(V0__A,V4__x)
=> ! [V5__y] :
( c_24__type__7___24t(V0__A,V5__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V4__x,V5__y)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V0__A,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.cross_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33649___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__33633___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2ecross__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.crsE',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__sym___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___24a1(V0__A)),V1__r),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.crs_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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V2__r_27)))) ) ) ) ).
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.crs_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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a2(V0__A,V2__r_27))) ) ) ) ).
fof('hahn.HahnEquational.crt_double',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_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V1__r)))) ) ) ).
fof('hahn.HahnEquational.csE',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__sym___24a2(V0__A,V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.cs_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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V2__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__r_27)))) ) ) ) ).
fof('hahn.HahnEquational.cs_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,V2__r)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__s,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__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.cs_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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V1__r),chahn_2eHahnRelationsBasic_2eclos__sym___24a2(V0__A,V2__r_27))) ) ) ) ).
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__33091___24a1(V0__A),c_24__lam__33800___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)
=> p(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)
=> ( p(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__3___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)
=> ( p(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__3___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__31___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)
=> ( p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V6__k)),V4__r_27)) ) )
=> p(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__31___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__x] :
( c_24__type__90___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)
=> ( p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V8__k),V6__r_27))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V4__r,V8__k)),V6__r_27)) ) )
=> p(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__31___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)
=> ( p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__k,V3__r)),V4__r_27)) ) )
=> p(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)
=> p(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)
=> p(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__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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.dom_rel_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> chahn_2eHahnSets_2eset__subset___24a3(V0__A,chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2edom__rel___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.dom_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A)),chahn_2eHahnRelationsBasic_2edom__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.eqv_rel_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__7___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__7___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__subset___24a3(V0__A,V1__x,V2__y)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__y))) ) ) ) ) ).
fof('hahn.HahnEquational.eqv_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33633___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.fun_seq_minus_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__S] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__S)
=> ! [V3__T] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__T)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__R))
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__S,V3__T)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,V2__S),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,V3__T))) ) ) ) ) ) ).
fof('hahn.HahnEquational.functional_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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),cCoq_2eProgram_2eBasics_2eimpl),chahn_2eHahnRelationsBasic_2efunctional___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.functional_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.functional_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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_2efunctional___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__31___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__31___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__31658___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__31628___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__31625___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.good_ctx_seq_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__31___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__31634___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__31___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__31640___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__31___24t(V0__A,V1__P)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V1__P)
=> ! [V3__Q] :
( c_24__type__31___24t(V0__A,V3__Q)
=> ( chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,V3__Q)
=> chahn_2eHahnEquational_2egood__ctx___24a2(V0__A,c_24__lam__31649___24a3(V0__A,V1__P,V3__Q)) ) ) ) ) ) ).
fof('hahn.HahnEquational.id_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,V2__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V1__s,V2__s_27)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s_27))) ) ) ) ).
fof('hahn.HahnEquational.id_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,V2__s_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__union___24a3(V0__A,V1__s,V2__s_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__s_27))) ) ) ) ).
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.immediate_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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_2eimmediate___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inclusion_ct_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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',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)
=> ! [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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V4__x))
<=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__17___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_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_2eProgram_2eBasics_2eflip___24a6(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),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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__x,V5__y))
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V4__x),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inclusion_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__22___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__17___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_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)),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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27)))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27))
=> p(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_rel_relation',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___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__7___24t(V0__A,V2__dom)
=> p(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__7___24t(V0__A,V2__dom)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> ( p(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)))
=> p(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)
=> ( p(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)))
=> p(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)
=> ( p(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)
=> ( p(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__13___24a1(V0__A),V1__r),c_24__lam__13___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__13___24a1(V0__A)),c_24__lam__13___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)
=> p(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__13___24a1(V0__A))
<=> p(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_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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_2einter__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.inter_rel_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__x,V5__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.inter_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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_2einter__rel___24a1(V0__A)) ) ).
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)
=> p(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.inter_union_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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r1,V3__r2),V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r1,V1__r),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V3__r2,V1__r))) ) ) ) ) ).
fof('hahn.HahnEquational.inter_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_2einter__rel___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_2einter__rel___24a3(V0__A,V1__r,V2__r1),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r,V3__r2))) ) ) ) ) ).
fof('hahn.HahnEquational.irreflexive_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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',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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__x),chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.irreflexive_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33495___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__17___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',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__7___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__7___24t(V0__A,V2__y)
=> ( cCoq_2eProgram_2eBasics_2eflip___24a6(c_24__type__7___24a1(V0__A),c_24__type__7___24a1(V0__A),cProp,chahn_2eHahnSets_2eset__subset___24a1(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__x,V5__y))
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(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_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33495___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__17___24a1(V0__A),cCoq_2eProgram_2eBasics_2eflip___24a4(c_24__type__7___24a1(V0__A),c_24__type__7___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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V1__B,V3__r))
=> p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_compose',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__C] :
( cType___24t(V2__C)
=> ! [V3__f] :
( c_24__type__57___24t(V0__A,V1__B,V3__f)
=> ! [V4__g] :
( c_24__type__8009___24t(V0__A,V1__B,V2__C,V4__g)
=> ! [V5__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V2__C,V5__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V2__C,cCoq_2eProgram_2eBasics_2ecompose___24a5(V0__A,V1__B,V2__C,V4__g,V3__f),V5__r),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V3__f,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V1__B,V2__C,V4__g,V5__r))) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___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,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V1__B,V3__r)))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_crt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__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__refl__trans___24a2(V1__B,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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> p(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_eqv',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__d] :
( c_24__type__31783___24t(V0__A,V1__B,V3__d)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__map___24a4(V0__A,V1__B,V2__f,V3__d)),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V1__B,V3__d)))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V1__B,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(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,V4__r_27))) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_irr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V1__B,V3__r))
=> p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V1__B,V3__r,V4__r_27)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(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,V4__r_27))) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33475___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__57___24a2(V0__A,V1__B),c_24__type__33483___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__57___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A))),chahn_2eHahnRelationsBasic_2emap__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.map_rel_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__57___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__57___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V6__y)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__B,V5__x,V6__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V3__y,V6__y))) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33475___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__57___24a2(V0__A,V1__B),c_24__type__33483___24a2(V0__A,V1__B),c_3d___24a1(c_24__type__57___24a2(V0__A,V1__B)),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V1__B),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A))),chahn_2eHahnRelationsBasic_2emap__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.map_rel_seq',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(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,V4__r_27)),chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V1__B,V3__r,V4__r_27)))) ) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_transp',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V1__B,V3__r)),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.map_rel_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V3__r)
=> ! [V4__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V1__B,V4__r_27)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2emap__rel___24a4(V0__A,V1__B,V2__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V1__B,V3__r,V4__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(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,V4__r_27))) ) ) ) ) ) ).
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__13___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)
=> ( p(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__13___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnEquational.minus_eqv_rel_helper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__R] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__R)
=> ! [V2__T] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__T)
=> ! [V3__d1] :
( c_24__type__7___24t(V0__A,V3__d1)
=> ! [V4__d2] :
( c_24__type__7___24t(V0__A,V4__d2)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__R,V2__T),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d2))),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d1),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__R,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__d2))),V2__T)) ) ) ) ) ) ).
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__13___24a1(V0__A),V1__r),c_24__lam__13___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__13___24a1(V0__A)),V1__r) ) ) ).
fof('hahn.HahnEquational.minus_rel_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)
=> ! [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)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.minus_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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',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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___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_2eProgram_2eBasics_2eflip___24a6(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),V4__x,V5__y)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.minus_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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_nm',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
=> ! [V2__m] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
=> ! [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,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V3__r,V1__n),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V3__r,V2__m)),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V3__r,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m))) ) ) ) ) ).
fof('hahn.HahnEquational.pow_rel_more_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33513___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_24__type__33194___24a1(V0__X),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__X))),chahn_2eHahnRelationsBasic_2epow__rel___24a1(V0__X)) ) ).
fof('hahn.HahnEquational.pow_rel_mori',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__x)
=> ! [V2__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V2__y)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__X,V1__x,V2__y))
=> ! [V4__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V4__x)
=> ! [V5__y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V5__y)
=> ( V4__x = V5__y
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__X,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__X,V1__x,V4__x),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__X,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.pow_rel_mori_Proper',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33513___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_24__type__33194___24a1(V0__X),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__X),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__X),c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__X))),chahn_2eHahnRelationsBasic_2epow__rel___24a1(V0__X)) ) ).
fof('hahn.HahnEquational.pow_rt',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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V1__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V1__A,V2__r,V0__n),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V1__A,V2__r))) ) ) ) ).
fof('hahn.HahnEquational.pow_seq',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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,V1__n),V2__r),chahn_2eHahnRelationsBasic_2epow__rel___24a3(V0__A,V2__r,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__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)
=> p(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.pow_unit',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_2epow__rel___24a3(V0__A,V1__r,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)),V1__r) ) ) ).
fof('hahn.HahnEquational.restrC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__7___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_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__7___24t(V1__B,V2__f)
=> ! [V3__s] :
( c_24__type__308___24t(V0__A,V1__B,V3__s)
=> ! [V4__rr] :
( c_24__type__31774___24t(V0__A,V1__B,V4__rr)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V1__B,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V1__B,V2__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__33849___24a3(V0__A,V1__B,V4__rr))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V1__B,V3__s,c_24__lam__33859___24a4(V0__A,V1__B,V2__f,V4__rr))) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_ct',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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_bunion',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__B] :
( cType___24t(V2__B)
=> ! [V3__rr] :
( c_24__type__31774___24t(V0__A,V2__B,V3__rr)
=> ! [V4__C] :
( cType___24t(V4__C)
=> ! [V5__f] :
( c_24__type__8009___24t(V0__A,V2__B,V4__C,V5__f)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V2__B,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V2__B,V4__C,V5__f,chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V2__B,V1__s,c_24__lam__33898___24a4(V0__A,V2__B,V3__rr,V4__C))),chahn_2eHahnRelationsBasic_2ebunion___24a4(V0__A,V2__B,V1__s,c_24__lam__33910___24a5(V0__A,V2__B,V3__rr,V4__C,V5__f))) ) ) ) ) ) ) ).
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__57___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_eq_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33455___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__57___24a2(V0__A,V1__B),c_24__type__31___24a1(V0__A),c_3d___24a1(c_24__type__57___24a2(V0__A,V1__B)),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_2erestr__eq__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.restr_eq_rel_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__x] :
( c_24__type__57___24t(V0__A,V1__B,V2__x)
=> ! [V3__y] :
( c_24__type__57___24t(V0__A,V1__B,V3__y)
=> ( V2__x = V3__y
=> ! [V5__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V5__x)
=> ! [V6__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__y)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V5__x,V6__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__x,V5__x),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V3__y,V6__y))) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_eq_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33455___24a2(V0__A,V1__B),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__57___24a2(V0__A,V1__B),c_24__type__31___24a1(V0__A),c_3d___24a1(c_24__type__57___24a2(V0__A,V1__B)),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_2erestr__eq__rel___24a2(V0__A,V1__B)) ) ) ).
fof('hahn.HahnEquational.restr_eq_seq_eqv_l',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__57___24t(V0__A,V2__B,V3__f)
=> ! [V4__dom] :
( c_24__type__308___24t(V0__A,V2__B,V4__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom),V1__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r))) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_eq_seq_eqv_r',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__57___24t(V0__A,V2__B,V3__f)
=> ! [V4__dom] :
( c_24__type__308___24t(V0__A,V2__B,V4__dom)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V2__B,V3__f,V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V4__dom))) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_eq_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__B] :
( cType___24t(V3__B)
=> ! [V4__f] :
( c_24__type__57___24t(V0__A,V3__B,V4__f)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V1__r),chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V3__B,V4__f,V2__r_27))) ) ) ) ) ) ).
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__31589___24a1(V0__A),V1__r),V1__r) ) ) ).
fof('hahn.HahnEquational.restr_inter',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r,V3__r_27)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27))) ) ) ) ) ).
fof('hahn.HahnEquational.restr_minus',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27))) ) ) ) ) ).
fof('hahn.HahnEquational.restr_minus_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),V3__r_27)) ) ) ) ) ).
fof('hahn.HahnEquational.restr_relE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,V2__r),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__d)))) ) ) ) ).
fof('hahn.HahnEquational.restr_rel_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33125___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__31___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___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_2erestr__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.restr_rel_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__x] :
( c_24__type__7___24t(V0__A,V1__x)
=> ! [V2__y] :
( c_24__type__7___24t(V0__A,V2__y)
=> ( chahn_2eHahnSets_2eset__subset___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__x,V5__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.restr_rel_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33125___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(c_24__type__7___24a1(V0__A),c_24__type__31___24a1(V0__A),chahn_2eHahnSets_2eset__subset___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_2erestr__rel___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.restr_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__d_27] :
( c_24__type__7___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,chahn_2eHahnSets_2eset__inter___24a3(V0__A,V2__d_27,V1__d),V3__r)) ) ) ) ) ).
fof('hahn.HahnEquational.restr_seq_compl_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__d] :
( c_24__type__7___24t(V0__A,V1__d)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__d,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnSets_2eset__compl___24a2(V0__A,V1__d)),V2__r)),c_24__lam__13___24a1(V0__A)) ) ) ) ).
fof('hahn.HahnEquational.restr_seq_eqv_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [V2__d] :
( c_24__type__7___24t(V0__A,V2__d)
=> ! [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__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),V3__r)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__d),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r))) ) ) ) ) ).
fof('hahn.HahnEquational.restr_seq_eqv_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ! [V3__d] :
( c_24__type__7___24t(V0__A,V3__d)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d))),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V3__d))) ) ) ) ) ).
fof('hahn.HahnEquational.restr_sym',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___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.restr_union',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r,V3__r_27)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27))) ) ) ) ) ).
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__31589___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__33091___24a1(V0__A),c_24__lam__33094___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__31589___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_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__refl__trans___24a2(V0__A,V1__r),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_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__31589___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__31___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___24a1(V0__A))),V4__r_27))
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V3__r,V6__k)),V4__r_27)) ) )
=> p(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_ind_right',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__P] :
( c_24__type__31___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___24a1(V0__A))),V4__r_27))
=> ( ! [V6__k] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V6__k)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,V6__k),V4__r_27))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V1__P,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V6__k,V3__r)),V4__r_27)) ) )
=> p(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)
=> p(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_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1(V0__A)) ) ).
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__7___24t(V0__B,V2__P)
=> ! [V3__rr] :
( c_24__type__31774___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__33730___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__308___24t(V0__B,V1__A,V3__P)
=> ! [V4__rr] :
( c_24__type__31774___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__33742___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__7___24t(V0__A,V1__doma)
=> ! [V2__domb] :
( c_24__type__7___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__7212___24a3(V0__A,V1__doma,V2__domb))) ) ) ) ).
fof('hahn.HahnEquational.seq_eqvC',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__doma] :
( c_24__type__7___24t(V0__A,V1__doma)
=> ! [V2__domb] :
( c_24__type__7___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__7___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_eqvK_l',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom1] :
( c_24__type__7___24t(V0__A,V1__dom1)
=> ! [V2__dom2] :
( c_24__type__7___24t(V0__A,V2__dom2)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V2__dom2,V3__x))
=> p(happ(V1__dom1,V3__x)) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom1),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom2)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom2)) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqvK_r',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom1] :
( c_24__type__7___24t(V0__A,V1__dom1)
=> ! [V2__dom2] :
( c_24__type__7___24t(V0__A,V2__dom2)
=> ( ! [V3__x] :
( t(V3__x,V0__A)
=> ( p(happ(V1__dom1,V3__x))
=> p(happ(V2__dom2,V3__x)) ) )
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom1),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V2__dom2)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom1)) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_inter_ll',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__7___24t(V0__A,V1__S)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S),V2__r),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r,V3__r_27))) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_inter_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__S] :
( c_24__type__7___24t(V0__A,V1__S)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S)),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V2__r,V3__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__S))) ) ) ) ) ).
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__7___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__7223___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__7___24t(V0__A,V2__dom1)
=> ! [V3__dom2] :
( c_24__type__7___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__54___24a4(V0__A,V1__r,V2__dom1,V3__dom2)) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_minus_ll',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),V2__r),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27))) ) ) ) ) ).
fof('hahn.HahnEquational.seq_eqv_minus_lr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s)),V3__r_27),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V2__r,V3__r_27),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__s))) ) ) ) ) ).
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__7___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__31669___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__13___24a1(V0__A),V1__r),c_24__lam__13___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__13___24a1(V0__A)),c_24__lam__13___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__31589___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__31589___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)
=> p(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',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)
=> ! [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)
=> cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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',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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__x,V5__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__x,V4__x),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.seq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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_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,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27),V1__r),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(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,V2__r_27,V1__r)))) ) ) ) ).
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.symmetricE',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)
<=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ) ).
fof('hahn.HahnEquational.symmetricEE',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_2esame__relation___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r)) ) ) ) ).
fof('hahn.HahnEquational.symmetric_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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_2esymmetric___24a1(V0__A)) ) ).
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__7___24t(V0__X,V2__dom)
=> ( p(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.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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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__17___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_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_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___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_inter',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_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,V1__r1,V2__r2)),chahn_2eHahnRelationsBasic_2einter__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2))) ) ) ) ).
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_minus',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_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r1,V2__r2)),chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2))) ) ) ) ).
fof('hahn.HahnEquational.transp_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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_2etransp___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.transp_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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__x,V2__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__x),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__y))) ) ) ) ) ).
fof('hahn.HahnEquational.transp_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__31___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_2etransp___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.transp_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_2etransp___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,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnEquational.transp_seq',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_2etransp___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r1,V2__r2)),chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1))) ) ) ) ).
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.transp_union',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_2etransp___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r1,V2__r2)),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r1),cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V2__r2))) ) ) ) ).
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)
=> ( p(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)
=> ( p(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__13___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__13___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__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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',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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__x,V5__y))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__x,V4__x),cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__y,V5__y))) ) ) ) ) ) ) ) ).
fof('hahn.HahnEquational.union_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__28___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__31___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_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__f] :
( c_24__type__7___24t(V0__A,V1__f)
=> ! [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_2esame__relation___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V2__r),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,V3__r_27)),chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__A,V1__f,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r,V3__r_27))) ) ) ) ) ).
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.HahnEquational.well_founded_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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_2eInit_2eWf_2ewell__founded___24a1(V0__A)) ) ).
fof('hahn.HahnEquational.well_founded_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V1__x),cCoq_2eInit_2eWf_2ewell__founded___24a2(V0__A,V2__y)) ) ) ) ) ).
fof('hahn.HahnEquational.well_founded_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__17___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),cCoq_2eInit_2eWf_2ewell__founded___24a1(V0__A)) ) ).
fof('hahn.HahnFuneq.funeq_cr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> p(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__57___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)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> p(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__57___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)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t))
=> p(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__57___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)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> ( p(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)))
=> p(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__57___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)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> p(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_more_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34107___24a2(V0__A,V1__B),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_2eHahnFuneq_2efuneq___24a3(V0__A,V1__B,V2__f)) ) ) ) ).
fof('hahn.HahnFuneq.funeq_mori',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__x] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__x)
=> ! [V4__y] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V4__y)
=> ( cCoq_2eProgram_2eBasics_2eflip___24a6(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),V3__x,V4__y)
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__x),chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__y)) ) ) ) ) ) ) ).
fof('hahn.HahnFuneq.funeq_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__34107___24a2(V0__A,V1__B),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_2eHahnFuneq_2efuneq___24a3(V0__A,V1__B,V2__f)) ) ) ) ).
fof('hahn.HahnFuneq.funeq_restr',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__B] :
( cType___24t(V1__B)
=> ! [V2__f] :
( c_24__type__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> ! [V5__dom] :
( c_24__type__308___24t(V0__A,V1__B,V5__dom)
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> ! [V5__C] :
( cType___24t(V5__C)
=> ! [V6__dom] :
( c_24__type__34095___24t(V0__A,V1__B,V5__C,V6__dom)
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> p(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__57___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)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t))
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> p(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__57___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)
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V3__r))
=> ( p(chahn_2eHahnFuneq_2efuneq___24a4(V0__A,V1__B,V2__f,V4__t))
=> p(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_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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)),chahn_2eHahnSets_2eset__subset___24a1(V0__A)),chahn_2eHahnMaxElt_2emax__elt___24a1(V0__A)) ) ).
fof('hahn.HahnMaxElt.max_elt_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( V4__x = V5__y
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__x,V4__x),chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.max_elt_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,c_3d___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl)),chahn_2eHahnMaxElt_2emax__elt___24a1(V0__A)) ) ).
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__57___24t(V0__A,V3__B,V4__f)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a))
=> p(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_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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a))
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a))
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V2__r_27,V3__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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)
=> ( p(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__13___24a1(V0__A)) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max_r',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)
=> ( p(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)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_max_rt',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)
=> ( p(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__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
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)
=> ( p(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__13___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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b))
=> p(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_r',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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__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)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_3d___24a2(V0__A,V2__b))) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_eq_wmax_rt',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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__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__refl__trans___24a2(V0__A,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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__b))
=> p(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__13___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max_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,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnMaxElt.seq_eqv_max_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,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r)),cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))) ) ) ).
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__13___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)
=> ( p(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__13___24a1(V0__A)) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max_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__b] :
( t(V3__b,V0__A)
=> ( p(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,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_max_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__b] :
( t(V3__b,V0__A)
=> ( p(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__refl__trans___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
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)
=> ( p(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__13___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)
=> ( p(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__13___24a1(V0__A)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_max_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(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),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
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)
=> ( p(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)
=> ( p(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__13___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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b))
=> p(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_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)
=> ! [V3__b] :
( t(V3__b,V0__A)
=> ( p(chahn_2eHahnMaxElt_2ewmax__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),chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V1__r)),chahn_2eHahnRelationsBasic_2esingl__rel___24a3(V0__A,V2__a,V3__b)) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_singl_wmax_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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__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_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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__b))
=> p(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)
=> ( p(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 ) ) )
=> p(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_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__b] :
( t(V3__b,V0__A)
=> ( p(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_2esame__relation___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,chahn_2eHahnRelationsBasic_2eclos__refl___24a2(V0__A,V2__r_27)),V1__r) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.seq_wmax_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__b] :
( t(V3__b,V0__A)
=> ( p(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_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)),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)
=> ( p(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 ) ) )
=> p(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)
=> ( p(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)
=> ( p(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__13___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.transp_seq_eqv_max_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,chahn_2eHahnRelationsBasic_2eclos__refl___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))),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))) ) ) ).
fof('hahn.HahnMaxElt.transp_seq_eqv_max_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,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))),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,chahn_2eHahnMaxElt_2emax__elt___24a2(V0__A,V1__r))) ) ) ).
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__13___24a1(V0__A)) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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)),chahn_2eHahnSets_2eset__subset___24a1(V0__A)),chahn_2eHahnMaxElt_2ewmax__elt___24a1(V0__A)) ) ).
fof('hahn.HahnMaxElt.wmax_elt_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_2eProgram_2eBasics_2eflip___24a6(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),V1__x,V2__y)
=> ! [V4__x] :
( t(V4__x,V0__A)
=> ! [V5__y] :
( t(V5__y,V0__A)
=> ( V4__x = V5__y
=> cCoq_2eProgram_2eBasics_2eimpl___24a2(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__x,V4__x),chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__y,V5__y)) ) ) ) ) ) ) ) ).
fof('hahn.HahnMaxElt.wmax_elt_mori_Proper',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33706___24a1(V0__A),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),c_24__type__7___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_2eClasses_2eMorphisms_2erespectful___24a4(V0__A,cProp,c_3d___24a1(V0__A),cCoq_2eProgram_2eBasics_2eimpl)),chahn_2eHahnMaxElt_2ewmax__elt___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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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__57___24t(V0__A,V3__B,V4__f)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2emax__elt___24a3(V0__A,V1__r,V3__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a))
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V2__a))
=> p(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)
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V1__r,V3__a))
=> ( p(chahn_2eHahnMaxElt_2ewmax__elt___24a3(V0__A,V2__r_27,V3__a))
=> p(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__2563___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)
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r))
<=> ~ ? [V2__f] :
( c_24__type__2563___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.eqmod_S',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ! [V2__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__j)
=> ( cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V1__i),V0__n) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V2__j),V0__n)
<=> cCoq_2eInit_2eNat_2emodulo___24a2(V1__i,V0__n) = cCoq_2eInit_2eNat_2emodulo___24a2(V2__j,V0__n) ) ) ) ) ).
fof('hahn.HahnMinPath.eqmod_add_idemp_r',axiom,
! [V0__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
=> ! [V1__i] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V1__i)
=> ! [V2__j] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V2__j)
=> ! [V3__k] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V3__k)
=> ( cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V1__i,V3__k),V0__n) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eNat_2eadd___24a2(V2__j,V3__k),V0__n)
<=> cCoq_2eInit_2eNat_2emodulo___24a2(V1__i,V0__n) = cCoq_2eInit_2eNat_2emodulo___24a2(V2__j,V0__n) ) ) ) ) ) ).
fof('hahn.HahnMinPath.get_first_nat',axiom,
! [V0__P] :
( c_24__type__273___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__273___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__7___24t(V0__X,V3__dom)
=> ( p(chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V3__dom,V2__r_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r)))
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27)))
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r))
<=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,chahn_2eHahnRelationsBasic_2erestr__rel___24a3(V0__X,c_24__lam__2869___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__2873___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__7___24t(V0__X,V3__d)
=> ! [V4__nd] :
( c_24__type__7___24t(V0__X,V4__nd)
=> ( V4__nd = c_24__lam__2880___24a2(V0__X,V3__d)
=> ( p(chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__X,V3__d,V2__r_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__X,V2__r_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__X,V2__r_27,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__X,V1__r)))
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__X,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__X,V1__r,V2__r_27)))
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__X,V1__r))
<=> ( p(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)))))
& p(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)))))
& p(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__2563___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_step',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__2563___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)
=> ( p(happ(happ(V1__r,happ(V2__f,V5__i)),happ(V2__f,V6__j)))
<=> cCoq_2eInit_2eNat_2emodulo___24a2(V6__j,V3__n) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V5__i),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__2563___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__7___24t(V0__X,V6__P)
=> ( p(happ(V6__P,happ(V2__f,V5__i)))
=> ? [V8__f] :
( c_24__type__2563___24t(V0__X,V8__f)
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__34187___24a4(V0__X,V1__r,V3__n,V8__f))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__34194___24a3(V0__X,V6__P,V8__f)) ) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.mp_min',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__2563___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)
=> ( p(happ(happ(V1__r,happ(V2__f,V5__i)),happ(V2__f,V6__j)))
=> cCoq_2eInit_2eNat_2emodulo___24a2(V6__j,V3__n) = cCoq_2eInit_2eNat_2emodulo___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V5__i),V3__n) ) ) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.mp_modulo',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__2563___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__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)) ) ) ) ) ) ) ).
fof('hahn.HahnMinPath.mp_nonzero',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__2563___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)
=> V3__n != cCoq_2eInit_2eDatatypes_2eO ) ) ) ) ) ).
fof('hahn.HahnMinPath.mp_step',axiom,
! [V0__X] :
( cType___24t(V0__X)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__X,V1__r)
=> ! [V2__f] :
( c_24__type__2563___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)
=> p(happ(happ(V1__r,happ(V2__f,V5__i)),happ(V2__f,cCoq_2eInit_2eDatatypes_2eS___24a1(V5__i)))) ) ) ) ) ) ) ).
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__2563___24t(V0__X,V5__f)
& ? [V6__n] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2570___24a3(V0__X,V2__a,V5__f))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2577___24a4(V0__X,V3__b,V5__f,V6__n))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2595___24a4(V0__X,V1__r,V5__f,V6__n))
& chahn_2eHahnBase_2eNW___24a1(c_24__lam__2637___24a4(V0__X,V1__r,V5__f,V6__n)) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.acyclic_antisymmetric',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( p(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__57___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__31808___24a3(V0__A,V1__r,V2__r_27),V3__x,V4__y)
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V0__A,c_24__lam__31816___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__7___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__57___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)
=> p(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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V1__r)) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functionalE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
=> ? [V3__f] :
( c_24__type__34212___24t(V0__A,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) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V5__y) ) ) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_alt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
<=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,cCoq_2eRelations_2eRelation__Operators_2etransp___24a2(V0__A,V1__r),V1__r),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___24a1(V0__A)))) ) ) ) ).
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)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
=> p(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)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27))
=> p(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)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
=> p(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__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r))
=> p(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)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27))
=> p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27))) ) ) ) ) ) ).
fof('hahn.HahnRelationsBasic.functional_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)
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V1__r))
=> ( p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,V2__r_27))
=> ( ! [V5__x] :
( t(V5__x,V0__A)
=> ( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V1__r,V5__x)
=> ( chahn_2eHahnRelationsBasic_2edom__rel___24a3(V0__A,V2__r_27,V5__x)
=> p(c_24False) ) ) )
=> p(chahn_2eHahnRelationsBasic_2efunctional___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(chahn_2eHahnRelationsBasic_2eacyclic___24a2(V0__A,V2__r_27))
=> p(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__31783___24t(V0__A,V1__B,V3__P)
=> ! [V4__rr] :
( c_24__type__31787___24t(V0__A,V1__B,V4__rr)
=> ( ! [V5__x] :
( t(V5__x,V1__B)
=> ( p(happ(V3__P,V5__x))
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,happ(V4__rr,V5__x),V2__r_27)) ) )
=> p(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__31783___24t(V0__A,V1__B,V4__P)
=> ! [V5__rr] :
( c_24__type__31787___24t(V0__A,V1__B,V5__rr)
=> ( p(happ(V4__P,V3__x))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,happ(V5__rr,V3__x)))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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_rel_true',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__7___24t(V0__A,V1__dom)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,V1__dom),chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___24a1(V0__A)))) ) ) ).
fof('hahn.HahnRelationsBasic.inclusion_eqv_rt',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__dom] :
( c_24__type__7___24t(V0__A,V1__dom)
=> ! [V2__r_27] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r_27)
=> p(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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___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)
=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eeqv__rel___24a2(V0__A,c_24__lam__31589___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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> p(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_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__s] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__s)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(V0__A,V1__r,V2__r_27),V3__s))
<=> p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V2__r_27,V3__s))) ) ) ) ) ) ).
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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V4__s_27,V3__s))
=> p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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_refl',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A),cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1(V0__A)) ) ).
fof('hahn.HahnRelationsBasic.inclusion_refl2',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V1__r)
=> p(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__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> p(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__57___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__r,V4__r_27))
=> p(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__7___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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r,V3__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27))
=> p(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_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_2ereflexive___24a2(V0__A,V2__r_27)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V2__r_27)))
=> p(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)
=> ( p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> ( p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2(V0__A,V3__r_27_27)))
=> ( p(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)))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__t))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__t))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V2__r_27)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27),V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V2__r_27,V1__r),V2__r_27))
=> p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2(V0__A,V2__r_27)))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V2__r_27,V3__r_27_27))
=> p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V3__s,V4__s_27))
=> p(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)
=> ( ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
| p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27)) )
=> p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> p(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)
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V3__r_27_27))
=> p(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)
=> ( p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V0__A,V1__r,V2__r_27))
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r_27))
=> p(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__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V2__r))
=> p(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__57___24t(V0__A,V1__B,V2__f)
=> ! [V3__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V3__r)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4(V0__A,V1__B,V2__f,V3__r)))
<=> p(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)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,chahn_2eHahnRelationsBasic_2eseq___24a3(V0__A,V1__r,V2__r_27)))
<=> p(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)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,cCoq_2eRelations_2eRelation__Operators_2eunion___24a3(V0__A,V1__r,V2__r_27)))
<=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r))
& p(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__7___24t(V0__A,V1__dom)
=> ! [V2__r] :
( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V0__A,V2__r)
=> ( p(chahn_2eHahnRelationsBasic_2eis__total___24a3(V0__A,V1__dom,V2__r))
=> p(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__57___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)
=> ( p(chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V0__A,V1__r))
=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V0__A,V1__r)
=> p(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)
=> ( p(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__7___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__7___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__7___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__7___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)
=> ( p(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)
=> p(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)
=> p(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)
=> p(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)
=> p(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)
=> ( p(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)
=> p(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)
=> ( p(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)
=> p(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)
=> ( p(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)
=> p(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)
=> ( p(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)
=> p(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)
=> ( p(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)
=> p(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)
=> ( p(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_equivE',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> ! [V1__s] :
( c_24__type__7___24t(V0__A,V1__s)
=> ! [V2__s_27] :
( c_24__type__7___24t(V0__A,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('hahn.HahnSets.set_equiv_rel',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)) ) ).
fof('hahn.HahnSets.set_equiv_rel_Reflexive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)) ) ).
fof('hahn.HahnSets.set_equiv_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)) ) ).
fof('hahn.HahnSets.set_equiv_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__equiv___24a1(V0__A)) ) ).
fof('hahn.HahnSets.set_subset_rel_Transitive',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2(c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__subset___24a1(V0__A)) ) ).
fof('hahn.HahnSets.set_subset_trans',axiom,
! [V0__A] :
( cType___24t(V0__A)
=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(c_24__type__7___24a1(V0__A),chahn_2eHahnSets_2eset__subset___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('$adef_$_lam_33192_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33192,V_24X1),V_24X2) = c_24__lam__33192___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Logic.ChoiceFacts.FunctionalChoice_on_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on,V_24X1),V_24X2))
<=> cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_lam_32101_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__32101,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__32101___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).
fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Even.even_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
<=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).
fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
<=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$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('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$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('$adef_$_lam_33049_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33049,V_24X1),V_24X2) = c_24__lam__33049___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_2869_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2869,V_24X1),V_24X2) = c_24__lam__2869___24a2(V_24X1,V_24X2) ).
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('$adef_Coq.Relations.Relation_Definitions.preorder_$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('$adef_Coq.NArith.BinNat.N.lt_$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('$adef_$_lam_33874_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33874,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33874___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).
fof('$adef_$_lam_2577_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2577,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2577___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('$adef_Coq.micromega.VarMap.t_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).
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('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_34187_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__34187,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__34187___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.prime_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eZArith_2eZnumtheory_2eprime,V_24X1))
<=> cCoq_2eZArith_2eZnumtheory_2eprime___24a1(V_24X1) ) ).
fof('$adef_$_prop_36986_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36986,V_24X1),V_24X2),V_24X3) = c_24__prop__36986___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzMulC_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Program.Basics.flip_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2eflip,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eProgram_2eBasics_2eflip___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnDom.dom_cond_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnDom_2edom__cond,V_24X1) = chahn_2eHahnDom_2edom__cond___24a1(V_24X1) ).
fof('$adef_Coq.Init.Wf.well_founded_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1) = cCoq_2eInit_2eWf_2ewell__founded___24a1(V_24X1) ).
fof('$adef_$_lam_31658_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__31658,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__31658___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_33029_$a1',axiom,
! [V_24X1] : happ(c_24__lam__33029,V_24X1) = c_24__lam__33029___24a1(V_24X1) ).
fof('$adef_$_lam_33200_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33200,V_24X1),V_24X2),V_24X3) = c_24__lam__33200___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eacyclic___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.restr_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2erestr__rel,V_24X1) = chahn_2eHahnRelationsBasic_2erestr__rel___24a1(V_24X1) ).
fof('$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_Coq.micromega.EnvRing.Pol_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).
fof('$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_$_lam_32101_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__32101,V_24X1),V_24X2),V_24X3) = c_24__lam__32101___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$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_54_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__54,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__54___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_Coq.micromega.RMicromega.CMult_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMult,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(V_24X1,V_24X2) ).
fof('$adef_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_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_hahn.HahnBase.Equality.class_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eEquality_2eclass,V_24X1) = chahn_2eHahnBase_2eEquality_2eclass___24a1(V_24X1) ).
fof('$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_$_lam_31658_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31658,V_24X1),V_24X2),V_24X3) = c_24__lam__31658___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_34043_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__34043,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__34043___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_31628_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31628,V_24X1),V_24X2) = c_24__lam__31628___24a2(V_24X1,V_24X2) ).
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('$adef_$_lam_7212_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7212,V_24X1),V_24X2),V_24X3) = c_24__lam__7212___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.Init.Decimal.Pos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).
fof('$adef_$_lam_33859_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33859,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33859___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$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('$adef_$_case_Coq.Numbers.BinNums.N$34253_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eN_2434253,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eNumbers_2eBinNums_2eN_2434253___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.micromega.Env.Env_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnv_2eEnv,V_24X1) = cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1) ).
fof('$adef_hahn.HahnMaxElt.max_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : 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('$adef_$_lam_34043_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__34043,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__34043___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
<=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33148_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33148,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33148___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_let_var_6_p_23045_23047_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__23045__23047,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__23045__23047___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_33859_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33859,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33859___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
<=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).
fof('$adef_$_lam_33148_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33148,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33148___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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_hahn.HahnRelationsBasic.eqv_dom_rel_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnRelationsBasic_2eeqv__dom__rel,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$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.HahnMaxElt.max_elt_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnMaxElt_2emax__elt,V_24X1) = chahn_2eHahnMaxElt_2emax__elt___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).
fof('$adef_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.micromega.VarMap.Elt_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33849_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33849,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33849___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_hahn.HahnRelationsBasic.dom_rel_$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('$adef_hahn.HahnList.undup_$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('$adef_$_lam_2595_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2595,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2595___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_36985_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36985,V_24X1),V_24X2),V_24X3) = c_24__prop__36985___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_34194_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__34194,V_24X1),V_24X2),V_24X3) = c_24__lam__34194___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.Relations.Relation_Operators.clos_refl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2) = cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.BinInt.Z.lt_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2elt,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Arith.Compare_dec.le_lt_dec_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__lt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__lt__dec___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_31640_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__31640,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__31640___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnDom.domb_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnDom_2edomb,V_24X1) = chahn_2eHahnDom_2edomb___24a1(V_24X1) ).
fof('$adef_$_prop_36987_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__36987,V_24X1),V_24X2) = c_24__prop__36987___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.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_hahn.HahnSets.set_union_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnSets_2eset__union,V_24X1),V_24X2),V_24X3) = chahn_2eHahnSets_2eset__union___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_prop_7342_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__7342,V_24X1),V_24X2),V_24X3) = c_24__prop__7342___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_hahn.HahnRelationsBasic.cross_rel_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2ecross__rel,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2ecross__rel___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_33783_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33783,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33783___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).
fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).
fof('$adef_$_lam_33759_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33759,V_24X1),V_24X2) = c_24__lam__33759___24a2(V_24X1,V_24X2) ).
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_7223_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__7223,V_24X1),V_24X2),V_24X3) = c_24__lam__7223___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_31634_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31634,V_24X1),V_24X2),V_24X3) = c_24__lam__31634___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_13_$a1',axiom,
! [V_24X1] : happ(c_24__lam__13,V_24X1) = c_24__lam__13___24a1(V_24X1) ).
fof('$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_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_$_lam_33730_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33730,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33730___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_2577_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2577,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2577___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_13_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__13,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__13___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Bool.Bool.reflect_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2ereflect,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33772_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33772,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33772___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnSets.set_inter_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnSets_2eset__inter,V_24X1),V_24X2),V_24X3) = chahn_2eHahnSets_2eset__inter___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_33910_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33910,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33910___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_let_5_f\'_34240_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__5__f_27__34240,V_24X1),V_24X2) = c_24__let__5__f_27__34240___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_34194_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__34194,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__34194___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_33800_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33800,V_24X1),V_24X2) = c_24__lam__33800___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_32402_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__32402,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__32402___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_$_lam_33742_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33742,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33742___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_hahn.HahnRelationsBasic.clos_sym_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__sym,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__sym___24a1(V_24X1) ).
fof('$adef_$_lam_33794_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33794,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33794___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_54_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__54,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__54___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPos.Pos.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnBase.NW_$a1',axiom,
! [V_24X1] :
( p(happ(chahn_2eHahnBase_2eNW,V_24X1))
<=> chahn_2eHahnBase_2eNW___24a1(V_24X1) ) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_32097_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__32097,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__32097___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.restr_eq_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2erestr__eq__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.LT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eLT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_hahn.HahnRelationsBasic.restr_rel_$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('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_subset_$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('$adef_hahn.HahnRelationsBasic.irreflexive_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1) = chahn_2eHahnRelationsBasic_2eirreflexive___24a1(V_24X1) ).
fof('$adef_$_lam_33800_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33800,V_24X1),V_24X2),V_24X3) = c_24__lam__33800___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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.micromega.EnvRing.PEopp_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.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_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eirreflexive,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eirreflexive___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33880_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33880,V_24X1),V_24X2),V_24X3) = c_24__lam__33880___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_33091_$a1',axiom,
! [V_24X1] : happ(c_24__lam__33091,V_24X1) = c_24__lam__33091___24a1(V_24X1) ).
fof('$adef_$_lam_31669_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31669,V_24X1),V_24X2),V_24X3) = c_24__lam__31669___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_prop_36982_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36982,V_24X1),V_24X2),V_24X3) = c_24__prop__36982___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Strings.String.String_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_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_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.micromega.RingMicromega.PsatzMulE_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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_$_lam_33874_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33874,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33874___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
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('$adef_$_lam_31589_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__31589,V_24X1),V_24X2))
<=> c_24__lam__31589___24a2(V_24X1,V_24X2) ) ).
fof('$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_$_lam_33208_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33208,V_24X1),V_24X2),V_24X3) = c_24__lam__33208___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('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.bunion_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ebunion,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ebunion___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Relations.Relation_Definitions.transitive_$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('$adef_hahn.HahnBase.Equality.Pack_$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('$adef_$_prop_2532_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__2532,V_24X1),V_24X2) = c_24__prop__2532___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnDom.dom_cond_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(chahn_2eHahnDom_2edom__cond,V_24X1),V_24X2),V_24X3),V_24X4))
<=> chahn_2eHahnDom_2edom__cond___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_33348_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__33348,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__33348___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Program.Basics.compose_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eProgram_2eBasics_2ecompose,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eProgram_2eBasics_2ecompose___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31640_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31640,V_24X1),V_24X2),V_24X3) = c_24__lam__31640___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_32402_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(c_24__lam__32402,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> c_24__lam__32402___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
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('$adef_$_lam_34030_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__34030,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__34030___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_2869_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2869,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2869___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Logic.EqdepFacts.eq_dep_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
<=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).
fof('$adef_$_lam_33029_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33029,V_24X1),V_24X2) = c_24__lam__33029___24a2(V_24X1,V_24X2) ).
fof('$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_Coq.micromega.EnvRing.PExpr_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).
fof('$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_$_lam_2873_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2873,V_24X1),V_24X2) = c_24__lam__2873___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33794_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33794,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33794___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$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.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_Coq.Classes.RelationClasses.RewriteRelation_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eRewriteRelation,V_24X1),V_24X2))
<=> cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2(V_24X1,V_24X2) ) ).
fof('$adef_hahn.HahnRelationsBasic.acyclic_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eacyclic,V_24X1) = chahn_2eHahnRelationsBasic_2eacyclic___24a1(V_24X1) ).
fof('$adef_$_lam_33898_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33898,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33898___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_33165_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__33165,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__33165___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_34187_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__34187,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__34187___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.codom_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2ecodom__rel,V_24X1) = chahn_2eHahnRelationsBasic_2ecodom__rel___24a1(V_24X1) ).
fof('$adef_$_lam_33094_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33094,V_24X1),V_24X2) = c_24__lam__33094___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31649_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31649,V_24X1),V_24X2),V_24X3) = c_24__lam__31649___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('$adef_$_lam_33192_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__33192,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__33192___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_let_var_6_p_23043_23046_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__23043__23046,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__23043__23046___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('$adef_Coq.Init.Decimal.D9_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).
fof('$adef_Coq.Classes.RelationClasses.Reflexive_$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('$adef_$_lam_3_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__3,V_24X1),V_24X2) = c_24__lam__3___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_31649_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__31649,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__31649___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('$adef_hahn.HahnSets.set_empty_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__empty,V_24X1) = chahn_2eHahnSets_2eset__empty___24a1(V_24X1) ).
fof('$adef_hahn.HahnMaxElt.wmax_elt_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : 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('$adef_Coq.micromega.EnvRing.vmon_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2evmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
<=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).
fof('$adef_Coq.micromega.Tauto.X_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eX,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eX___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$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('$adef_hahn.HahnRelationsBasic.immediate_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1) = chahn_2eHahnRelationsBasic_2eimmediate___24a1(V_24X1) ).
fof('$adef_Coq.Init.Specif.sumor_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumor,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33759_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__33759,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__33759___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_Coq.micromega.RMicromega.CInv_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCInv,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(V_24X1) ).
fof('$adef_Coq.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_$_lam_33274_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33274,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33274___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_prop_36981_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__36981,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__36981___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_2570_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2570,V_24X1),V_24X2),V_24X3) = c_24__lam__2570___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('$adef_$_let_5_f\'_34240_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__let__5__f_27__34240,V_24X1),V_24X2),V_24X3) = c_24__let__5__f_27__34240___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.is_total_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnRelationsBasic_2eis__total,V_24X1),V_24X2),V_24X3) = chahn_2eHahnRelationsBasic_2eis__total___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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.ZArith.Znumtheory.Bezout_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).
fof('$adef_Coq.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_$_prop_36983_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36983,V_24X1),V_24X2),V_24X3) = c_24__prop__36983___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_hahn.HahnSets.set_map_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnSets_2eset__map,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnSets_2eset__map___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
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('$adef_hahn.HahnRelationsBasic.singl_rel_$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('$adef_$_lam_33208_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33208,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33208___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_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_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_Coq.micromega.EnvRing.Pinj_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2) = cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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.micromega.RMicromega.CPlus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Init.Decimal.D1_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33200_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33200,V_24X1),V_24X2) = c_24__lam__33200___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Definitions.equiv_$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('$adef_$_lam_2570_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__2570,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__2570___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnDom.dom_cond_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnDom_2edom__cond,V_24X1),V_24X2),V_24X3) = chahn_2eHahnDom_2edom__cond___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.transp_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Operators_2etransp,V_24X1) = cCoq_2eRelations_2eRelation__Operators_2etransp___24a1(V_24X1) ).
fof('$adef_$_lam_2637_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2637,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2637___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).
fof('$adef_Coq.Logic.ClassicalDescription.excluded_middle_informative_$a1',axiom,
! [V_24X1] : happ(cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative,V_24X1) = cCoq_2eLogic_2eClassicalDescription_2eexcluded__middle__informative___24a1(V_24X1) ).
fof('$adef_hahn.HahnFuneq.funeq_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnFuneq_2efuneq,V_24X1),V_24X2),V_24X3) = chahn_2eHahnFuneq_2efuneq___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_32097_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__32097,V_24X1),V_24X2),V_24X3) = c_24__lam__32097___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_let_4_P\'_34239_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__let__4__P_27__34239,V_24X1),V_24X2) = c_24__let__4__P_27__34239___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33910_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__33910,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__33910___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_$_lam_2637_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2637,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2637___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).
fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.immediate_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2eimmediate,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2eimmediate___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Arith.Even.odd_$a1',axiom,
! [V_24X1] :
( p(happ(cCoq_2eArith_2eEven_2eodd,V_24X1))
<=> cCoq_2eArith_2eEven_2eodd___24a1(V_24X1) ) ).
fof('$adef_Coq.ZArith.BinIntDef.Z.succ_$a1',axiom,
! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V_24X1) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$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('$adef_hahn.HahnRelationsBasic.map_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2emap__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2emap__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Nat.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnBase.Equality.sort_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnBase_2eEquality_2esort,V_24X1) = chahn_2eHahnBase_2eEquality_2esort___24a1(V_24X1) ).
fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_31628_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31628,V_24X1),V_24X2),V_24X3) = c_24__lam__31628___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.ZArith.BinInt.Z.divide_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2edivide,V_24X1),V_24X2))
<=> cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V_24X1,V_24X2) ) ).
fof('$adef_Coq.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_$_lam_33772_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33772,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33772___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.restr_rel_$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('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).
fof('$adef_Coq.Program.Basics.impl_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(cCoq_2eProgram_2eBasics_2eimpl,V_24X1),V_24X2))
<=> cCoq_2eProgram_2eBasics_2eimpl___24a2(V_24X1,V_24X2) ) ).
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('$adef_$_prop_36984_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__36984,V_24X1),V_24X2),V_24X3) = c_24__prop__36984___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_hahn.HahnRelationsBasic.collect_rel_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2ecollect__rel,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2ecollect__rel___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31589_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31589,V_24X1) = c_24__lam__31589___24a1(V_24X1) ).
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('$adef_hahn.HahnRelationsBasic.cross_rel_$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('$adef_$_prop_2531_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__prop__2531,V_24X1),V_24X2) = c_24__prop__2531___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnSets.set_bunion_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(chahn_2eHahnSets_2eset__bunion,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> chahn_2eHahnSets_2eset__bunion___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_$_lam_33348_$a1',axiom,
! [V_24X1] : happ(c_24__lam__33348,V_24X1) = c_24__lam__33348___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.functional_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2efunctional,V_24X1) = chahn_2eHahnRelationsBasic_2efunctional___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.eqv_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eeqv__rel,V_24X1) = chahn_2eHahnRelationsBasic_2eeqv__rel___24a1(V_24X1) ).
fof('$adef_hahn.HahnDom.doma_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnDom_2edoma,V_24X1) = chahn_2eHahnDom_2edoma___24a1(V_24X1) ).
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('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_31808_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31808,V_24X1),V_24X2),V_24X3) = c_24__lam__31808___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).
fof('$adef_$_lam_31816_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__31816,V_24X1),V_24X2),V_24X3) = c_24__lam__31816___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.Init.Datatypes.S_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).
fof('$adef_$_lam_33880_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33880,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33880___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_31808_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__31808,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__31808___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).
fof('$adef_hahn.HahnRelationsBasic.pow_rel_$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('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_33730_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33730,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33730___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.micromega.VarMap.Empty_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).
fof('$adef_$_lam_31625_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__31625,V_24X1),V_24X2) = c_24__lam__31625___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_33091_$a2',axiom,
! [V_24X1,V_24X2] :
( p(happ(happ(c_24__lam__33091,V_24X1),V_24X2))
<=> c_24__lam__33091___24a2(V_24X1,V_24X2) ) ).
fof('$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_hahn.HahnDom.doma_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(chahn_2eHahnDom_2edoma,V_24X1),V_24X2),V_24X3) = chahn_2eHahnDom_2edoma___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$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_$_lam_31816_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__31816,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__31816___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('$adef_hahn.HahnRelationsBasic.pow_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2epow__rel,V_24X1) = chahn_2eHahnRelationsBasic_2epow__rel___24a1(V_24X1) ).
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('$adef_$_lam_2595_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__2595,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__2595___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).
fof('$adef_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.Relations.Relation_Definitions.inclusion_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2einclusion,V_24X1),V_24X2),V_24X3) = cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_$_lam_31625_$a1',axiom,
! [V_24X1] : happ(c_24__lam__31625,V_24X1) = c_24__lam__31625___24a1(V_24X1) ).
fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.bunion_$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('$adef_$_prop_7330_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__7330,V_24X1),V_24X2),V_24X3) = c_24__prop__7330___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.Init.Specif.existT2_$a6',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).
fof('$adef_Coq.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.micromega.RingMicromega.PsatzC_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.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_hahn.HahnMaxElt.wmax_elt_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnMaxElt_2ewmax__elt,V_24X1) = chahn_2eHahnMaxElt_2ewmax__elt___24a1(V_24X1) ).
fof('$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_$_lam_33094_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33094,V_24X1),V_24X2),V_24X3) = c_24__lam__33094___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).
fof('$adef_$_lam_33783_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33783,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33783___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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.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_hahn.HahnRelationsBasic.cross_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2ecross__rel,V_24X1) = chahn_2eHahnRelationsBasic_2ecross__rel___24a1(V_24X1) ).
fof('$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_$_lam_33849_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__33849,V_24X1),V_24X2),V_24X3) = c_24__lam__33849___24a3(V_24X1,V_24X2,V_24X3) ).
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('$adef_$_lam_2873_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2873,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2873___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_$_lam_2880_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__2880,V_24X1),V_24X2) = c_24__lam__2880___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33274_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__33274,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__33274___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_hahn.HahnFuneq.funeq_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(chahn_2eHahnFuneq_2efuneq,V_24X1),V_24X2),V_24X3),V_24X4) = chahn_2eHahnFuneq_2efuneq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$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_$_lam_31634_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__31634,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__31634___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_$_lam_7212_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(c_24__lam__7212,V_24X1),V_24X2),V_24X3),V_24X4))
<=> c_24__lam__7212___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.inter_rel_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2einter__rel,V_24X1) = chahn_2eHahnRelationsBasic_2einter__rel___24a1(V_24X1) ).
fof('$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_$_lam_33742_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__33742,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__33742___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_33049_$a1',axiom,
! [V_24X1] : happ(c_24__lam__33049,V_24X1) = c_24__lam__33049___24a1(V_24X1) ).
fof('$adef_hahn.HahnRelationsBasic.clos_refl_sym_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eclos__refl__sym,V_24X1) = chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a1(V_24X1) ).
fof('$adef_$_lam_34030_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__34030,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__34030___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).
fof('$adef_$_lam_3_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__3,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__3___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_$_let_4_P\'_34239_$a1',axiom,
! [V_24X1] : happ(c_24__let__4__P_27__34239,V_24X1) = c_24__let__4__P_27__34239___24a1(V_24X1) ).
fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).
fof('$adef_hahn.HahnSets.set_equiv_$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('$adef_Coq.Init.Specif.left_$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('$adef_$_lam_31669_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__31669,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__31669___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$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.Init.Specif.sigT_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).
fof('$adef_$_prop_2533_$a1',axiom,
! [V_24X1] : happ(c_24__prop__2533,V_24X1) = c_24__prop__2533___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).
fof('$adef_Coq.Init.Decimal.D8_$a1',axiom,
! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD8,V_24X1) = cCoq_2eInit_2eDecimal_2eD8___24a1(V_24X1) ).
fof('$adef_hahn.HahnDom.domb_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : 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_2880_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(c_24__lam__2880,V_24X1),V_24X2),V_24X3))
<=> c_24__lam__2880___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$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_Coq.micromega.RMicromega.CQ_$a1',axiom,
! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).
fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).
fof('$adef_$_lam_33165_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(c_24__lam__33165,V_24X1),V_24X2) = c_24__lam__33165___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_$_lam_7223_$a5',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
( p(happ(happ(happ(happ(happ(c_24__lam__7223,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
<=> c_24__lam__7223___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).
fof('$adef_Coq.micromega.EnvRing.PEc_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Relations.Relation_Definitions.symmetric_$a1',axiom,
! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a1(V_24X1) ).
fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
<=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).
fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] :
( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
<=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).
fof('$adef_hahn.HahnRelationsBasic.seq_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnRelationsBasic_2eseq,V_24X1) = chahn_2eHahnRelationsBasic_2eseq___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_hahn.HahnSets.set_full_$a1',axiom,
! [V_24X1] : happ(chahn_2eHahnSets_2eset__full,V_24X1) = chahn_2eHahnSets_2eset__full___24a1(V_24X1) ).
fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] :
( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
<=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).
fof('$adef_Coq.Init.Specif.sig2_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.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.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_hahn.HahnSets.set_compl_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnSets_2eset__compl,V_24X1),V_24X2) = chahn_2eHahnSets_2eset__compl___24a2(V_24X1,V_24X2) ).
fof('$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_$_lam_33898_$a4',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__33898,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__33898___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).
fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).
fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).
fof('$adef_hahn.HahnRelationsBasic.functional_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(chahn_2eHahnRelationsBasic_2efunctional,V_24X1),V_24X2) = chahn_2eHahnRelationsBasic_2efunctional___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Datatypes.andb_$a2',axiom,
! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eandb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eandb___24a2(V_24X1,V_24X2) ).
fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
! [V_24X1,V_24X2] : 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('$tdef_$_type_33046',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33046___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33046___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31266',axiom,
! [V_24Y] :
( c_24__type__31266___24t(V_24Y)
<=> t(V_24Y,c_24__type__31266) ) ).
fof('$tdef_$_type_32833',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32833___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32833___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).
fof('$tdef_$_type_33211',axiom,
! [V_24Y] :
( c_24__type__33211___24t(V_24Y)
<=> t(V_24Y,c_24__type__33211) ) ).
fof('$tdef_$_type_33125',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33125___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33125___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3696',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__3696___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__3696___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.EnvRing.Mon',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).
fof('$tdef_$_type_81',axiom,
! [V_24Y] :
( c_24__type__81___24t(V_24Y)
<=> t(V_24Y,c_24__type__81) ) ).
fof('$tdef_$_type_3789',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__3789___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__3789___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.VarMap.t',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).
fof('$tdef_$_type_36825',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36825___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36825___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Init.Specif.sigT2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_549',axiom,
! [V_24Y] :
( c_24__type__549___24t(V_24Y)
<=> t(V_24Y,c_24__type__549) ) ).
fof('$tdef_$_type_36232',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__36232___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__36232___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_36833',axiom,
! [V_24Y] :
( c_24__type__36833___24t(V_24Y)
<=> t(V_24Y,c_24__type__36833) ) ).
fof('$tdef_$_type_33394',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33394___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33394___24a1(V_24X1)) ) ).
fof('$tdef_$_type_32877',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32877___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32877___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_34316',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34316___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34316___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2985',axiom,
! [V_24Y] :
( c_24__type__2985___24t(V_24Y)
<=> t(V_24Y,c_24__type__2985) ) ).
fof('$tdef_$_type_9409',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9409___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9409___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_31727',axiom,
! [V_24Y] :
( c_24__type__31727___24t(V_24Y)
<=> t(V_24Y,c_24__type__31727) ) ).
fof('$tdef_$_type_2905',axiom,
! [V_24Y] :
( c_24__type__2905___24t(V_24Y)
<=> t(V_24Y,c_24__type__2905) ) ).
fof('$tdef_$_type_31774',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31774___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31774___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31769',axiom,
! [V_24Y] :
( c_24__type__31769___24t(V_24Y)
<=> t(V_24Y,c_24__type__31769) ) ).
fof('$tdef_$_type_33041',axiom,
! [V_24Y] :
( c_24__type__33041___24t(V_24Y)
<=> t(V_24Y,c_24__type__33041) ) ).
fof('$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_$_type_9499',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9499___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9499___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Datatypes.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_2450',axiom,
! [V_24Y] :
( c_24__type__2450___24t(V_24Y)
<=> t(V_24Y,c_24__type__2450) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ) ).
fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).
fof('$tdef_$_type_33706',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33706___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33706___24a1(V_24X1)) ) ).
fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Datatypes.option',axiom,
! [V_24X1,V_24Y] :
( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).
fof('$tdef_$_type_264',axiom,
! [V_24Y] :
( c_24__type__264___24t(V_24Y)
<=> t(V_24Y,c_24__type__264) ) ).
fof('$tdef_$_type_23570',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23570___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__23570___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2460',axiom,
! [V_24Y] :
( c_24__type__2460___24t(V_24Y)
<=> t(V_24Y,c_24__type__2460) ) ).
fof('$tdef_$_type_34107',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__34107___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__34107___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_308',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__308___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__308___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_32792',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32792___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32792___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ) ).
fof('$tdef_$_type_273',axiom,
! [V_24Y] :
( c_24__type__273___24t(V_24Y)
<=> t(V_24Y,c_24__type__273) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ) ).
fof('$tdef_$_type_65',axiom,
! [V_24Y] :
( c_24__type__65___24t(V_24Y)
<=> t(V_24Y,c_24__type__65) ) ).
fof('$tdef_$_type_2443',axiom,
! [V_24Y] :
( c_24__type__2443___24t(V_24Y)
<=> t(V_24Y,c_24__type__2443) ) ).
fof('$tdef_$_type_33649',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33649___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33649___24a1(V_24X1)) ) ).
fof('$tdef_$_type_28038',axiom,
! [V_24Y] :
( c_24__type__28038___24t(V_24Y)
<=> t(V_24Y,c_24__type__28038) ) ).
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_3092',axiom,
! [V_24Y] :
( c_24__type__3092___24t(V_24Y)
<=> t(V_24Y,c_24__type__3092) ) ).
fof('$tdef_$_type_33116',axiom,
! [V_24Y] :
( c_24__type__33116___24t(V_24Y)
<=> t(V_24Y,c_24__type__33116) ) ).
fof('$tdef_$_type_36777',axiom,
! [V_24Y] :
( c_24__type__36777___24t(V_24Y)
<=> t(V_24Y,c_24__type__36777) ) ).
fof('$tdef_$_type_33513',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33513___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33513___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3138',axiom,
! [V_24Y] :
( c_24__type__3138___24t(V_24Y)
<=> t(V_24Y,c_24__type__3138) ) ).
fof('$tdef_$_type_29591',axiom,
! [V_24Y] :
( c_24__type__29591___24t(V_24Y)
<=> t(V_24Y,c_24__type__29591) ) ).
fof('$tdef_$_type_36154',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__36154___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__36154___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
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_35714',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__35714___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__35714___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sig2',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( cCoq_2eInit_2eSpecif_2esig2___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_29626',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29626___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29626___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_7491',axiom,
! [V_24Y] :
( c_24__type__7491___24t(V_24Y)
<=> t(V_24Y,c_24__type__7491) ) ).
fof('$tdef_$_type_23943',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23943___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23943___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_22',axiom,
! [V_24X1,V_24Y] :
( c_24__type__22___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__22___24a1(V_24X1)) ) ).
fof('$tdef_$_type_4057',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__4057___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__4057___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Init.Specif.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_76',axiom,
! [V_24Y] :
( c_24__type__76___24t(V_24Y)
<=> t(V_24Y,c_24__type__76) ) ).
fof('$tdef_$_type_32815',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32815___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32815___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_36654',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__36654___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__36654___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
! [V_24Y] :
( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
<=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).
fof('$tdef_$_type_3467',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3467___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3467___24a1(V_24X1)) ) ).
fof('$tdef_$_type_3004',axiom,
! [V_24Y] :
( c_24__type__3004___24t(V_24Y)
<=> t(V_24Y,c_24__type__3004) ) ).
fof('$tdef_$_type_3000',axiom,
! [V_24Y] :
( c_24__type__3000___24t(V_24Y)
<=> t(V_24Y,c_24__type__3000) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).
fof('$tdef_$_type_35604',axiom,
! [V_24Y] :
( c_24__type__35604___24t(V_24Y)
<=> t(V_24Y,c_24__type__35604) ) ).
fof('$tdef_$_type_336',axiom,
! [V_24Y] :
( c_24__type__336___24t(V_24Y)
<=> t(V_24Y,c_24__type__336) ) ).
fof('$tdef_$_type_36769',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36769___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36769___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_31864',axiom,
! [V_24Y] :
( c_24__type__31864___24t(V_24Y)
<=> t(V_24Y,c_24__type__31864) ) ).
fof('$tdef_$_type_473',axiom,
! [V_24X1,V_24Y] :
( c_24__type__473___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__473___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23390',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23390___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__23390___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_36761',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36761___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36761___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_35418',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__35418___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__35418___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_33475',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33475___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33475___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).
fof('$tdef_$_type_36600',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__36600___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__36600___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_35593',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35593___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35593___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_57',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__57___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__57___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_320',axiom,
! [V_24Y] :
( c_24__type__320___24t(V_24Y)
<=> t(V_24Y,c_24__type__320) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).
fof('$tdef_Coq.micromega.RMicromega.Rcst',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRMicromega_2eRcst___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRMicromega_2eRcst) ) ).
fof('$tdef_$_type_31713',axiom,
! [V_24Y] :
( c_24__type__31713___24t(V_24Y)
<=> t(V_24Y,c_24__type__31713) ) ).
fof('$tdef_$_type_2540',axiom,
! [V_24Y] :
( c_24__type__2540___24t(V_24Y)
<=> t(V_24Y,c_24__type__2540) ) ).
fof('$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_33483',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33483___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33483___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3143',axiom,
! [V_24Y] :
( c_24__type__3143___24t(V_24Y)
<=> t(V_24Y,c_24__type__3143) ) ).
fof('$tdef_$_type_237',axiom,
! [V_24Y] :
( c_24__type__237___24t(V_24Y)
<=> t(V_24Y,c_24__type__237) ) ).
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_$_type_2895',axiom,
! [V_24Y] :
( c_24__type__2895___24t(V_24Y)
<=> t(V_24Y,c_24__type__2895) ) ).
fof('$tdef_$_type_24024',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__24024___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__24024___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_23913',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23913___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23913___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Datatypes.sum',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eDatatypes_2esum___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34370',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34370___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34370___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33565',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33565___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33565___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_30772',axiom,
! [V_24Y] :
( c_24__type__30772___24t(V_24Y)
<=> t(V_24Y,c_24__type__30772) ) ).
fof('$tdef_$_type_3387',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3387___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3387___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Strings.Ascii.ascii',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).
fof('$tdef_$_type_27995',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__27995___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__27995___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
! [V_24Y] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(V_24Y)
<=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ) ).
fof('$tdef_$_type_33526',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33526___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33526___24a2(V_24X1,V_24X2)) ) ).
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_$_type_34281',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34281___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34281___24a1(V_24X1)) ) ).
fof('$tdef_$_type_2684',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__2684___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__2684___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_3882',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__3882___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__3882___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35057',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35057___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35057___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_35500',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35500___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35500___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_90',axiom,
! [V_24X1,V_24Y] :
( c_24__type__90___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__90___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Init.Decimal.uint',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2euint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2euint) ) ).
fof('$tdef_Prop',axiom,
! [V_24Y] :
( cProp___24t(V_24Y)
<=> t(V_24Y,cProp) ) ).
fof('$tdef_$_type_36817',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__36817___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__36817___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_3058',axiom,
! [V_24Y] :
( c_24__type__3058___24t(V_24Y)
<=> t(V_24Y,c_24__type__3058) ) ).
fof('$tdef_$_type_7536',axiom,
! [V_24Y] :
( c_24__type__7536___24t(V_24Y)
<=> t(V_24Y,c_24__type__7536) ) ).
fof('$tdef_$_type_33633',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33633___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33633___24a1(V_24X1)) ) ).
fof('$tdef_$_type_24051',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__24051___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__24051___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$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_4232',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__4232___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__4232___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_271',axiom,
! [V_24Y] :
( c_24__type__271___24t(V_24Y)
<=> t(V_24Y,c_24__type__271) ) ).
fof('$tdef_$_type_3246',axiom,
! [V_24Y] :
( c_24__type__3246___24t(V_24Y)
<=> t(V_24Y,c_24__type__3246) ) ).
fof('$tdef_$_type_35150',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__35150___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__35150___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7344',axiom,
! [V_24Y] :
( c_24__type__7344___24t(V_24Y)
<=> t(V_24Y,c_24__type__7344) ) ).
fof('$tdef_Coq.Init.Byte.byte',axiom,
! [V_24Y] :
( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).
fof('$tdef_$_type_33061',axiom,
! [V_24Y] :
( c_24__type__33061___24t(V_24Y)
<=> t(V_24Y,c_24__type__33061) ) ).
fof('$tdef_Coq.Init.Decimal.int',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).
fof('$tdef_$_type_34307',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34307___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34307___24a1(V_24X1)) ) ).
fof('$tdef_$_type_200',axiom,
! [V_24Y] :
( c_24__type__200___24t(V_24Y)
<=> t(V_24Y,c_24__type__200) ) ).
fof('$tdef_$_type_98',axiom,
! [V_24Y] :
( c_24__type__98___24t(V_24Y)
<=> t(V_24Y,c_24__type__98) ) ).
fof('$tdef_$_type_17',axiom,
! [V_24X1,V_24Y] :
( c_24__type__17___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__17___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35243',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__35243___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__35243___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.Strings.String.string',axiom,
! [V_24Y] :
( cCoq_2eStrings_2eString_2estring___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStrings_2eString_2estring) ) ).
fof('$tdef_$_type_22732',axiom,
! [V_24Y] :
( c_24__type__22732___24t(V_24Y)
<=> t(V_24Y,c_24__type__22732) ) ).
fof('$tdef_$_type_9207',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9207___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9207___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_32859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32859___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_29587',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__29587___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__29587___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_34466',axiom,
! [V_24Y] :
( c_24__type__34466___24t(V_24Y)
<=> t(V_24Y,c_24__type__34466) ) ).
fof('$tdef_$_type_3064',axiom,
! [V_24Y] :
( c_24__type__3064___24t(V_24Y)
<=> t(V_24Y,c_24__type__3064) ) ).
fof('$tdef_$_type_4139',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__4139___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__4139___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_2563',axiom,
! [V_24X1,V_24Y] :
( c_24__type__2563___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__2563___24a1(V_24X1)) ) ).
fof('$tdef_$_type_125',axiom,
! [V_24Y] :
( c_24__type__125___24t(V_24Y)
<=> t(V_24Y,c_24__type__125) ) ).
fof('$tdef_$_type_9701',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9701___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9701___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
! [V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).
fof('$tdef_Coq.Init.Specif.sigT',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31787',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31787___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31787___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36474',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__36474___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__36474___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_23859',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23859___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23859___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_9802',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9802___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9802___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$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_34296',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34296___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34296___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31250',axiom,
! [V_24Y] :
( c_24__type__31250___24t(V_24Y)
<=> t(V_24Y,c_24__type__31250) ) ).
fof('$tdef_$_type_2946',axiom,
! [V_24Y] :
( c_24__type__2946___24t(V_24Y)
<=> t(V_24Y,c_24__type__2946) ) ).
fof('$tdef_$_type_29630',axiom,
! [V_24Y] :
( c_24__type__29630___24t(V_24Y)
<=> t(V_24Y,c_24__type__29630) ) ).
fof('$tdef_$_type_7452',axiom,
! [V_24Y] :
( c_24__type__7452___24t(V_24Y)
<=> t(V_24Y,c_24__type__7452) ) ).
fof('$tdef_$_type_3964',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__3964___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__3964___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_Coq.micromega.EnvRing.Pol',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eEnvRing_2ePol___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35753',axiom,
! [V_24Y] :
( c_24__type__35753___24t(V_24Y)
<=> t(V_24Y,c_24__type__35753) ) ).
fof('$tdef_$_type_34276',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34276___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34276___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34269',axiom,
! [V_24Y] :
( c_24__type__34269___24t(V_24Y)
<=> t(V_24Y,c_24__type__34269) ) ).
fof('$tdef_$_type_33401',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33401___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33401___24a1(V_24X1)) ) ).
fof('$tdef_$_type_187',axiom,
! [V_24Y] :
( c_24__type__187___24t(V_24Y)
<=> t(V_24Y,c_24__type__187) ) ).
fof('$tdef_$_type_34016',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34016___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34016___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33495',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33495___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33495___24a1(V_24X1)) ) ).
fof('$tdef_Coq.Structures.OrderedType.Compare',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( cCoq_2eStructures_2eOrderedType_2eCompare___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_Coq.Init.Specif.sumor',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eInit_2eSpecif_2esumor___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumor___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_36717',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__36717___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__36717___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2523',axiom,
! [V_24Y] :
( c_24__type__2523___24t(V_24Y)
<=> t(V_24Y,c_24__type__2523) ) ).
fof('$tdef_$_type_31747',axiom,
! [V_24Y] :
( c_24__type__31747___24t(V_24Y)
<=> t(V_24Y,c_24__type__31747) ) ).
fof('$tdef_$_type_29755',axiom,
! [V_24Y] :
( c_24__type__29755___24t(V_24Y)
<=> t(V_24Y,c_24__type__29755) ) ).
fof('$tdef_$_type_23453',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23453___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__23453___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$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_31818',axiom,
! [V_24Y] :
( c_24__type__31818___24t(V_24Y)
<=> t(V_24Y,c_24__type__31818) ) ).
fof('$tdef_$_type_174',axiom,
! [V_24Y] :
( c_24__type__174___24t(V_24Y)
<=> t(V_24Y,c_24__type__174) ) ).
fof('$tdef_$_type_34381',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34381___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34381___24a1(V_24X1)) ) ).
fof('$tdef_$_type_367',axiom,
! [V_24Y] :
( c_24__type__367___24t(V_24Y)
<=> t(V_24Y,c_24__type__367) ) ).
fof('$tdef_$_type_2436',axiom,
! [V_24Y] :
( c_24__type__2436___24t(V_24Y)
<=> t(V_24Y,c_24__type__2436) ) ).
fof('$tdef_$_type_3234',axiom,
! [V_24Y] :
( c_24__type__3234___24t(V_24Y)
<=> t(V_24Y,c_24__type__3234) ) ).
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_$_type_7179',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7179___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7179___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34648',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34648___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34648___24a1(V_24X1)) ) ).
fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
! [V_24Y] :
( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
<=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).
fof('$tdef_hahn.HahnBase.Equality.type',axiom,
! [V_24Y] :
( chahn_2eHahnBase_2eEquality_2etype___24t(V_24Y)
<=> t(V_24Y,chahn_2eHahnBase_2eEquality_2etype) ) ).
fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
! [V_24Y] :
( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
<=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).
fof('$tdef_Coq.Init.Datatypes.nat',axiom,
! [V_24Y] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
<=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).
fof('$tdef_$_type_23829',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23829___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23829___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_35325',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__35325___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__35325___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_404',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__404___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__404___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
! [V_24Y] :
( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(V_24Y)
<=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ) ).
fof('$tdef_$_type_35627',axiom,
! [V_24Y] :
( c_24__type__35627___24t(V_24Y)
<=> t(V_24Y,c_24__type__35627) ) ).
fof('$tdef_$_type_31783',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__31783___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__31783___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_Coq.micromega.RingMicromega.Formula',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34212',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34212___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34212___24a1(V_24X1)) ) ).
fof('$tdef_$_type_23507',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23507___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__23507___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_2550',axiom,
! [V_24Y] :
( c_24__type__2550___24t(V_24Y)
<=> t(V_24Y,c_24__type__2550) ) ).
fof('$tdef_$_type_2548',axiom,
! [V_24Y] :
( c_24__type__2548___24t(V_24Y)
<=> t(V_24Y,c_24__type__2548) ) ).
fof('$tdef_Coq.micromega.RingMicromega.PolC',axiom,
! [V_24X1,V_24Y] :
( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V_24X1,V_24Y)
<=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34256',axiom,
! [V_24X1,V_24Y] :
( c_24__type__34256___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__34256___24a1(V_24X1)) ) ).
fof('$tdef_$_type_33455',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33455___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33455___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31260',axiom,
! [V_24Y] :
( c_24__type__31260___24t(V_24Y)
<=> t(V_24Y,c_24__type__31260) ) ).
fof('$tdef_$_type_9600',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__9600___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__9600___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_23967',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23967___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23967___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3198',axiom,
! [V_24X1,V_24Y] :
( c_24__type__3198___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__3198___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31',axiom,
! [V_24X1,V_24Y] :
( c_24__type__31___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__31___24a1(V_24X1)) ) ).
fof('$tdef_$_type_7184',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7184___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7184___24a1(V_24X1)) ) ).
fof('$tdef_$_type_31825',axiom,
! [V_24Y] :
( c_24__type__31825___24t(V_24Y)
<=> t(V_24Y,c_24__type__31825) ) ).
fof('$tdef_$_type_36193',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__36193___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__36193___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_2538',axiom,
! [V_24Y] :
( c_24__type__2538___24t(V_24Y)
<=> t(V_24Y,c_24__type__2538) ) ).
fof('$tdef_Coq.Vectors.VectorDef.t',axiom,
! [V_24X1,V_24X2,V_24Y] :
( cCoq_2eVectors_2eVectorDef_2et___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_3094',axiom,
! [V_24Y] :
( c_24__type__3094___24t(V_24Y)
<=> t(V_24Y,c_24__type__3094) ) ).
fof('$tdef_$_type_23327',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__23327___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__23327___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_35733',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__35733___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__35733___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_3021',axiom,
! [V_24Y] :
( c_24__type__3021___24t(V_24Y)
<=> t(V_24Y,c_24__type__3021) ) ).
fof('$tdef_$_type_28',axiom,
! [V_24X1,V_24Y] :
( c_24__type__28___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__28___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34021',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34021___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34021___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_346',axiom,
! [V_24Y] :
( c_24__type__346___24t(V_24Y)
<=> t(V_24Y,c_24__type__346) ) ).
fof('$tdef_Type',axiom,
! [V_24Y] :
( cType___24t(V_24Y)
<=> t(V_24Y,cType) ) ).
fof('$tdef_$_type_32746',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32746___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32746___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
! [V_24Y] :
( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
<=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).
fof('$tdef_$_type_92',axiom,
! [V_24Y] :
( c_24__type__92___24t(V_24Y)
<=> t(V_24Y,c_24__type__92) ) ).
fof('$tdef_$_type_7447',axiom,
! [V_24Y] :
( c_24__type__7447___24t(V_24Y)
<=> t(V_24Y,c_24__type__7447) ) ).
fof('$tdef_$_type_33194',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33194___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33194___24a1(V_24X1)) ) ).
fof('$tdef_$_type_35980',axiom,
! [V_24Y] :
( c_24__type__35980___24t(V_24Y)
<=> t(V_24Y,c_24__type__35980) ) ).
fof('$tdef_$_type_29671',axiom,
! [V_24Y] :
( c_24__type__29671___24t(V_24Y)
<=> t(V_24Y,c_24__type__29671) ) ).
fof('$tdef_$_type_7',axiom,
! [V_24X1,V_24Y] :
( c_24__type__7___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__7___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34271',axiom,
! [V_24Y] :
( c_24__type__34271___24t(V_24Y)
<=> t(V_24Y,c_24__type__34271) ) ).
fof('$tdef_$_type_2886',axiom,
! [V_24Y] :
( c_24__type__2886___24t(V_24Y)
<=> t(V_24Y,c_24__type__2886) ) ).
fof('$tdef_$_type_285',axiom,
! [V_24Y] :
( c_24__type__285___24t(V_24Y)
<=> t(V_24Y,c_24__type__285) ) ).
fof('$tdef_$_type_9308',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y] :
( c_24__type__9308___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24Y)
<=> t(V_24Y,c_24__type__9308___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).
fof('$tdef_$_type_7471',axiom,
! [V_24Y] :
( c_24__type__7471___24t(V_24Y)
<=> t(V_24Y,c_24__type__7471) ) ).
fof('$tdef_$_type_31843',axiom,
! [V_24Y] :
( c_24__type__31843___24t(V_24Y)
<=> t(V_24Y,c_24__type__31843) ) ).
fof('$tdef_$_type_331',axiom,
! [V_24Y] :
( c_24__type__331___24t(V_24Y)
<=> t(V_24Y,c_24__type__331) ) ).
fof('$tdef_$_type_2968',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__2968___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__2968___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_8009',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__8009___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__8009___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_33066',axiom,
! [V_24X1,V_24Y] :
( c_24__type__33066___24t(V_24X1,V_24Y)
<=> t(V_24Y,c_24__type__33066___24a1(V_24X1)) ) ).
fof('$tdef_$_type_34095',axiom,
! [V_24X1,V_24X2,V_24X3,V_24Y] :
( c_24__type__34095___24t(V_24X1,V_24X2,V_24X3,V_24Y)
<=> t(V_24Y,c_24__type__34095___24a3(V_24X1,V_24X2,V_24X3)) ) ).
fof('$tdef_$_type_23883',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__23883___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__23883___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_32769',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
( c_24__type__32769___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
<=> t(V_24Y,c_24__type__32769___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).
fof('$tdef_$_type_36537',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
( c_24__type__36537___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y)
<=> t(V_24Y,c_24__type__36537___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).
fof('$tdef_$_type_34857',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
( c_24__type__34857___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
<=> t(V_24Y,c_24__type__34857___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).
fof('$tdef_$_type_33536',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33536___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33536___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_33557',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__33557___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__33557___24a2(V_24X1,V_24X2)) ) ).
fof('$tdef_$_type_31689',axiom,
! [V_24Y] :
( c_24__type__31689___24t(V_24Y)
<=> t(V_24Y,c_24__type__31689) ) ).
fof('$tdef_$_type_24000',axiom,
! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
( c_24__type__24000___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
<=> t(V_24Y,c_24__type__24000___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).
fof('$tdef_$_type_8654',axiom,
! [V_24X1,V_24X2,V_24Y] :
( c_24__type__8654___24t(V_24X1,V_24X2,V_24Y)
<=> t(V_24Y,c_24__type__8654___24a2(V_24X1,V_24X2)) ) ).
fof('_HAMMER_GOAL',conjecture,
p(cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3(cA,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(cA,chahn_2eHahnRelationsBasic_2eseq___24a3(cA,cr,cr_27),cr_27),chahn_2eHahnRelationsBasic_2eseq___24a3(cA,chahn_2eHahnRelationsBasic_2eminus__rel___24a3(cA,cr,cr_27),cr_27))) ).
%------------------------------------------------------------------------------